Quantum Protocol Zoo - User contributions [en]

Quantum Money

2024-09-27T12:15:18Z

Shraddha:

== Functionality Description ==

Quantum Money is a quantum cryptographic scheme that was first introduced by Wiesner [Wie83] in 1983. Informally, the quantum money object is a unique (e.g. has a public classical serial number) and unforgeable (e.g. unclonable) physical object that is created by a third party called Mint (that could be trusted or not trusted). Then, it is circulated among potentially untrusted parties, Holder, who might attempt to forge it for double spending. However a Merchant, upon receiving it, should be able to verify the money has not been forged and originated from Mint. There are various verification schemes based on different types of communication and types of key encryption used by Mint (see Protocols).

==Use-cases==
* [[Cross-platform finance]]
* [[Toward regulation for security and privacy]]
== Protocols ==

=== Private Key with Quantum Verification ===

Mint generates the quantum money and hands it to Holder. Bank shares a secret classical key with Mint for all distributed money. For verification, Merchant sends the quantum money to Bank through a quantum channel. Bank performs local quantum measurements, dictated by the secret classical key, and accepts or rejects the money conditioned on the measurement outcomes.

*[[Wiesner Quantum Money]]: [[:Category: Quantum Memory Network Stage|Quantum Memory Network Stage]]
*[[Quantum Cheque]]

=== Private Key with Classical Verification ===

Mint generates the quantum money and hands it to Holder. Bank shares a secret classical key with Mint for all distributed money. For verification, Merchant performs local quantum operations on the money and sends classical data to Bank who accepts or rejects based on the secret key they hold.

*[[Quantum Coin]]: [[:Category: Quantum Memory Network Stage|Quantum Memory Network Stage]]
*[[Quantum Token]]: [[:Category: Quantum Memory Network Stage|Quantum Memory Network Stage]]

=== Public Key with Quantum Verification ===

Mint generates the quantum money and hands it to Holder. All Holder and Merchant parties can verify the authenticity of the money themselves with the help of a public key.

== Properties ==

*A QMoney scheme is '''correct''' if an original quantum money issued by Mint is accepted by Bank with unit probability.
*A QMoney scheme is information-theoretically (resp. computationally) '''secure''' if no adversarial holder with unlimited (resp. computational) power can pass verification with different Merchants or Banks at the same time with high probability.
* A QMoney is '''reusable''' if an honest Holder can pass verification with different Merchants or Banks at different times.

==Knowledge Graph==
{{graph}}

== Further Information ==

<div style='text-align: right;'>''*contributed by Mahshid Delavar and Mathieu Bozzio''</div>

Quantum Secret Sharing using GHZ States

2024-09-27T11:39:18Z

Shraddha: /* Simplest Case ((2,2)) */

Quantum secret sharing (QSS) is a quantum protocol that grants unconditional security for communication. The scheme allows a secret holder Alice can split her secret into <math>n</math> shares and send them to <math>n</math> others, when and only when <math>k (\frac{n}{2}< k \le n)</math> or more shares work together can recover the secret. In formal, we call the scheme ((k,n)) secret sharing.

== Simplest Case ((2,2)) ==
The simplest case is ((2,2)). In this case, the secret holder Alice sends two receivers Bob and Charlie, to a qubit. When and only when Bob and Charlie work together, they can recover the secret message from Alice. Neither Bob nor Charlie can extract Alice’s secret on their own. The scheme has a [https://github.com/Yichi-Lionel-Cheung/QuantumSecretSharingDEMO qiskit implementation].

'''Step1'''

Alice initiates the protocol by sharing with each of Bob and Charlie one particle from a GHZ triplet in the (standard) Z-basis: <math>|\mathrm{\Psi}\rangle_{\rm GHZ} = \frac{|000\rangle + |111\rangle}{\sqrt{2}}</math> through a quantum channel. Alice keeps the first qubit herself, Bob holds the second one and Charlie holds the third one. We denote the three qubits as <math>a,b,c</math>.

'''Step2'''

Alice, Bob, and Charlie measure their qubit on an X- or Y-basis chosen at random and share the basis via a public classical channel. Note they just share the information of the measurement basis, but don’t share the measurement results.

