Single-Qubit Optical Quantum Fingerprinting

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.

Figure 1

(a) Quantum circuit of the original fingerprinting protocol [2, 3]. (b) Linear optical implementation: Alice (A) and Bob (B) each receive a two-bit message from Sapna (S) and a single photon in a known polarization state from a source. The photons are transformed (represented by △) to particular tetrahedral states according to the received message. The photons are sent to Roger (R) who mixes them at a symmetric beam splitter ⊠ and uses coincidence detection (two detectors ⊏⊃ and a multiplier ⊗) to infer if the messages were the same or different. (c) Coincidence dip with state $|{\Omega }_1⟩$ mixed with $|{\Omega }_0⟩$ (○), $|{\Omega }_1⟩$ (●), $|{\Omega }_2⟩$ (+), and $|{\Omega }_3⟩$ (×). The plots correspond to the normalized coincidence rate $R/R_{\max }$ (with $R_{\max }=474{\mathrm{s}}^{-1}$ the maximum observed rate, or background rate, for the HOM dip) vs the relative delay between two photons. $v_{\mathrm{same}}$ and $v_{\mathrm{diff}}$ represent the dip depth $1-R_{\min }/R_{\max }$ for photons in same or different states, respectively.