Experimental Quantum Process Discrimination

Discrimination between unknown processes chosen from a finite set is experimentally shown to be possible even in the case of nonorthogonal processes. We demonstrate unambiguous deterministic quantum process discrimination of nonorthogonal processes using properties of entanglement, additional known unitaries, or classical communication. Single qubit measurement and unitary processes and multipartite unitaries (where the unitary acts nonseparably across two distant locations) acting on photons are discriminated with a confidence of $\ge 97\%$ in all cases.

Figure 1

Quantum process discrimination. (a) The Bloch Sphere showing nonorthogonal measurement directions $X$ and $Z$ and nonorthogonal Hermitian unitaries ${\sigma }_z$ and $\widehat{\mathrm{H}}$. ${\sigma }_z$ and $\widehat{\mathrm{T}}$ can always be discriminated with a finite number of qubits with $\theta$ arbitrarily acute. (b) Entanglement-assisted QPD. (c) QPD without entanglement. (d) Multipartite unitary discrimination without entanglement.

Figure 2

Experimental QPD. A 2 mm Type 1 BBO crystal is pumped with a vertically polarized 60 mW 402 nm continuous wave laser. Pairs of horizontally polarized 804 nm photons are detected at a rate $\approx 3,500\mathrm{Hz}$ when collected into single mode polarization maintaining fibres (PMF) after 2 nm interference filters. Polarizing beam splitters (${\mathrm{PBS}}_1$ and ${\mathrm{PBS}}_2$) further purify the polarization; indistinguishability of the photons was confirmed by a Hong-Ou-Mandel dip [21] visibility of $96.9\pm 0.3\%$. A half-wave plate (${\mathrm{HWP}}_1$) rotates the photon in mode 1 from horizontal (H) to vertical (V), and the two orthogonally polarized photons impinge on the input ports of the central $1/2$ reflectivity beam splitter (BS) to produce the output state: $|{\psi }_{\mathrm{out}}⟩=(|H_1{V}_1⟩+|H_1{V}_2⟩+|V_1{H}_2⟩+|V_2{H}_2⟩)/2$, where the subscript labels the mode. Phase corrections are implemented with the quarter-half-quarter-wave plate combination (QHQ) [22] on mode 2. The optic axes of ${\mathrm{HWP}}_2$ and ${\mathrm{HWP}}_3$ are set to 0° or 22.5° to perform ${\sigma }_z$ or $\widehat{\mathrm{H}}$, respectively. Orthogonal polarizations are detected by a PBS followed by two single photon counting modules (SPCMs) in each mode. Each SPCM corresponds to a particular eigenvalue—e.g., in mode 1, if we have set ${\mathrm{HWP}}_3$ to 22.5° to measure in the Bloch $x$ axis ($D/A$ basis), a diagonally polarized photon would be transmitted to the SPCM corresponding to a “$+1$” eigenvalue, while an antidiagonal photon would be reflected to the SPCM corresponding to the “$-1$” eigenvalue.

Figure 3

Experimental results for QPD of nonorthogonal quantum processes. (a) Entanglement-assisted QPD of nonorthogonal measurement bases distinguishes between measurements in the $H/V$ (along Bloch $z$ axis) and $D/A$ basis (along Bloch $x$ axis) with a confidence of $(97.8\pm 0.05)\%$. Changing measurement basis from $H/V$ to $D/A$ is achieved by changing unitary from ${\sigma }_z$ (half-wave plate with optic axis set at 0°) to $\widehat{\mathrm{H}}$ (half-wave plate with optic axis set at 22.5°). (b) The scheme demonstrating unitary QPD without entanglement discriminates between ${\sigma }_z$ and $\widehat{\mathrm{H}}$ with a confidence of $(99.0\pm 0.02)\%$. (c) The bipartite unitaries $\widehat{J}$ and $\widehat{I}$ are distinguished with a $(96.6\pm 0.4)\%$ confidence.