Revisiting the GHZ state can be written in the following 4 forms:
* <math>|\mathrm{\Psi}\rangle_{\rm GHZ} = \frac{1}{2\sqrt{2}}[({|+x\rangle_{a}|+x\rangle_{b} + |-x\rangle_{a}|-x\rangle_{b}})(|0\rangle_{c} + |1\rangle_{c}) + ({|+x\rangle_{a}|-x\rangle_{b} + |-x\rangle_{a}|+x\rangle_{b}})(|0\rangle_{c} - |1\rangle_{c})]</math>
* <math>|\mathrm{\Psi}\rangle_{\rm GHZ} = \frac{1}{2\sqrt{2}}[({|+y\rangle_{a}|+x\rangle_{b} + |-y\rangle_{a}|-x\rangle_{b}})(|0\rangle_{c} - i|1\rangle_{c}) + ({|+y\rangle_{a}|-x\rangle_{b} + |-y\rangle_{a}|+x\rangle_{b}})(|0\rangle_{c} + i|1\rangle_{c})]</math>
* <math>|\mathrm{\Psi}\rangle_{\rm GHZ} = \frac{1}{2\sqrt{2}}[({|+x\rangle_{a}|+y\rangle_{b} + |-x\rangle_{a}|-y\rangle_{b}})(|0\rangle_{c} - i|1\rangle_{c}) + ({|+x\rangle_{a}|-y\rangle_{b} + |-x\rangle_{a}|+y\rangle_{b}})(|0\rangle_{c} + i|1\rangle_{c})]</math>
* <math>|\mathrm{\Psi}\rangle_{\rm GHZ} = \frac{1}{2\sqrt{2}}[({|+y\rangle_{a}|+y\rangle_{b} + |-y\rangle_{a}|-y\rangle_{b}})(|0\rangle_{c} - |1\rangle_{c}) + ({|+y\rangle_{a}|-y\rangle_{b} + |-y\rangle_{a}|+y\rangle_{b}})(|0\rangle_{c} + |1\rangle_{c})]</math>

In the first expansion, if Charlie chooses the X-basis (with 50% probability) to perform the measurement, he will know whether Alice and Bob have correlated results. But Charlie does not know Alice’s actual result because he does not know Bob’s result. Also, Bob does not know Alice’s actual result because he does not know whether his result is correlated or anticorrelated to Alice’s result.
Also, if Charlie chooses Y-basis, he will get no information. Since Charlie has 50% probability to get $|+y\rangle$ and 50% probability to get $|-y\rangle$. Therefore they will cancel this turn and repeat.
The [https://arxiv.org/pdf/quant-ph/9806063.pdf below table] shows the relationship of Alice's and Bob's measurements on Charlie's state for the standard GHZ triplet:
{| class="wikitable"
|-
!
! colspan="5" | Alice
|-
|
|
| <math>+x</math>
| <math>-x</math>
| <math>+y</math>
| <math>-y</math>
|-
| rowspan="4" | Bob
| <math>+x</math>
| <math>|0\rangle + |1\rangle</math>
| <math>|0\rangle - |1\rangle</math>
| <math>|0\rangle - i |1\rangle</math>
| <math>|0\rangle + i |1\rangle</math>
|-
| <math>-x</math>
| <math>|0\rangle - |1\rangle</math>
| <math>|0\rangle + |1\rangle</math>
| <math>|0\rangle + i |1\rangle</math>
| <math>|0\rangle - i |1\rangle</math>
|-
| <math>+y</math>
| <math>|0\rangle - i |1\rangle</math>
| <math>|0\rangle + i |1\rangle</math>
| <math>|0\rangle - |1\rangle</math>
| <math>|0\rangle + |1\rangle</math>
|-
| <math>-y</math>
| <math>|0\rangle + i |1\rangle</math>
| <math>|0\rangle - i |1\rangle</math>
| <math>|0\rangle + |1\rangle</math>
| <math>|0\rangle - |1\rangle</math>
|}

'''Step3'''

Charlie works with Bob by telling Bob his measurement result if he chooses the correct basis.

* Charlie provides the information on whether Alice and Bob have correlated results
* Bob provides his measurement result

<div style='text-align: right;'>''*contributed by Yichi Lionel Zhang''</div>

(Symmetric) Private Information Retrieval

2024-09-27T11:33:58Z

Shraddha:

