Wiesner Quantum Money

A classical money/banknote has a unique serial number and the bank can provide a verification according to these serial numbers. However, Wiesner suggests that a quantum money has also a number of isolated two-state quantum system and the two-state systems are located in one of four states. Assumptions 1) The two state systems must be isolated from the rest of universe enoughly 2) When Wiesner wrote his thesis, there was no device operating in which the phase coherence of a two state system was preserved for longer then about a second OUTLINE Let’s us think that the money has twenty isoleted system Si, i=1....20. At the mint created two random binary sequences of twenty digits each which we can call M i and N i, i=1,,...20, M i = 0 or 1 and Ni = 0 or 1. Then the two-state systems are placed in one of the four states a, b, alpha, beta in accordance with the scheme shown in Fig. 1) Bank prepares a pair of orthonormal base states for each state system. Then two state system are located in one of the four states a, b, alpha, beta in accordance 2) The bank records all polarizations and their serial numbers. On the bank note/ quantum money the serial number can be seen, while polarizations are kept secret 3) If the money is returned to the mint, then check that if each isolated system is still in its initial state or not. 4) If someone copies the money then she/he cannot recover Ni because since she does not know Mi. She does not know what measurement to make an Si NOTATION Si = isolated system Mi and Ni = random binary sequences a,b,alpha,beta = states REQUIREMENTS 1) Network stage: quantum memory network PROPERTIES 1) Wiesner’s schema requires a central bank for verifying the money 2) The “qubit” was used firstly in Wiesner’s article 3) Pairs of conjugate variables has same relation with Heisenberg uncertanity principle Pseudocode Input: ​Product state of N qubit and a serial number Outout: ​approved/rejected 1) Money has two component (|S>,k), k is a serial number of the banknote and S is a product state of N qubits. For every N qubits of the product states are choosen randomly in {|0>, |1>,|+>,| ->} 2) Serial numbers and their states are recorded and kept at the mint7 3) For verifying the money, the mint looks the serial number and their correspending states. Thus, each qubit is measured in the right basis, {|0>,|1>} or {|+>,|->}, and looked if corresponded to the classical description of the state. 4) If the result(measurement) <1, rejected (If somebody wants to copy a piece of quantum money, she can choose the measurement basis at random for each qubit of a quantum money state. For each qubit, If he guesses the right basis, she will find the right value with probability 1. In the other case, she will find the right value with probability 1/2. so, the probability that an attacker guesses correctly the quantum money state is (3/4)^N ) Furthermore Information http://users.cms.caltech.edu/~vidick/teaching/120_qcrypto/wiesner.pdf