Einstein-Podolsky-Rosen steering measure for two-mode continuous variable states
arXiv:1411.0444 · doi:10.1364/JOSAB.32.000A27
Abstract
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, 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 the optimal guaranteed key rate in semi-device independent quantum key distribution.
8 pages, 1 figure. Published in JOSA B, Special Issue on "80 years of Steering and the Einstein-Podolsky-Rosen Paradox"
References in corpus (40)
- Quantum entanglement
- Bell nonlocality
- Peres-Horodecki separability criterion for continuous variable systems
- Inseparability criterion for continuous variable systems
- Steering, Entanglement, Nonlocality, and the EPR Paradox
- Continuous variable quantum information: Gaussian states and beyond
- One-sided Device-Independent Quantum Key Distribution: Security, feasibility, and the connection with steering
- Extremal entanglement and mixedness in continuous variable systems
- The Einstein-Podolsky-Rosen paradox: from concepts to applications
- Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox
- Entanglement, EPR-correlations, Bell-nonlocality, and Steering
- Quantum versus classical correlations in Gaussian states
- Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
- Experimental EPR-Steering of Bell-local States
- Quantification of Gaussian quantum steering
- Observation of one-way Einstein-Podolsky-Rosen steering
- Quantifying Einstein-Podolsky-Rosen steering
- Multipartite Einstein-Podolsky-Rosen steering and genuine tripartite entanglement with optical networks
- Secure continuous variable quantum teleportation and Einstein-Podolsky-Rosen steering
- Extremality of Gaussian quantum states
- EPR Steering Inequalities from Entropic Uncertainty Relations
- Proposal for a loophole-free Bell test using homodyne detection
- Genuine multipartite Einstein-Podolsky-Rosen steering
- Loophole-free Einstein-Podolsky-Rosen experiment via quantum steering
- Conclusive quantum steering with superconducting transition edge sensors
- Measuring Gaussian quantum information and correlations using the Renyi entropy of order 2
- Proposed Test of Quantum Nonlocality for Continuous Variables
- Ultimate communication capacity of quantum optical channels by solving the Gaussian minimum-entropy conjecture
- Arbitrarily loss-tolerant Einstein-Podolsky-Rosen steering allowing a demonstration over 1 km of optical fiber with no detection loophole
- Gaussian Entanglement of Formation
- Entanglement of two-mode Gaussian states: characterization and experimental production and manipulation
- Signifying quantum benchmarks for qubit teleportation and secure communication using Einstein-Podolsky-Rosen steering inequalities
- Asymmetric Gaussian steering: when Alice and Bob disagree
- Monogamy inequalities for the EPR paradox and quantum steering
- Entanglement verification and steering when Alice and Bob cannot be trusted
- Experimental device-independent verification of quantum steering
- Strong Einstein-Podolsky-Rosen steering with unconditional entangled states
- Optimality of Gaussian Discord
- Postulates for measures of genuine multipartite correlations
- Strong Einstein-Podolsky-Rosen entanglement from a single squeezed light source
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- Quantum steering: a review with focus on semidefinite programming
- Secure continuous variable quantum teleportation and Einstein-Podolsky-Rosen steering
- Inequivalence of entanglement, steering, and Bell nonlocality for general measurements
- Multipartite Gaussian steering: monogamy constraints and quantum cryptography applications
- Hierarchy of Steering Criteria Based on Moments for All Bipartite Quantum Systems
- Quantatitive relations between measurement incompatibility, quantum steering, and nonlocality
- Schur complement inequalities for covariance matrices and monogamy of quantum correlations
- Sharing of Non-Local Advantage of Quantum Coherence by sequential observers
- Feedback Control of Two-mode Output Entanglement and Steering in Cavity Optomechanics
- Steering maps and their application to dimension-bounded steering
- Controlling Stationary One-Way Steering via Thermal Effects in Optomechanics
- Quantum steering of Gaussian states via non-Gaussian measurements
- Strong subadditivity for log-determinant of covariance matrices and its applications
- Investigating Einstein-Podolsky-Rosen steering of continuous variable bipartite states by non-Gaussian pseudospin measurements
- EPR Steering inequalities with Communication Assistance
- Dynamical Gaussian quantum steering in optomechanics
- Efficient Scheme for Perfect Collective Einstein-Podolsky-Rosen Steering
- Einstein-Podolsky-Rosen uncertainty limits for bipartite multimode states
- Einstein-Podolsky-Rosen-like separability indicators for two-mode Gaussian states
- Manipulating the direction of one-way steering in an optomechanical ring cavity
- EPR steering in symmetrical Gaussian states
- Creation of bipartite steering correlations by a fast damped auxiliary mode
- Quantum entanglement and Einstein-Podolsky-Rosen steering in ultrastrongly light-matter coupled system