==Description==

Private information retrieval (PIR) is a classical cryptographic functionality that allows one party (user) to privately retrieve an element from a classical database owned by another party (server), i.e., without revealing to the other party which element is being retrieved (user privacy).<br></br>
Symmetric private information (SPIR) retrieval is PIR with the additional requirement that throughout and after the protocol, the user remains oblivious to other database elements, i.e., apart from the queried one (data privacy).<br></br>
In the quantum setting, the use of quantum systems is allowed to achieve (S)PIR: this may imply the use of a quantum channel between the user and the server, and the capability to prepare quantum states, apply quantum gates or measure quantum systems by one or both parties. (S)PIR in this setting is known as quantum (symmetric) private information retrieval (Q(S)PIR).<br></br>
In the classical or quantum setting, (Q)SPIR and one-out-of-n (quantum) [[Oblivious Transfer|oblivious transfer]] (OT) are similar cryptographic tasks; the only minor difference between those functionalities is that protocols for OT are two-party protocols, while attempts at achieving SPIR have considered both two-party and multi-party protocols where the user communicates with several servers, each holding a copy of the database.<br></br>
Apart from using quantum techniques to enhance the classical (S)PIR functionality (i.e., design better protocols than their classical counterparts in terms of different metrics like e.g., communication complexity), there has also been a recent interest in a ‘fully’ quantum (S)PIR where a user wants to query a quantum database (items are quantum states)[[#References|[1]]].<br></br>

'''Tags:'''
[[:Category:Two Party Protocols|Two Party Protocol]],[[Category:Two Party Protocols]]
[[:Category:Specific Task|Specific Task]], [[Category:Specific Task]]
[[:Category: Quantum Enhanced Classical Functionality|Quantum Enhanced Classical Functionality]].[[Category:Quantum Enhanced Classical Functionality]]


==Use-cases==

===Classical database===
*Location-based services (to protect user location privacy).
*Queries of electronic medical records (these require decades of information confidentiality; hence security against quantum computing based attacks is necessary) or medical test reports.
*Music and film streaming (user does not want his/her tastes to be revealed to the server).
*Pay-per-view services, where the user should pay a fee to access every single database element.

Quantum (S)PIR protocols may be preferred to their classical counterparts to:
*Achieve (S)PIR with better communication complexity: this is convenient in the case of large databases.
*Achieve (S)PIR with better security: for instance, to secure classical channels as in [[#References|[5]]].

==Properties==


===Security definitions===
(Quantum) private information retrieval protocols are said to be secure if they satisfy the following conditions:
*'''Correctness''': assuming that all the parties in the protocol are honest, then the output of the protocol on the user’s side must be the queried database element.
*'''User privacy''': assuming that the user is honest, then, throughout the protocol, any query of the user to a server leaks no information about the desired database item.
In addition to the above requirements, symmetric (quantum) private information retrieval protocols must also satisfy the following condition:
*'''Data(base) privacy''': assuming that the server(s) is (are) honest(s), then, throughout the protocol, the user is unable to obtain any information beyond a single database element.

===Cost parameters===
The most common cost parameter used to characterise a given (Q)(S)PIR protocol is:
*'''Communication complexity''': total number of (qu)bits exchanged between the user and the server(s) throughout the protocol.
For (Q)(S)PIR protocols in general:
*'''(Q)(S)PIR capacity''': maximal achievable ratio of the retrieved database element size to the total download size.
Some less common cost parameters include:
*'''Storage overhead''' (for multi-database (Q)(S)PIR protocols): ratio between the total number of (qu)bits stored on all servers and the number of (qu)bits in the (resp. quantum) classical database.
*'''Access complexity''': total amount of data to be accessed by the server(s) for answering queries throughout a (Q)(S)PIR protocol.

==Protocols==


===Classical database===
In the quantum setting, protocols aiming at achieving (S)PIR for a ''classical'' database fall into two main categories:
====Single-database protocols====
As in the classical setting, in the case of the database being owned by a ''single'' server, the trivial solution (downloading the whole database) is the only way to achieve information-theoretically secure PIR – even in the case of a specious (may deviate from the protocol if its malicious operations are unknown to the user) server [[#References|[2]]]. <br>
As for (quantum or classical) SPIR, it is impossible to achieve information-theoretic security with a single-server; this result was proved in the quantum setting by Lo [[#References|[3]]]. Intuitively, this comes from the fact that the (unique) trivial solution of information-theoretically secure PIR is the worst in terms of data privacy. Therefore, to design efficient PIR protocols or to achieve SPIR, several assumptions have been considered; they include:
* Hardness assumptions: PIR protocols with computational security.
* Assumptions on the adversarial model:
** to achieve SPIR: cheat-sensitive protocols (also known as quantum private queries (QPQ) protocols) where it is assumed that the server will not cheat if there is a non-zero probability that he will be caught cheating.
***[[Quantum Private Queries Protocol Based on Quantum Oblivious Key Distribution|QPQ protocols based on quantum oblivious key distribution]]
***[[Quantum Private Queries Protocol Based on Quantum Random Access Memory|QPQ protocols based on quantum random access memory]]
** to achieve efficient PIR: assuming an honest server.
***[[Single-Database Quantum Private Information Retrieval in the Honest Server Model|QPIR protocols in the honest server model]]
* Prior shared entanglement between server and user: in the honest server model, efficient PIR protocols exist, however for a specious or malicious server, the trivial solution is optimal for PIR[[#References|[4]]].
**[[Single-Database Quantum Private Information Retrieval with Prior Shared Entanglement in the Honest Server Model|QPIR protocols with prior shared entanglement in the honest server model]]
* Relativistic assumptions: quantum SPIR protocols whose security uses properties from special relativity.
**[[Relativistic Quantum Oblivious Transfer|Relativistic QOT protocols]]

