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European Quantum Electronics Conference (EQEC)

Quantum state discrimination via linear optics and continuous photon counting

Masahiro Takeoka, Masahide Sasaki, Peter van Loock, Norbert Lütkenhaus

Published Jan 18, 2006• 0 citations
Publisher

Abstract

In this paper, an expansion of the formulae to check whether one can implement a step via linear optics and photon counting was derived, to the limit of continuous photon counting, The limit that the coupling between the signal and measurement apparatus is infinitesimal at each step and the number of the step is infinitely large was discussed. As an example, a specific case where the states to be discriminated are single-mode states and any nonclassical ancillas are excluded.

DOI
10.1109/eqec.2005.1567490

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In this paper, an expansion of the formulae to check whether one can implement a step via linear optics and photon counting was derived, to the limit of continuous photon counting, The limit that the coupling between the signal and measurement apparatus is infinitesimal at each step and the number of the step is infinitely large was discussed. As an example, a specific case where the states to be discriminated are single-mode states and any nonclassical ancillas are excluded.
The possibility of implementing a given photonic projective measurement with linear optics and photon detectors is discussed. This problem can be viewed as a single-shot discrimination of orthogonal pure quantum states. It is particularly shown that any two orthogonal states can be perfectly discriminated using only linear optics, photon counting, coherent ancillary states, and feedforward. This means that one can construct any binary projective measurement with these means, but without any nonclassical ancillary state. The statement holds in the asymptotic limit of a large number of these physical resources. To extend this result, we also address the problem of discriminating a simple set of three orthogonal states.
We propose a framework to analyze linear optical circuits based on an analogy with stabilizer formalism in quantum circuits, which provides efficiently computable formulas related to state discriminations. Hence, we analyze a Bell-state discrimination scheme with linear optics and ancillary single photons. With an increasing number of ancilla photons, the success probability of Bell-state discrimination has a maximum of 403512≃0.787\frac{403}{512} \simeq 0.787512403​≃0.787 at 282828 ancilla photons. By contrast, the corresponding two-qubit measurement asymptotically approaches a maximally entangling measurement.
The possibility of implementing a given photonic projective measurement with linear optics and photon detectors is discussed. This problem can be viewed as a single-shot discrimination of orthogonal pure quantum states. It is particularly shown that any two orthogonal states can be perfectly discriminated using only linear optics, photon counting, coherent ancillary states, and feedforward. This means that one can construct any binary projective measurement with these means, but without any nonclassical ancillary state . The state- ment holds in the asymptotic limit of a large number of these physical resources. To extend this result, we also address the problem of discriminating a simple set of three orthogonal states.