Optimal detection of losses by thermal probes

Abstract

We consider the discrimination of lossy bosonic channels and focus to the case when one of the values for the loss parameter is zero, i.e., we address the detection of a possible loss against the alternative hypothesis of an ideal lossless channel. This discrimination is performed by inputting one-mode or two-mode squeezed thermal states with fixed total energy. By optimizing over this class of states, we find that the optimal inputs are pure, thus corresponding to single-and two-mode squeezed vacuum states. In particular, we show that for any value of the damping rate smaller than a critical value there is a threshold on the energy that makes the two-mode squeezed vacuum state more convenient than the corresponding single-mode state, whereas for damping larger than this critical value two-mode squeezed vacua are always better. We then consider the discrimination in realistic conditions, where it is unlikely to have pure squeezing. Thus by fixing both input energy and squeezing, we show that two-mode squeezed thermal states are always better than their singlemode counterpart when all the thermal photons are directed into the dissipative channel. Besides, this result also holds approximately for unbalanced distribution of the thermal photons. Finally, we also investigate the role of correlations in the improvement of detection. For fixed input squeezing (single-mode or two-mode), we find that the reduction of the quantum Chernoff bound is a monotone function of the two-mode entanglement as well as the quantum mutual information and the quantum discord. We thus verify that employing squeezing in the form of correlations (quantum or classical) is always a resource for loss detection whenever squeezed thermal states are taken as input.

Quantum parameter estimation using multi-mode Gaussian states

“…We believe the main achievement of this article is in the usefulness of the derived formulae. It allows for the study of the optimal input states of Gaussian nature [31], it helps predict the ultimate sensitivity of a physical detector's particular implementation [3,4], or to analyse the effects of temperature on the current gravitational wave detector proposal [5]. It gives a limit in the estimation of time [32] or temperature [33].…”

Quantum reading capacity

“…Note that this approach has been first considered in Ref. [39] for individuating the optimal thermal probes (i.e., the optimal squeezed thermal vacua) for detecting the presence of loss in bosonic channels. While this stronger energy constraint does not make any difference for the classical reading capacity (since the optimal classical transmitter involves signal modes only) it clearly affects the EPR transmitters where the mean total energy of the TMSV states is split exactly in two between signal and reference modes.…”

Ultimate Precision of Adaptive Noise Estimation

“…Our no-go theorem also establishes that this limit is achievable by using entanglement without adaptiveness, so that the quantum Fisher information (QFI) [1] assumes a remarkably simple expression in terms of the channel's Choi matrix. As an application, we set the ultimate adaptive limit for estimating thermal noise in Gaussian channels, which has implications for continuous-variable quantum key distribution (QKD) and, more generally, for measurements of temperature in quasi-monochromatic bosonic baths.Because our methodology applies to any functional of quantum states which is monotonic under completelypositive trace-preserving (CPTP) maps, we may simplify other types of adaptive protocols, including those for quantum hypothesis testing [30][31][32][33][34]. Here we find that the ultimate error probability for discriminating two teleportation-covariant channels is reached without adaptiveness and determined by their Choi matrices.…”