====Multi-database protocols====
It is possible to achieve information-theoretic (S)PIR with reduced communication complexity (i.e., compared to this of the trivial solution) by considering several servers instead of one, each holding a copy of the database, and with the help of extra assumptions. Usually, to achieve (S)PIR, it is assumed that the servers cannot communicate with each other during and after the protocol ended (no-communication assumption), and that servers share randomness (in the symmetric case only). Examples of such protocols are:

* [[Multi-Database Quantum Symmetric Private Information Retrieval without Shared Randomness|Quantum multi-database SPIR protocols without shared randomness]] (replaced by prior shared entanglement between servers)
* [[Multi-Database Classical Symmetric Private Information Retrieval with Quantum Key Distribution|Classical multi-database SPIR protocols with QKD secured classical channels]]
* [[Multi-Database Quantum Symmetric Private Information Retrieval for Communicating and Colluding Servers|Multi-database quantum (S)PIR protocols for communicating and colluding servers]] – to do without the no-communication assumption
* [[Multi-Database Quantum Symmetric Private Information Retrieval for Coded Servers|Multi-database quantum (S)PIR protocols for coded servers]]

===Quantum database===
For the case of a ''quantum'' database, the trivial solution of downloading the whole database is proved to be optimal for one-round QPIR, and for multi-round QPIR in the blind setting (i.e., the servers do not have a classical description of the quantum states of the database) and for the honest server model (and any other attack model)[[#References|[1]]].<br>

Prior shared entanglement between the user and the server allows for efficient one-server QPIR protocols in the honest server model and in the blind setting. Multi-database QSPIR protocols for a quantum database with pure states, in the visible setting (servers know a classical description of the quantum database elements) exist as shown by Song and Hayashi [[#References|[1]]].

* [[Single-Database Quantum Private Information Retrieval for a Quantum Database|Single-database quantum PIR protocols in the honest server model and in the blind setting for a quantum database]]
* [[Multi-Database Quantum Symmetric Private Information Retrieval for a Quantum Database|Multi-database quantum SPIR protocols in the visible setting for a quantum database]]

==Further Information==

===Optimal communication complexity of the (Q)(S)PIR problem===
Below are summarised known bounds for the communication complexity of information-theoretically secure (S)PIR protocols in the classical and quantum settings, for a quantum or classical database.

*<math>f</math> : number of database elements (quantum states in the 'fully' quantum setting)
*<math>m</math> : total size of database elements (i.e., the sum of the sizes, in bits, of each database element)
*<math>d</math> : dimension of the quantum states stored in the quantum database (<math>d=2</math> if they are qubits)
*<math>k</math> : number of servers (or equivalently of replicated databases)

====Single-database case====
{| class="wikitable plainrowheaders"
! scope="col" | Problem
! scope="col" | Additional assumptions
! scope="col" | Optimal communication complexity
! scope="col" | Reference
|-
! scope="row" | Classical PIR
| || <math>\Theta(m)</math> || [http://www.wisdom.weizmann.ac.il/~oded/PSX/pir2.pdf Chor et al (1995)]
|-
! scope="row" | Classical SPIR
| || NA (impossible) ||
|-
! scope="row" rowspan="4" | Quantum PIR (Classical database)
| Specious server || <math>\Theta(m)</math> || [https://arxiv.org/pdf/1304.5490.pdf Baumeler and Broadbent (2015)]
|-
| Specious server & prior entanglement || <math>\Theta(m)</math> || [https://arxiv.org/pdf/1902.09768.pdf Aharonov et al (2019)]
|-
| Honest server || <math>O(poly \log (m))</math> || [https://repository.ubn.ru.nl/bitstream/handle/2066/155747/155747.pdf Kerenidis et al (2016)]
|-
| Honest server & prior entanglement || <math>O(\log (m))</math> || [https://repository.ubn.ru.nl/bitstream/handle/2066/155747/155747.pdf Kerenidis et al (2016)]
|-
! scope="row" rowspan="2" | Quantum SPIR (Classical database)
| || NA (impossible) || [https://arxiv.org/pdf/quant-ph/9611031.pdf Lo (1997)]
|-
| The server will not cheat if there is a non-zero probability of being caught cheating & imperfect data privacy (the user should get at most two database items) || <math>O(\log (m))</math> || [https://arxiv.org/pdf/0708.2992.pdf Giovannetti et al (2008)]
|-
! scope="row" rowspan="3" | Quantum PIR (Quantum database)
| Honest server & blind setting || <math>\Theta(m)</math> || [https://arxiv.org/pdf/2101.09041.pdf Song and Hayashi (2021)]
|-
| Honest server & visible setting || <math>\Theta(m)</math> (for one-round) || [https://arxiv.org/pdf/2101.09041.pdf Song and Hayashi (2021)]
|-
| Honest server & prior entanglement || <math>O(\log (m))</math> || [https://arxiv.org/pdf/2101.09041.pdf Song and Hayashi (2021)]
|-
! scope="row" | Quantum SPIR (Quantum database)
| || ||
|}

