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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Single-qubit optical quantum fingerprinting

Rolf T. Horn, Karl-Peter Marzlin, Barry C. Sanders

Published Oct 19, 2004• 10 citations
Publisher

Abstract

We show that single qubit quantum fingerprinting without shared randomness is feasible with linear optics and is demonstrably superior to its classical counterpart. Furthermore a shared source of entanglement, provided for example by a parametric down converter, permits 100% reliable quantum fingerprinting, which outperforms classical fingerprinting even with arbitrary amounts of shared randomness.

DOI
10.1117/12.562449

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We show that single qubit quantum fingerprinting without shared randomness is feasible with linear optics and is demonstrably superior to its classical counterpart. Furthermore a shared source of entanglement, provided for example by a parametric down converter, permits 100% reliable quantum fingerprinting, which outperforms classical fingerprinting even with arbitrary amounts of shared randomness.
We analyze and demonstrate the feasibility and superiority of linear optical single-qubit fingerprinting over its classical counterpart. For one-qubit fingerprinting of two-bit messages, we prepare "tetrahedral" qubit states experimentally and show that they meet the requirements for quantum fingerprinting to exceed the classical capability. We prove that shared entanglement permits 100% reliable quantum fingerprinting, which will outperform classical fingerprinting even with arbitrary amounts of shared randomness.
One of the standard communication complexity problems is deciding whether bit strings held by two separate parties Alice (A) and Bob (B) are equal or different. In the simultaneous message passing model, A and B send certain information to a Referee, who makes the decision. The overall goal is to minimize the amount of communication involved while not exceeding desired error probability. This is achieved by sending only fingerprints of the original n-bit strings. In the best classical protocols, these scale as O(√n) if A and B have no access to shared randomness [1]. The recently proposed [2] and demonstrated quantum fingerprinting [3], exploiting phase-modulated weak coherent pulses, provides O(log2n) scaling in the number of used qubits, but needs phase stability between A and B. Here we introduce and analyse a quantum fingerprinting protocol based on two-photon interference which does require a shared phase reference and works in scenarios when the global phase of transmitted signals becomes completely random. Interestingly, the performance of this protocol, quantified in terms of the Chernoff information [4], is enhanced through the use of non-classical single-photon states, even in the regime of high transmission loss.
Quantum fingerprinting allows two remote parties to determine whether their datasets are identical or different by sending exponentially less information compared to the classical protocol with equivalent performance. Optical implementations of the quantum protocol based on weak coherent states have been proposed and realized. However, in these realizations phase stability between the sending parties is required. Here we analyze the practical feasibility of the recently introduced quantum fingerprinting protocol based on higher-order interference, which does not require a phase lock between transmitters. We show that an experimental demonstration of a quantum fingerprinting protocol beating the known bound on the performance of classical schemes should be possible using currently available technology.
We present a quantum fingerprinting protocol relying on two-photon interference which does not require a shared phase reference between the parties preparing optical signals carrying data fingerprints. We show that the scaling of the protocol, in terms of transmittable classical information, is analogous to the recently proposed and demonstrated scheme based on coherent pulses and first-order interference, offering comparable advantage over classical fingerprinting protocols without access to shared prior randomness. We analyze the protocol taking into account non-Poissonian photon statistics of optical signals and a variety of imperfections, such as transmission losses, dark counts, and residual distinguishability. The impact of these effects on the protocol performance is quantified with the help of Chernoff information.