Single-Qubit Optical Quantum Fingerprinting

Abstract

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. . Here we establish the feasibility of single-qubit optical quantum fingerprinting, by theoretical analysis and also by experimentally generating and assessing the appropriate quantum optical states for encoding. In particular we (i) develop an optical protocol for single-qubit fingerprinting, (ii) show that two-photon coincidence measurements suffice as the experimental test for comparing fingerprints, (iii) prove that one shared entangled bit between Alice and Bob allows zero-error quantum fingerprinting which outperforms classical fingerprinting even with unlimited shared randomness between Alice and Bob, and (iv) present experimental results on the supply of fingerprint states that demonstrates the feasibility of the protocol. Our results open the prospect of experimental quantum communication complexity; although here we focus on singlequbit fingerprinting and correlated photon pairs, scalability will become possible as multiphoton entanglement capabilities improve [4].

swap test and Hong-Ou-Mandel effect are equivalent

“…In fact, the equivalence of the SWAP test and the HOM effect has already been noticed in the single-qubit case and has been put to use in a quantum fingerprinting scheme with one-qubit fingerprints, which still has some advantages with respect to any classical method [19]. The equivalence can be extended to arbitrary mixed single-photon input states with density matrices ρ A and ρ B .…”

Quantum sketching protocols for Hamming distance and beyond

“…Theoretically, it has been used to shed new light on the two-slit experiment [11] and detailed studies of fingerprinting schemes using few qubits have been undertaken [12,13]. Proof-ofprinciple quantum fingerprinting experiments have been carried out with states of 1 qubit realized using linear optics [14] and nuclear magnetic resonance [15]. More recently, a variant of the quantum fingerprinting protocol based on coherent states [16] has also been implemented experimentally, surpassing the best known classical protocols [17] and even the classical theoretical limit [18].…”

Precise space–time positioning for entanglement harvesting

“…The resultant pair of entangled detectors can in principle serve as a resource for performing quantum information tasks such as teleportation [7,8], superdense coding [9,10], or fingerprinting [11,12]. This resource is especially useful when enhanced by entanglement-farming protocols using successive pairs of detectors [13].…”