====Multi-database case====
{| class="wikitable plainrowheaders"
! scope="col" | Problem
! scope="col" | Additional assumptions
! scope="col" | Optimal communication complexity
! scope="col" | Reference
|-
! scope="row" | Classical PIR
| || ||
|-
! scope="row" | Classical SPIR
| Servers do not communicate with each other & secure classical channels || <math>O(m^{\frac{1}{2k-1}}) \text{ bits}</math> || [https://dl.acm.org/doi/abs/10.1145/276698.276723 Gertner et al (2000)]
|-
! scope="row" | Quantum PIR (Classical database)
| || ||
|-
! scope="row" rowspan="2" | Quantum SPIR (Classical database)
| Servers do not communicate with each other || <math>O(m^{\frac{1}{2k-1}}) \text{ bits}+ \text{ comm. complexity of QKD}</math> || [https://www.mdpi.com/1099-4300/23/1/54/htm Kon and Lim (2021)]
|-
| Servers do not communicate with each other & honest user & prior entanglement || <math>m^{O(\log \log (k)/k \log(k))}</math> || [https://arxiv.org/pdf/quant-ph/0307076.pdf Kerenidis and de Wolf (2004)]
|-
! scope="row" | Quantum PIR (Quantum database)
| || ||
|-
! scope="row" rowspan="3" | Quantum SPIR (Quantum database)
| Servers do not communicate with each other & prior entanglement & visible setting & database contains pure qubit states || <math>O(f) \text{ bits} + O(1) \text{ qubits} + O(1) \text{ ebits}</math> || [https://arxiv.org/pdf/2101.09041.pdf Song and Hayashi (2021)]
|-
| Servers do not communicate with each other & prior entanglement & visible setting & database contains pure qudit states || <math>O(f) \text{ bits} + O(d^d \log (d)) \text{ qubits} + O(d^d \log (d)) \text{ ebits}</math> || [https://arxiv.org/pdf/2101.09041.pdf Song and Hayashi (2021)]
|-
| Servers do not communicate with each other & prior entanglement & visible setting & database contains commutative unitaries || <math>O(f) \text{ bits} + O(\log (d)) \text{ qubits} + O(\log (d)) \text{ ebits}</math> || [https://arxiv.org/pdf/2101.09041.pdf Song and Hayashi (2021)]
|}

==References==
#[https://arxiv.org/pdf/2101.09041.pdf Song and Hayashi (2021)]
#[https://arxiv.org/pdf/1304.5490.pdf Baumeler and Broadbent (2015)]
#[https://arxiv.org/pdf/quant-ph/9611031.pdf Lo (1997)]
#[https://arxiv.org/pdf/1902.09768.pdf Aharonov et al (2019)]
#[https://www.mdpi.com/1099-4300/23/1/54/htm Kon and Lim (2021)]

<div style='text-align: right;'>''*contributed by Marine Demarty''</div>

Secure Client- Server Delegated Computation

2024-08-29T13:27:06Z

News

2024-01-15T19:47:19Z

Shraddha: /* January 2024 */

2019-07-12T12:07:02Z

Shraddha: /* Protocol Description */

This [https://arxiv.org/abs/1108.2879 example protocol] achieves the task of [[bit commitment]] securely by using a relativistic scheme.
In bit commitment, the committer "commits" to a particular bit value.
The receiver knows nothing about the committed bit value until the committer chooses to do so (''hiding property'').
The receiver has a guarantee that once committed, the committer cannot change the committed bit value (''binding property'').
Information-theoretic secure bit commitment cannot be done with non-relativistic schemes see this review paper [https://arxiv.org/abs/quant-ph/9712023].

