Abstract
Einstein-Podolsky-Rosen steering incarnates a useful nonclassical correlation which sits between entanglement and Bell nonlocality. While a number of qualitative steering criteria exist, very little has been achieved for what concerns quantifying steerability. We introduce a computable measure of steering for arbitrary bipartite Gaussian states of continuous variable systems. For two-mode Gaussian states, the measure reduces to a form of coherent information, which is proven never to exceed entanglement, and to reduce to it on pure states. We provide an operational connection between our measure and the key rate in one-sided device-independent quantum key distribution. We further prove that Peres' conjecture holds in its stronger form within the fully Gaussian regime: namely, steering bound entangled Gaussian states by Gaussian measurements is impossible.
Highlights
Quantum correlations have been intensively investigated in recent years after the realization that, besides their foundational importance, they can be exploited to outperform any classical approach in certain tasks, e.g., in computation [1], secure communication [2,3], and metrology [4]
The first experimental criterion for the demonstration of the EPR paradox, i.e., for the detection of quantum steering, was later proposed by Reid [17], but it was not until 2007 that the particular type of nonlocality captured by the concept of steering [8,9,12] was formalized [10,18]
At variance with the case of Bell tests, a demonstration of steering free of detection and locality loopholes is in reach [19,20,21,22], which makes one-sided device-independent quantum key distribution (QKD) appealing for current technology and quantum steering a practically useful concept
Summary
Every time Alice makes a measurement RA and gets an outcome rA, Bob’s conditioned state ρrBAjRA is Gaussian with a CM given by BRA 1⁄4 B − CðTRA þ AÞ−1CT, independent of Alice’s outcome It can be shown [10] that a general (n þ m)-mode Gaussian state ρAB is A → B steerable by Alice’s Gaussian measurements iff the condition σAB þ ið0A ⊕ ΩBÞ ≥ 0. We propose to quantify how much a bipartite (m þ n)-mode Gaussian state with CM σAB is steerable (by Gaussian measurements on Alice’s side) via the following quantity: X This quantity, hereby defined as Gaussian A → B steerability, is invariant under local unitaries (symplectic operations at the CM level), it vanishes iff the state described by σAB is nonsteerable by Gaussian measurements, and it generally quantifies the amount by which condition (3) fails to be fulfilled.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
