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Boosted linear-optical measurements on single-rail qubits with unentangled ancillas

Aqil Sajjad, Isack Padilla, Saikat Guha

Abstract

Any quantum state of the radiation field, sliced in small non-overlapping space-time bins is a collection of single-rail qubits, each spanning the vacuum and single-photon Fock state of a mode. Quantum logic on these qubits would enable arbitrary measurements on information-bearing light, but is hard due to the lack of strong nonlinearities. With unentangled ancilla single-rail qubits, an $8$-port interferometer and photon detection, we show any single-rail qubit measurement in the $XY$ Bloch plane is realizable with success probability $147/256$, which beats the prior-known $1/2$ limit.

Boosted linear-optical measurements on single-rail qubits with unentangled ancillas

Abstract

Any quantum state of the radiation field, sliced in small non-overlapping space-time bins is a collection of single-rail qubits, each spanning the vacuum and single-photon Fock state of a mode. Quantum logic on these qubits would enable arbitrary measurements on information-bearing light, but is hard due to the lack of strong nonlinearities. With unentangled ancilla single-rail qubits, an -port interferometer and photon detection, we show any single-rail qubit measurement in the Bloch plane is realizable with success probability , which beats the prior-known limit.
Paper Structure (12 sections, 58 equations, 3 figures, 1 table, 1 algorithm)

This paper contains 12 sections, 58 equations, 3 figures, 1 table, 1 algorithm.

Table of Contents

  1. Supplementary material
  2. Motivation: the state transfer protocol and $X$ basis measurement
  3. Generating single-rail $|+\rangle$ or $|+_\phi\rangle$ ancilla qubits
  4. Implementing power of 2 Hadamard unitaries
  5. Breaking down the success and failure rates in terms of the photon counts of the click patterns
  6. Our algorithm for calculating the success and failure rates
  7. Results broken down in terms of total photon counts $\mathcal{I}$
  8. Expressions for the total success rates for $\mathcal{I}$ photon click patterns
  9. The 2-component Green Machine, i.e. a 50-50 beam splitter
  10. The 4-component Green Machine
  11. Non-power of 2 Hadamard unitaries and results for the 12-component case
  12. Using coherent state ancillas instead of $|+\rangle$

Figures (3)

  • Figure 1: (a) A linear-optical unitary $U$---either an $8$-th order Quantum Fourier Transform (QFT) or an $8$-mode Hadamard 'Green Machine' (GM) circuit---receives in the first input mode the single-rail qubit that we wish to measure in the $|\pm_\phi\rangle \equiv (|0\rangle\pm e^{i\phi} |1\rangle)/\sqrt{2}$ basis. Remaining inputs are fed $|+_\phi\rangle$ ancillas that help boost the success probability of measuring in the desired basis. (b) The GM circuit $U_{\rm{GM}}$ is realized with a mesh of 50-50 beam splitters and (c) the QFT $U_{\rm{QFT}}$ adds phase shifters, following the construction from Ref. Barak2007.
  • Figure 2: Success probabilities $s_{n}$ of measuring $|\pm_\phi\rangle$ as well as the overall success, as a function of the number of inputs $n$ of the Green Machine (only applies for $n=2^j$, $j\in\{1,2,3,\dots\}$) and QFT (all values of $n$ apply). The maximum overall success is found to be $s_{8,\text{overall}}=147/256$ or $\sim 57.42\%$.
  • Figure 3: The Green Machine transformation for size $n$ being powers-of-two can be recursively constructed from Green Machines of size $n=2$ (the balanced beam splitter) and size $n/2$.