'''Tags:''' [[:Category:Two Party Protocols|Two Party Protocols]], [[:Category:Quantum Enhanced Classical Functionality|Quantum Enhanced Classical Functionality]], [[:Category:Specific Task|Specific Task]],
[[:Category:Information-theoretic security|Information-theoretic security]],
[[Category:Two Party Protocols]] [[Category:Quantum Enhanced Classical Functionality]][[Category:Specific Task]]
[[Category:Information-theoretic security]]

==Assumptions==

* Quantum theory is correct.
* The background space-time is approximately Minkowski.
* The committer can signal at precisely light speed.
* All information processing is instantaneous.

==Outline==

Both the receiver and the committer have 2 agents each which are the parties they send their qubits to and receive the committed value from. The agents are light-like separated from the committer.

The receiver securely pre-prepares a set of qubits randomly chosen from the BB84 states and sends them to the committer.
To commit to the bit 0, the committer measures the received qubits in the standard basis and in Hadamard basis to commit to 1.
The committer then sends the outcomes to their agents over secure classical channels.
To unveil the committed bit, the committer's agents reveal the outcomes to the receiver's agents.
The receiver's agents then check if the outcomes they have received are the same and consistent with the states sent to the committer.
If the check passes, the receiver accepts the commitment.

==Notation==

* <math>N</math>: Number of random qubits used in the commitment.
* <math>|\psi_i\rangle</math>: Random BB84 qubit with index <math>i</math>.
* <math>P</math>: Space-time origin point for the Minkowski space which is the position of the committer.
* <math>Q_0</math>: Commiter's first agent.
* <math>Q_1</math>: Commiter's second agent.
* <math>Q^{'}_0</math>: Receiver's first agent.
* <math>Q^{'}_1</math>: Receiver's second agent.

==Requirements==

* Secure classical channels between the parties and their agents.
* Basic state preparation abilities for the receiver.
* Instantaneous measurement capabilities for the committer.

<br/>

[[File:Quantum Bit Commitment.png|center|Quantum Bit Commitment]]

==Properties==

* There is no need of quantum memory for the parties.
* The protocol is unconditionally secure.

==Protocol Description==
[https://github.com/apassenger/CQC-Python/tree/release/1.0/QuantumBitCommitment <u>click here for Python code</u>]</br>
The committer and the receiver agree on the space-time origin point P and two light-like separated points where the two agents of each party will be stationed.

===Commitment Phase===

''Receiver''
# Prepare a set of <math>N</math> qubits <math>|\psi_i\rangle_{i=1}^N</math> chosen independently and randomly from the BB84 states - <math>\{|0\rangle, |1\rangle, |+\rangle, |-\rangle\}</math>.
# Send the qubits to the commiter at point P.

''Commiter''
# To commit to 0, measure in the <math>\{|0\rangle, |1\rangle\}</math> basis.
# To commit to 1, measure in the <math>\{|+\rangle, |-\rangle\}</math> basis.
# Send the measurement outcomes to the agents <math>Q_0</math> and <math>Q_1</math> via the secure classical channels.

===Unveiling Phase===

''Committer''
# The committer's agents reveal the measurement outcomes to the receiver's agents <math>Q'_0</math> and <math>Q'_1</math>.

''Receiver''
# Check if the revealed outcomes of both the agents are same, if not, then abort.
# Check if the revealed outcomes are consistent with the sent states, if not, then abort.
# If the checks pass, accept the commitment.

==Further Information==
<div style='text-align: right;'>''*contributed by Natansh Mathur''</div>

Quantum Bit Commitment

2019-07-12T12:06:23Z

Shraddha: /* Protocol Description */

This [https://arxiv.org/abs/1108.2879 example protocol] achieves the task of [[bit commitment]] securely by using a relativistic scheme.
In bit commitment, the committer "commits" to a particular bit value.
The receiver knows nothing about the committed bit value until the committer chooses to do so (''hiding property'').
The receiver has a guarantee that once committed, the committer cannot change the committed bit value (''binding property'').
Information-theoretic secure bit commitment cannot be done with non-relativistic schemes see this review paper [https://arxiv.org/abs/quant-ph/9712023].

'''Tags:''' [[:Category:Two Party Protocols|Two Party Protocols]], [[:Category:Quantum Enhanced Classical Functionality|Quantum Enhanced Classical Functionality]], [[:Category:Specific Task|Specific Task]],
[[:Category:Information-theoretic security|Information-theoretic security]],
[[Category:Two Party Protocols]] [[Category:Quantum Enhanced Classical Functionality]][[Category:Specific Task]]
[[Category:Information-theoretic security]]

==Assumptions==

* Quantum theory is correct.
* The background space-time is approximately Minkowski.
* The committer can signal at precisely light speed.
* All information processing is instantaneous.

