Quantum-Limited Discrimination between Laser Light and Noise

Abstract

To determine the fundamental sensitivity limit of an optical receiver one must have a complete quantum mechanical description of the incoming signals, even if those signals are from "classical" sources of light, i.e., ones whose photo-detection statistics with conventional receivers can be explained correctly using the shot-noise theory. In this work, we calculate the fundamental (quantum) limit for discriminating between two types of classical states in the low photon number regime: a coherent state, a pure-state quantum description of ideal (coherent) laser light with Poisson distributed photon statistics, and a thermal state, a (incoherent) mixed state with Bose-Einstein photon statistics. The Helstrom bound for discrimination error probability for single mode measurement is computed along with error probability bounds for direct detection, coherent homodyne detection and the Kennedy receiver. The generalized Kennedy (GK) receiver is shown to closely approach the Helstrom limit. We experimentally validate these results by generating coherent and thermal light and demonstrate that for signal strengthsns > 0.01 photons/mode, using a GK receiver with a quasi-photon-number resolving detector, we can approach quantum-limited discrimination performance, out-performing the discrimination capability achievable with traditional optical sensors. We demonstrate ∼ 17 dB improvement in discrimination sensitivity over direct detection using a GK receiver, and an improvement of 17% in error probability over coherent detection at a mean signal photon numberns = 0.4 photons/mode. PACS numbers:

Demonstration of quantum-limited discrimination of multi-copy pure versus mixed states

“…The experiments showed that the GK receiver closely approaches the Helstrom bound, while the Kennedy receiver was shown to be sub-optimal. Our work here shows both experimentally and analytically that the situation is reversed for multi-copy discrimination: the Kennedy receiver exactly attains the QCB, as expected [13,22], whereas the GK receiver is decidedly not optimal by a provable factor.…”

“…We observe that ξ QCB > ξ GK > ξ Helstrom , with the quantum Chernoff bound (achieved by the Kennedy receiver) exceeding both ξ GK and ξ Helstrom by at least a factor of two. We also note that coherent homodyne detection, another common classical receiver, achieves a discrimination error exponent equal to that for the ideal Helstrom receiver, as shown in [13].…”

“…More recently, investigations have examined discrimination between a broader class of quantum states to include mixed states [13][14][15][16][17]. Experimental work has demonstrated techniques for improved discrimination be-tween single-copy pure and mixed quantum states [18] including a demonstration that approached the Helstrom bound [19].…”

Phase tracking for sub-shot-noise-limited receivers

“…As a proof-of-concept, we investigate a NN-based method for tracking phase and amplitude channel noise, that uses only the data collected during the state discrimination measurement. This NN-based method can be easily extended to perform higher dimensional parameter estimation for tracking additional sources of noise in the channel such as thermal noise [33,34] or phase diffusion [35][36][37]. In this section, we describe (A) the measurement strategy of the non-Gaussian receiver for coherent state discrimination; (B) how the data from the measurement is used by the NN; and (C) the NN estimator, which can be used for estimation of channel noise from multiple sources.…”

“…In more realistic situations there may be multiple sources of noise present in the communication channel, such as thermal noise [33,34], phase diffusion [35][36][37], phase noise, and amplitude noise. In such situations the non-Gaussian receiver must perform efficient highdimensional parameter estimation and tracking in order to maintain the expected sub-QNL performance.…”