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Non-deterministic approximation of photon number discriminating detectors using non-discriminating detectors

Peter P. Rohde

Published Nov 16, 2004• 7 citations
OpenAlex

Abstract

We present a scheme for non-deterministically approximating photon number resolving detectors using non-discriminating detectors. The model is simple in construction and employs very few physical resources. Despite its non-determinism, the proposal may nonetheless be suitable for use in some quantum optics experiments in which non-determinism can be tolerated. We analyse the detection scheme in the context of an optical implementation of the controlled-NOT gate, an inherently non-deterministic device. This allows the gate's success probability to be traded away for improved gate fidelity, assuming high efficiency detectors. The scheme is compared to two other proposals, both deterministic, for approximating discriminating detectors using non-discriminating detectors: the cascade and time division multiplexing schemes. © 2005 IOP Publishing Ltd.

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Non-deterministic approximation of photon number discriminating detectors using non-discriminating detectors

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We present a scheme for non-deterministically approximating photon number resolving detectors using non-discriminating detectors. The model is simple in construction and employs very few physical resources. Despite its non-determinism, the proposal may nonetheless be suitable for use in some quantum optics experiments in which non-determinism can be tolerated. We analyse the detection scheme in the context of an optical implementation of the controlled-NOT gate, an inherently non-deterministic device. This allows the gate's success probability to be traded away for improved gate fidelity, assuming high efficiency detectors. The scheme is compared to two other proposals, both deterministic, for approximating discriminating detectors using non-discriminating detectors: the cascade and time division multiplexing schemes. © 2005 IOP Publishing Ltd.
We present a scheme for non-deterministically approximating photon number resolving detectors using non-discriminating detectors. The model is simple in construction and employs very few physical resources. Despite its non-determinism, the proposal may nonetheless be suitable for use in some quantum optics experiments in which non-determinism can be tolerated. We analyse the detection scheme in the context of an optical implementation of the controlled-NOT gate, an inherently non-deterministic device. This allows the gate's success probability to be traded away for improved gate fidelity, assuming high efficiency detectors. The scheme is compared to two other proposals, both deterministic, for approximating discriminating detectors using non-discriminating detectors: the cascade and time division multiplexing schemes.
Number-resolving photo-detection is necessary for many quantum optics experiments, especially in the application of entangled state preparation. Several schemes have been proposed for approximating number-resolving photo-detection using non-number-resolving detectors. Such techniques include multi-port detection and time-division multiplexing. We provide a detailed analysis and comparison of different number-resolving detection schemes, with a view to creating a useful reference for experimentalists. We show that the ideal architecture for projective measurements is a function of the detector's dark count and efficiency parameters. We also describe a process for selecting an appropriate topology given actual experimental component parameters.
Although some non-trivial photon number resolving detectors exist, it may still be convenient to discriminate photon number states with the method of multiplexed detection. Multiplexing can be performed with paths in real space, with paths in time, and in principle with any degree of freedom that has a sufficient number of eigenstates and that can be coupled to the photon number. Previous works have addressed the probabilities involved in these measurements with Monte Carlo simulations, or by restricting the number of detectors to powers of 2, or without including quantum efficiency or noise. In this work we find an analytical expression of the detection probabilities for any number of input photons and any number of on/off photon detectors with a quantum efficiency 0%≤η≤100%0\%\leqη\leq100\%0%≤η≤100% and a false count probability ε≥0\varepsilon\geq0ε≥0. This allows us to retrodict the number of photons that we had at the input in the least unbiased way possible. We conclude our work with some examples.
In quantum optical computing and quantum cryptography a very important problem is that of developing an efficient photon-number resolving detector. Such a device is critical for the development of linear optical quantum computing (LOQC) [1], and can be also used in quantum cryptography [2]. A recent paper claims to have demonstrated the operation of a superconducting, number-resolving photon detector, developed by a group at NIST [3]. However, this device operates with a quantum efficiency of only about 20%, and we show here that it cannot discriminate photon number, even in principal. However, the NIST device has a very low dark-count rate, much less than 1%, which means that it can quite efficiently discriminate against the absence of photons of particular numbers. We call such a device a number-discriminating non-photon detector. Interestingly enough, even though this detector cannot yield photon number—its ability to discriminate against photons of certain numbers allows it to be used, under suitable assumptions, to reconstruct the ensemble photostatistics of the incoming photon field. However, such a low-efficiency device cannot be used, say, in LOQC, where single-shot photon number discrimination is required.
Number-resolving photo-detection is necessary for many quantum optics experiments, especially in the application of entangled state preparation. Several schemes have been proposed for approximating number-resolving photo-detection using non-number-resolving detectors. Such techniques include multi-port detection and time-division multiplexing. We provide a detailed analysis and comparison of different number-resolving detection schemes, with a view to creating a useful reference for experimentalists. We show that the ideal architecture for projective measurements is a function of the detector's dark count and efficiency parameters. We also describe a process for selecting an appropriate topology given actual experimental component parameters.
Common methods to achieve photon number resolution rely on fast on-off single-photon detectors in conjunction with temporal or spatial mode multiplexing. Yet, these methods suffer from an inherent trade-off between the efficiency of photon number discrimination and photon detection rate. Here, we introduce a method of photon number resolving detection that overcomes these limitations by replacing mode multiplexing with coherent absorption of a single optical mode in a distributed detector array. Distributed coherent absorption ensures complete and uniform absorption of light among the constituent detectors, enabling fast and efficient photon number resolution. As a proof-of-concept, we consider the case of a distributed array of superconducting nanowire single-photon detectors with realistic parameters and show that deterministic absorption and arbitrarily high photon number discrimination efficiency can be achieved by increasing the number of detectors in the array. Photon number resolution without optical mode multiplication provides a simple yet effective method to discriminate an arbitrary number of photons in large arrays of on-off detectors or in smaller arrays of mode multiplexed detectors.