==Outline==

Both the receiver and the committer have 2 agents each which are the parties they send their qubits to and receive the committed value from. The agents are light-like separated from the committer.

The receiver securely pre-prepares a set of qubits randomly chosen from the BB84 states and sends them to the committer.
To commit to the bit 0, the committer measures the received qubits in the standard basis and in Hadamard basis to commit to 1.
The committer then sends the outcomes to their agents over secure classical channels.
To unveil the committed bit, the committer's agents reveal the outcomes to the receiver's agents.
The receiver's agents then check if the outcomes they have received are the same and consistent with the states sent to the committer.
If the check passes, the receiver accepts the commitment.

==Notation==

* <math>N</math>: Number of random qubits used in the commitment.
* <math>|\psi_i\rangle</math>: Random BB84 qubit with index <math>i</math>.
* <math>P</math>: Space-time origin point for the Minkowski space which is the position of the committer.
* <math>Q_0</math>: Commiter's first agent.
* <math>Q_1</math>: Commiter's second agent.
* <math>Q^{'}_0</math>: Receiver's first agent.
* <math>Q^{'}_1</math>: Receiver's second agent.

==Requirements==

* Secure classical channels between the parties and their agents.
* Basic state preparation abilities for the receiver.
* Instantaneous measurement capabilities for the committer.

<br/>

[[File:Quantum Bit Commitment.png|center|Quantum Bit Commitment]]

==Properties==

* There is no need of quantum memory for the parties.
* The protocol is unconditionally secure.

==Protocol Description==
[https://github.com/apassenger/CQC-Python/tree/release/1.0/QuantumBitCommitment click here for Python code]
The committer and the receiver agree on the space-time origin point P and two light-like separated points where the two agents of each party will be stationed.

===Commitment Phase===

''Receiver''
# Prepare a set of <math>N</math> qubits <math>|\psi_i\rangle_{i=1}^N</math> chosen independently and randomly from the BB84 states - <math>\{|0\rangle, |1\rangle, |+\rangle, |-\rangle\}</math>.
# Send the qubits to the commiter at point P.

''Commiter''
# To commit to 0, measure in the <math>\{|0\rangle, |1\rangle\}</math> basis.
# To commit to 1, measure in the <math>\{|+\rangle, |-\rangle\}</math> basis.
# Send the measurement outcomes to the agents <math>Q_0</math> and <math>Q_1</math> via the secure classical channels.

===Unveiling Phase===

''Committer''
# The committer's agents reveal the measurement outcomes to the receiver's agents <math>Q'_0</math> and <math>Q'_1</math>.

''Receiver''
# Check if the revealed outcomes of both the agents are same, if not, then abort.
# Check if the revealed outcomes are consistent with the sent states, if not, then abort.
# If the checks pass, accept the commitment.

==Further Information==
<div style='text-align: right;'>''*contributed by Natansh Mathur''</div>

Main Page

2019-07-12T11:29:07Z

Shraddha: /* Functionality Page */

'''Welcome to The Quantum Protocol Zoo -''' ''Explore, Learn, Code and Implement Quantum Protocols''<br/><br/>The quantum protocol zoo is an open repository of protocols for quantum networks. It provides a compact and canonical way to explore such protocols. Moreover, it allows for easy communication among computer scientists, engineers, and physicists on a single platform.
*[[Quantum Protocol Zoo:About|About us]]
*[[Quantum Protocol Zoo:General disclaimer| Disclaimer]]
*[[Quantum Protocol Zoo:Copyrights|Copyrights]]
== Getting started ==
Quantum Protocol Zoo is a repository of protocols for quantum networks. It presents a wiki of protocols for various functionalities classified in terms of the [[:Category: Network Stages|network stages]] for a quantum internet. It is important to note that, although there are several different ways of defining a protocol, we characterise it as something that involves more than one party. In particular, we define a protocol as a sequence of steps, specifically designed to accomplish a task. It may or may not involve an algorithm and could be run between trusted parties as well as parties who don't trust each other.

The wiki consists of two types of pages: The first type is a functionality page, describing a general task which can be realised in a quantum network (the "what"). The second type of page is a protocol page, which describes a specific protocol implementing the defined functionality (the "how"). These pages are listed in [[Protocol Library]]. Furthermore, a page on [[Supplementary Information]] has been provided for background information about quantum theory. Any information on [[How to Submit]] or contact can be found in the Navigation menu on the sidebar. Every page has a Discussion section, where users are welcome to leave their comments.

