Write, autoreview, editor, reviewer
3,129
edits
Quantum Token: Difference between revisions
m
no edit summary
m (Shraddha moved page Unforgeable Quantum Token to Quantum Token) |
mNo edit summary |
||
| Line 1: | Line 1: | ||
Money is issued by one party (bank) to a prover (client) such that when he presents it to a verifier | Money is issued by one party (bank) to a prover (client) such that when he presents it to a verifier | ||
(merchant), he/she is satisfied that the money presented by client comes from the bank. It comes | (merchant), he/she is satisfied that the money presented by client comes from the bank. It comes | ||
with the property of [[unforgeability]] and [[ | with the property of [[unforgeability]] and [[transferability]]. Unforgeability means that there should exist | ||
no method to produce an identical copy by anyone but the bank, and | no method to produce an identical copy by anyone but the bank, and transferability allows that this | ||
money can be used by the verifier as a client himself in the next round.</br> | money can be used by the verifier as a client himself in the next round.</br> | ||
| Line 13: | Line 13: | ||
==Assumptions== | ==Assumptions== | ||
* Money is physically transferred to the holders | * Money is physically transferred to the holders | ||
* If <math>F^{cv}_{tol} > (1+1/\sqrt{2})/2</math> , a dishonest user is exponentially unlikely to be authenticated by two independent verifiers (success in cheating to use same ticket for two independent verifiers by measuring in intermediate basis between the two bases, asked by the verifiers individually). | * If <math>F^{cv}_{tol} > (1+1/\sqrt{2})/2</math>, a dishonest user is exponentially unlikely to be authenticated by two independent verifiers (success in cheating to use the same ticket for two independent verifiers by measuring in intermediate basis between the two bases, asked by the verifiers individually). | ||
==Outline== | ==Outline== | ||
The protocol can be divided into three parts | The protocol can be divided into three parts | ||
* '''Preparation''' Bank prepares few rows of qubit-pairs chosen from two different non-orthogonal sets of basis. Each pair has at least one state from both bases, such that the qubit pair states are non-orthogonal. It associates each such chosen set with a serial number and shares the classical information about the choices for respective serial number with trusted merchants. | * '''Preparation''' Bank prepares few rows of qubit-pairs chosen from two different non-orthogonal sets of basis. Each pair has at least one state from both bases, such that the qubit pair states are non-orthogonal. It associates each such chosen set with a serial number and shares the classical information about the choices for respective serial number with trusted merchants. | ||
* '''Interaction''' This step involves challenge questions by verifier to prove that he has a valid token, by playing part of a [[non-local game]]. In this game, the merchant asks client to measure in one of the two bases in from which the qubit pairs were chosen. As each qubit pair contains at least one state from each basis chosen, after the measurement one of the qubits (encoded in the basis chosen by the merchant) would give the correct result. | * '''Interaction''' This step involves challenge questions by the verifier to prove that he has a valid token, by playing a part of a [[non-local game]]. In this game, the merchant asks the client to measure in one of the two bases in from which the qubit pairs were chosen. As each qubit pair contains at least one state from each basis chosen, after the measurement one of the qubits (encoded in the basis chosen by the merchant) would give the correct result. | ||
* '''Transaction''' The merchant compares this qubit outcome whose encoding basis matches with merchant's basis for the game. | * '''Transaction''' The merchant compares this qubit outcome whose encoding basis matches with merchant's basis for the game. The merchant accepts the ticket if the ratio of the number of valid outcomes to the total number of qubits measured is more than or equal to a certain threshold fidelity value. | ||
==Notation== | ==Notation== | ||