Quantum steering with positive operator valued measures

Abstract

We address the problem of quantum nonlocality with positive operator valued measures (POVM) in the context of Einstein-Podolsky-Rosen quantum steering. We show that, given a candidate for local hidden state (LHS) ensemble, the problem of determining the steerability of a bipartite quantum state of finite dimension with POVMs can be formulated as a nesting problem of two convex objects. One consequence of this is the strengthening of the theorem that justifies choosing the LHS ensemble based on symmetry of the bipartite state. As a more practical application, we study the classic problem of the steerability of two-qubit Werner states with POVMs. We show strong numerical evidence that these states are unsteerable with POVMs up to a mixing probability of $\frac{1}{2}$ within an accuracy of $10^{-3}$.

arXiv comment12 pages, 6 figures, comments welcome. This improved version has new discussion about symmetry of the state and its implications for LHS ensembles, moreover, we reveal that local hidden state models can always be taken over pure quantum states

References in corpus (22)

• Bell nonlocality
• Steering, Entanglement, Nonlocality, and the EPR Paradox
• One-sided Device-Independent Quantum Key Distribution: Security, feasibility, and the connection with steering
• Nonsequential positive-operator-valued measurements on entangled mixed states do not always violate a Bell inequality
• Loophole-free Einstein-Podolsky-Rosen experiment via quantum steering
• Conclusive quantum steering with superconducting transition edge sensors
• Inequivalence of entanglement, steering, and Bell nonlocality for general measurements
• Arbitrarily loss-tolerant Einstein-Podolsky-Rosen steering allowing a demonstration over 1 km of optical fiber with no detection loophole
• Classical randomness in quantum measurements
• Quantum randomness extraction for various levels of characterization of the devices
• Genuine hidden quantum nonlocality
• Optimal randomness certification from one entangled bit
• Optimal randomness certification in the quantum steering and prepare-and-measure scenarios
• Einstein-Podolsky-Rosen steering and the steering ellipsoid
• General method for constructing local-hidden-variable models for entangled quantum states
• Algorithmic construction of local hidden variable models for entangled quantum states
• Rigidity of quantum steering and one-sided device-independent verifiable quantum computation
• Necessary and sufficient condition for steerability of two-qubit states by the geometry of steering outcomes
• How continuous quantum measurements in finite dimension are actually discrete
• A two-qubit Bell inequality for which POVM measurements are relevant
• Most incompatible measurements for robust steering tests
• Non-separability and steerability of two-qubit states from the geometry of steering outcomes

Cited by in corpus (12)

• Quantum Steering
• The geometry of the Einstein--Podolsky--Rosen correlations
• Some quantum measurements with three outcomes can reveal nonclassicality where all two-outcome measurements fail to do so
• Exact Steering Bound for Two-Qubit Werner States
• Algorithmic construction of local models for entangled quantum states: optimization for two-qubit states
• Compatibility of Generalized Noisy Qubit Measurements
• Semidefinite relaxations for high-dimensional entanglement in the steering scenario
• Quantum steering of Bell-diagonal states with generalized measurements
• Assemblages and steering in general probabilistic theories
• Device-independent and semi-device-independent entanglement certification in broadcast Bell scenarios
• Axiomatic approach to measures of total correlations
• Certifying the activation of Bell nonlocality with finite data