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International Conference on Systems and Informatics (ICSAI)

Einstein-Podolsky-Rosen steering for non-Gaussian states based on moment matrices

Ying Xu, Li-zhen Jiang

Published Nov 1, 2016• 0 citations
Publisher

Abstract

The Einstein-Podolsky-Rosen(EPR) steering is a manifestation of the quantum correlation in quantum systems. In this article, we adopt moment matrices, which are proposed by Kogias et.al. in [1], to calculate the steering of quantum states. Firstly, we show that moment matrices are superior to Clauser-Horne-Shimony-Holt(CHSH) inequalities when applied to Inept states. Secondly, we use the method based on moment matrices to calculate the steering of non-Gaussian states. In particular, we deal with two mode vacuum squeezed states, photon subtracted states, and photon added states. Finally, we get the steering range of these non-Gaussian states respectively. The moment matrices behave useful for the calculation of the steering of Non-Gaussian states.

DOI
10.1109/icsai.2016.7811059

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The Einstein-Podolsky-Rosen(EPR) steering is a manifestation of the quantum correlation in quantum systems. In this article, we adopt moment matrices, which are proposed by Kogias et.al. in [1], to calculate the steering of quantum states. Firstly, we show that moment matrices are superior to Clauser-Horne-Shimony-Holt(CHSH) inequalities when applied to Inept states. Secondly, we use the method based on moment matrices to calculate the steering of non-Gaussian states. In particular, we deal with two mode vacuum squeezed states, photon subtracted states, and photon added states. Finally, we get the steering range of these non-Gaussian states respectively. The moment matrices behave useful for the calculation of the steering of Non-Gaussian states.
In view of the increasing importance of non-Gaussian entangled states in quantum information protocols like teleportation and violations of Bell inequalities, the steering of continuous variable non-Gaussian entangled states is investigated. Einstein-Podolsky-Rosen steering for Gaussian states may be demonstrated through the violation of the Reid inequality involving products of the inferred variances of noncommuting observables. However, for arbitrary states the Reid inequality is not always necessary because of the higher-order correlations in such states. One then needs to use the entropic steering inequality. We examine several classes of currently important non-Gaussian entangled states, such as the two-dimensional harmonic oscillator, the photon-subtracted two-mode squeezed vacuum, and the NOON state, in order to demonstrate the steering property of such states. A comparative study of the violation of the Bell inequality for these states shows that the entanglement present is more easily revealed through steering compared to Bell violation for several such states.
Einstein-Podolsky-Rosen (EPR) steering is an asymmetric form of correlations which is intermediate between quantum entanglement and Bell nonlocality, and can be exploited as a resource for quantum communication with one untrusted party. In particular, steering of continuous-variable Gaussian states has been extensively studied theoretically and experimentally, as a fundamental manifestation of the EPR paradox. While most of these studies focused on quadrature measurements for steering detection, two recent works revealed that there exist Gaussian states which are only steerable by suitable non-Gaussian measurements. In this paper we perform a systematic investigation of EPR steering of bipartite Gaussian states by pseudospin measurements, complementing and extending previous findings. We first derive the density-matrix elements of two-mode squeezed thermal Gaussian states in the Fock basis, which may be of independent interest. We then use such a representation to investigate steering of these states as detected by a simple nonlinear criterion, based on second moments of the correlation matrix constructed from pseudospin operators. This analysis reveals previously unexplored regimes where non-Gaussian measurements are shown to be more effective than Gaussian ones to witness steering of Gaussian states in the presence of local noise. We further consider an alternative set of pseudospin observables, whose expectation value can be expressed more compactly in terms of Wigner functions for all two-mode Gaussian states. However, according to the adopted criterion, these observables are found to be always less sensitive than conventional Gaussian observables for steering detection. Finally, we investigate continuous-variable Werner states, which are non-Gaussian mixtures of Gaussian states, and find that pseudospin measurements are always more effective than Gaussian ones to reveal their steerability. Our results provide useful insights on the role of non-Gaussian measurements in characterizing quantum correlations of Gaussian and non-Gaussian states of continuous-variable quantum systems.
Steering is a manifestation of quantum correlations that embodies the Einstein–Podolsky–Rosen (EPR) paradox. While there have been recent attempts to quantify steering, continuous variable systems remained elusive. We introduce a steering measure for two-mode continuous variable systems that is valid for arbitrary states. The measure is based on the violation of an optimized variance test for the EPR paradox by quadrature measurements and admits a computable and experimentally friendly lower bound only depending on the second moments of the state, which reduces to a recently proposed quantifier of steerability by Gaussian measurements. We further show that Gaussian states are extremal with respect to our measure, minimizing it among all continuous variable states with fixed second moments. As a byproduct of our analysis, we generalize and relate well-known EPR-steering criteria. Finally an operational interpretation is provided, as the proposed measure is shown to quantify a guaranteed key rate in semi-device-independent quantum key distribution.
We present an experimentally practical method to reveal Einstein-Podolsky-Rosen (EPR) steering in non-Gaussian spin states by exploiting a connection to quantum metrology. Our criterion is based on the quantum Fisher information, and uses bounds derived from generalized spin-squeezing parameters that involve measurements of higher-order moments. This leads us to introduce the concept of conditional spin-squeezing parameters, which quantify the metrological advantage provided by conditional states, as well as detect the presence of an EPR paradox.
Steering is a manifestation of quantum correlations that embodies the Einstein-Podolsky-Rosen (EPR) paradox. While there have been recent attempts to quantify steering, continuous variable systems remained elusive. We in-troduce a steering measure for two-mode continuous variable systems that is valid for arbitrary states. The measure is based on the violation of an optimized variance test for the EPR paradox, and admits a computable and exper-imentally friendly lower bound only depending on the second moments of the state, which reduces to a recently proposed quantifier of steerability by Gaussian measurements. We further show that Gaussian states are extremal with respect to our measure, minimizing it among all continuous variable states with fixed second moments. As a byproduct of our analysis, we generalize and relate well-known EPR-steering criteria. Finally an operational inter-pretation is provided, as the proposed measure is shown to quantify the optimal guaranteed key rate in semi-device independent quantum key distribution. 1.
Abstract Non-Gaussian quantum states are a known necessary resource for reaching a quantum advantage and for violating Bell inequalities in continuous variable systems. As one kind of manifestation of quantum correlations, Einstein–Podolsky–Rosen steering enables verification of shared entanglement even when one of the subsystems is not characterized. However, how to detect and classify such an effect for non-Gaussian states is far from being well understood. Here, we present an efficient non-Gaussian steering criterion based on the high-order observables and conduct a systematic investigation into the hierarchy of non-Gaussian steering criteria. Moreover, we apply our criterion to three experimentally-relevant non-Gaussian states under realistic conditions and, in particular, propose a feasible scheme to create multi-component cat states with tunable size by performing a suitable high-order quadrature measurement on the steering party. Our work reveals the fundamental characteristics of non-Gaussianity and quantum correlations, and offers new insights to explore their applications in quantum information processing.