Editing Quantum Fingerprinting (section)

==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 performing a SWAP test on the fingerprints to check their equality. The server repeats this test several times on the received fingerprints to reduce the error probability.

* '''Client's preparation''': 
** The client prepares the fingerprint of initial input which is sized <math>n</math>-bits. This fingerprint has a length of <math>O(\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 of <math>log{}m+1</math> bits.
** Here for error correcting code, [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 test''': The server receives the two fingerprints from both the clients and performs the [[Glossary#Quantum SWAP test|quantum 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.