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Physical Review A

Probing correlations in two-mode bosonic fields via Gaussian noise channels

Huihui Li, Nan Li, Shunlong Luo

Published Jun 15, 2023• 6 citations
Publisher

Abstract

Gaussian noise channels arise naturally in many physical situations and play an important role in information transmission involving continuous-variable quantum systems. In this work we employ Gaussian noise channels to probe and characterize correlations in two-mode bosonic fields. Based on the fact that local channels often cause more decoherence for global states than for local states due to correlations, we introduce a notion of conditional coherence relative to a local channel, which is defined as the difference between the global and local decoherence caused by the channel. We discuss its connections with quantum discord and relative quantum Fisher information and propose a class of correlation quantifiers for two-mode bosonic states in terms of conditional coherence relative to local Gaussian noise channels. We prove that any nonproduct state exhibits such correlations and show that these correlation quantifiers are measures of total correlations, which may include both classical and quantum parts. We further illustrate these correlation quantifiers through several typical two-mode bosonic states and make a comparative study between these correlation quantifiers and other known ones such as entanglement and discord.

DOI
10.1103/physreva.107.062415

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Gaussian noise channels arise naturally in many physical situations and play an important role in information transmission involving continuous-variable quantum systems. In this work we employ Gaussian noise channels to probe and characterize correlations in two-mode bosonic fields. Based on the fact that local channels often cause more decoherence for global states than for local states due to correlations, we introduce a notion of conditional coherence relative to a local channel, which is defined as the difference between the global and local decoherence caused by the channel. We discuss its connections with quantum discord and relative quantum Fisher information and propose a class of correlation quantifiers for two-mode bosonic states in terms of conditional coherence relative to local Gaussian noise channels. We prove that any nonproduct state exhibits such correlations and show that these correlation quantifiers are measures of total correlations, which may include both classical and quantum parts. We further illustrate these correlation quantifiers through several typical two-mode bosonic states and make a comparative study between these correlation quantifiers and other known ones such as entanglement and discord.
Quantum channels, in general, will disturb quantum states and will lead to decoherence (i.e., information leakage to the environment). For bipartite systems, local channels often cause more decoherence for global states than for local states due to correlations. Intuitively, the difference between these two kinds of decoherence (i.e., global and local ones) may be regarded as a quantifier characterizing certain aspects of correlations in the global bipartite states. Based on this idea, we introduce a quantifier of correlations (relative to a local channel) as the coherence difference and investigate its basic properties. We probe and quantify correlations relative to various channels including the unitary channels, the twirling channels, the projective measurements, and the weak measurements. In particular, we show that both product states and some natural classical-quantum states can be operationally characterized in terms of local channels: The product states are just those states with vanishing coherence difference relative to the twirling channel induced by the unitary group, whereas these natural classical-quantum states are just those states with vanishing coherence difference relative to the twirling channel induced by the subgroup of the unitary group that does not disturb the local states. We further illustrate the results by various examples.
Abstract Gaussian states, characterized by probability distributions in phase-space representations, play a fundamental role in quantum information processing. Despite their mathematical tractability, the presence of noise imposes limitations on achieving quantum protocols, impacting their effectiveness in continuous-variable quantum systems for various communication and computation tasks. Hence, investigating quantum entanglement and quantum correlations within the coherence of Gaussian states in noisy channels holds significant importance. In this study, we introduce and investigate a framework designed to precisely define and explore the dynamic evolution of quantum correlations within twomode Gaussian states subjected to the effects of a Gaussian thermal environment. We elucidate the temporal progression of quantum correlations within an open system comprising two interconnected bosonic modes embedded in a Gaussian thermal environment. We explore the impact of the environment by considering the evolution of the initial parameters of the input states. We measure the quantum correlations by employing the quantifiers: the Gaussian logarithmic negativity (GLN) N and the Gaussian quantum discord (GQD) D G . The behavior of these quantum correlation quantifiers is intricately related to the parameters of the input states utilized in the analysis. We demonstrate that the GQD D G serves as an appropriate measurement quantifier in capturing fundamental quantum correlations, outperforming other quantifiers. Furthermore, our findings reveal that the GQD D G exhibits greater resilience compared to GLN N , showing a reduced sensitivity to external influences.
Abstract Detecting and characterizing correlations are common subjects in quantum information theory, which have recently become increasingly essential in various quantum information tasks. A quantifier of correlations is introduced for two‐mode Bosonic states defined as the difference between global and local coherence caused by local photon subtraction. The fundamental properties and physical significance of this quantifier are revealed. Additionally, the amount of correlations is analyzed in the output states resulting from input product states through bilinear interactions. The quantifier of correlations is illustrated using typical two‐mode Bosonic states and its effectiveness is compared with other existing measures of correlations, such as entanglement and quantum discord.
In this Letter we exploit the recently solved conjecture on the bosonic minimum output entropy to show the optimality of Gaussian discord, so that the computation of quantum discord for bipartite Gaussian states can be restricted to local Gaussian measurements. We prove such optimality for a large family of Gaussian states, including all two-mode squeezed thermal states, which are the most typical Gaussian states realized in experiments. Our family also includes other types of Gaussian states and spans their entire set in a suitable limit where they become Choi matrices of Gaussian channels. As a result, we completely characterize the quantum correlations possessed by some of the most important bosonic states in quantum optics and quantum information.
In this Letter we exploit the recently-solved conjecture on the bosonic minimum output entropy to show the optimality of Gaussian discord, so that the computation of quantum discord for bipartite Gaussian states can be restricted to local Gaussian measurements. We prove such optimality for a large family of Gaussian states, including all two-mode squeezed thermal states, which are the most typical Gaussian states realized in experiments. Our family also includes other types of Gaussian states and spans their entire set in a suitable limit where they become Choi-matrices of Gaussian channels. As a result, we completely characterize the quantum correlations possessed by some of the most important bosonic states in quantum optics and quantum information.
In recent years the paradigm based on entanglement as the unique measure of quantum correlations has been challenged by the rise of new correlation concepts, such as quantum discord, able to reveal quantum correlations that are present in separable states. It is in general difficult to compute quantum discord, because it involves a minimization over all possible local measurements in a bipartition. In the realm of continuous-variable (CV) systems, a Gaussian version of quantum discord has been put forward upon restricting to Gaussian measurements. It is natural to ask whether non-Gaussian measurements can lead to a stronger minimization than Gaussian ones. Here we focus on two relevant classes of two-mode Gaussian states: squeezed thermal states and mixed thermal states, and allow for a range of experimentally feasible non-Gaussian measurements, comparing the results with the case of Gaussian measurements. We provide evidence that Gaussian measurements are optimal for Gaussian states.