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Quantum Fingerprinting: Difference between revisions
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This [https://arxiv.org/abs/quant-ph/0102001 example protocol] allows two parties (two quantum clients) to distinguish their quantum inputs while maintaining the privacy of their own input by comparing their fingerprints alone. The protocol does not permit the two parties to interact directly with each other, hence they send the fingerprints of their respective inputs to a trusted third party (quantum server), where the third party tests that distinguishes two unknown quantum fingerprints with high probability. The quantum fingerprints are exponentially shorter than the original inputs. | This [https://arxiv.org/abs/quant-ph/0102001 example protocol] allows two parties (two quantum clients) to distinguish their quantum inputs while maintaining the privacy of their own input by comparing their fingerprints alone. The protocol does not permit the two parties to interact directly with each other, hence they send the fingerprints of their respective inputs to a trusted third party (quantum server), where the third party tests that distinguishes two unknown quantum fingerprints with high probability. The quantum fingerprints are exponentially shorter than the original inputs. | ||
'''Tags:''' [[Fingerprinting]] | '''Tags:''' [[Fingerprinting]] | ||
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==Outline== | ==Outline== | ||
Here, two quantum clients want to check if their quantum inputs are distinct while also keeping their inputs secret. They prepare quantum fingerprints of their individual inputs and send these states to the server. Next stage involves the server a SWAP test on the fingerprints to check their equality. | Here, two quantum clients want to check if their quantum inputs are distinct while also keeping their inputs secret. They prepare quantum fingerprints of their individual inputs and send these states to the server. Next stage involves the server performing a SWAP test on the fingerprints to check their equality. The server repeats this several times on the received fingerprints to reduce the error probability. | ||
* '''Client's preparation''': | * '''Client's preparation''': | ||
** The client prepares the fingerprint of initial input sized <math>n</math>-bits. This fingerprint has a length | ** The client prepares the fingerprint of initial input which is sized <math>n</math>-bits. This fingerprint has a length of <math>\log_{}n</math> bits. | ||
** This fingerprint is prepared using particular error correcting codes, which converts the <math>n</math>-bit input to <math>m</math>-bits, where <math>m</math> is greater than <math>n</math>, and the two outputs of any two distinct inputs can be equal at atmost <math>\delta m</math> positions, where <math>\delta < 0</math>. The fingerprint has the length to be <math>log_{} m+1</math> | |||
** Hence for this purpose [https://ieeexplore.ieee.org/document/1054893|Justesen codes] are used. | |||
** The client now sends this fingerprint to the server through a quantum channel. Both the clients do this process simultaneously. | |||
* '''Server's | * '''Server's test''': The server receives the two fingerprints from both the clients and performs the [[SWAP test]] on these states to check if the states are distinguishable. The server independently repeats this SWAP test on fingerprints several times to reduce the error probability in detecting if the two states are different. | ||
If the initial inputs of the two parties are equal, this would be inferred from the corresponding fingerprints with no error probability and the outcome of the protocol would be correct. However, if the two fingerprints are of different inputs, there exists a non-zero probability that the outcome of the protocol is incorrect. Therefore, there exists a one sided error in the measurement. This one sided error is reduced by repeating the server operations several times with the same fingerprints. | |||
If the initial | |||
==Hardware Requirements== | ==Hardware Requirements== | ||