== The goal ==
The goal of this project is multifold. First, it aims to provide a compact and precise review of all the existing protocols in one place, such that it is accessible to both the young researchers motivated to enter into the field as well as quantum enthusiasts. Second, our platform enables the experts from academia and industry to find real-life use cases for the listed protocols and at the same time innovate on (or compose) the existing ones to tailor-made new protocol for a desired task. Finally, our main intention is to also develop standardised form for protocol descriptions to make the community quantum-internet ready. At the same time, we emphasise that our purpose is not to point out the strengths or weaknesses of any particular protocol or functionality.

As a direct consequence of this effort, hosting and analysing the protocols in this fashion provides an underlying link between several protocols and would enable everyone to gain a deeper understanding of their working. With the rapid progress in quantum technologies and improvements in the current protocols, it is extremely beneficial to have a resource for all the quantum protocols in one place that can be regularly updated to keep track of the advancements, something that can not be achieved with the review articles or a book. We, therefore, invite everyone from the quantum information science community to join and contribute to this initiative in collectively making the quantum protocol zoo a crucial source for quantum protocols.

== Wonder what's the format for contribution? ==
We welcome contributions from various fields, here we give the format of the kinds of pages, the wiki is composed of. A more detailed set of guidelines for submissions can be found on the [[How to Submit]] page.
=== Functionality Page===
----
Functionality page describes a general task which can be realized in a quantum network (the "what"). It consists of the following sections.
</br>
<div style="background-color: white; border: solid thin black;title=Functionality Description;">
* '''Functionality Description''' A lucid definition of functionality in discussion.
----
* '''Tags''' Any related page or list of protocols is connected by this section
----
* '''Use Case''' (if available) analyses how practical the protocol is, for industry use when compared to other alternatives. It answers the following questions:
**Quantum or classical task?
**Any classical or post-quantum secure analogue?
**Benchmark values for key length, security parameter, threshold values, etc?
**Scalabilty in terms of time, key length etc..
**Real World Applications?
----
*'''Protocols''' List of different types of example protocol achieving the functionality (each protocol in this list is written in the format given below) depending on the task achieved or [[:Category: Network Stages|Network Stages]] required to achieve the same functionality

----
*'''Properties''' All properties that should be satisfied by any protocol achieving the concerned functionality and other common terminologies used in all the protocols.

----
*'''Further Information''' Any issue that could not be addressed or find a place in the above sections or any review paper discussing a feature of various types of protocols related to the functionality.
</div>

=== Protocol Page ===
----
Protocol page describes a specific protocol implementing the defined functionality (the "how"). It consists of the following sections.
</br>
<div style="background-color: white; border: solid thin black;title=Functionality Description;">
*'''Link''' to the corresponding functionality together with a short description of the method used and properties satisfied by a protocol.
----
*'''Tags''' Any related page or list of protocols is connected by this section
----
*'''Assumptions''' It describes the setting in which the protocol will be successful. Any assumption on the setup for the protocol below is listed in this section.
----
*'''Outline''' A non-mathematical detailed outline which provides a rough idea of the concerned protocol. A figure is accommodated for most protocols.
----
*'''Notation''' Connects the non-mathematical outline with further sections.
----
*'''Requirements'''
**[[:Category:Network Stages|Network Stage]]
**Relevant network parameters
**Technology required by each party
**Availbale information from implementations like, order of digits related to threshold values, QBit Error Rate (QBER), parameters, etc..
It accommodates a figure on the '''decomposition of the protocol''' into various components required for implementation including the physical resources, nodal subroutines, and other protocols used.
'''Color Coding:'''
*** The protocols are shown in a blue rectangular box.
*** The nodal subroutines are shown in a green rounded rectangular box.
*** The physical resources are shown in red ovals.
----
*'''Properties''' A list of important information extracted from the protocol such as parameters (threshold values), security claim, success probability, etc..
----
*'''Protocol Description''' Mathematical step-wise protocol algorithm helpful to write a subroutine.
----
*'''Further Information''' Any useful information that could not find its place in the above description goes here. Also, some pages on protocols might include a short description as below for a list of protocols in the same class of functionality and network stage that are easy to interpret after reading the concerned formal description (or are variants of the protocol discussed above):
*Theoretical Papers:
**How is it different from the above protocol
**Requirements
**Security
*Experimental Papers:
**Which paper or protocol does it implement
**Benchmark values for this demonstration
</div>