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IEEE Journal of Selected Topics in Quantum Electronics

Limitations on building single-photon-resolution detection devices

Pieter Kok

Published Nov 1, 2003• 10 citations
Publisher

Abstract

Single-photon resolution (SPR) detectors can tell the difference between incoming wave packets of n and n+1 photons. Such devices are especially important for linear optical quantum computing with projective measurements. However, in this paper, I show that it is impossible to construct a photodetector with single-photon resolution when we are restricted to single-photon sources, linear optical elements, and projective measurements with standard (nonphoton-number discriminating) photodetectors. These devices include SPR detectors that sometimes fail to distinguish one- and two-photon inputs, but at the same time indicate this failure. PACS numbers: 42.79.Ta, 03.67.Hk, 42.79.Gn.

DOI
10.1109/jstqe.2003.820909

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Single-photon resolution (SPR) detectors can tell the difference between incoming wave packets of n and n+1 photons. Such devices are especially important for linear optical quantum computing with projective measurements. However, in this paper, I show that it is impossible to construct a photodetector with single-photon resolution when we are restricted to single-photon sources, linear optical elements, and projective measurements with standard (nonphoton-number discriminating) photodetectors. These devices include SPR detectors that sometimes fail to distinguish one- and two-photon inputs, but at the same time indicate this failure. PACS numbers: 42.79.Ta, 03.67.Hk, 42.79.Gn.
Single-photon resolution (SPR) detectors can tell the difference between incoming wave packets of n and n+1 photons. Such devices are especially important for linear optical quantum computing with projective measurements. However, in this paper I show that it is impossible to construct a photodetector with single-photon resolution when we are restricted to single-photon sources, linear optical elements and projective measurements with standard (non-photon-number discriminating) photodetectors. These devices include SPR detectors that sometimes fail to distinguish one- and two-photon inputs, but at the same time indicate this failure.
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.
In optical quantum information processing, two of the most basic elements are the sources of quantum mechanical states of light, and the devices that can detect these states. In this chapter, we narrow this down to photon sources and photodetectors. We will describe first how detectors work, starting from abstract ideal detectors, via a complete description of realistic detectors in terms of POVMS, to a brief overview of current photodetectors. Subsequently, we will define what is a single-photon source, and how we can determine experimentally whether a source produces single photons or something else. Having laid down the ground rules, we will survey some of the most popular ways photons are produced in the laboratory. Finally, we take a look at the production of entangled photon sources and quantum non-demolition measurements of photons. A mathematical model of photodetectors Photodetectors are devices that produce a macroscopic signal when triggered by one or more photons. In the ideal situation, every photon that hits the detector contributes to the macroscopic signal, and there are no ‘ghost’ signals, or so-called dark counts. In this situation we can define two types of detector, namely the ‘photon-number detector’, and ‘detectors without number resolution’. First, the photon number detector is a (largely hypothetical) device that tells us how many photons there are in a given optical mode that is properly localized in space and time. This property is called ‘photon-number resolution’.
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.
Optical quantum-nondemolition devices can provide essential tools for quantum information processing. Here, we describe several optical interferometers that signal the presence of a single photon in a particular input state without destroying it. We discuss both entanglement-assisted and nonentanglement-assisted interferometers, with ideal and realistic detectors. We found that the existing detectors with 88% quantum efficiency and single-photon resolution can yield output fidelities of up to 89%, depending on the input state. Furthermore, we construct expanded protocols to perform quantum-nondemolition detections of single photons that leave the polarization invariant. For detectors with 88% efficiency, we found polarization-preserving output fidelities of up to 98.5%.