Inequivalence of entanglement, steering, and Bell nonlocality for general measurements

Abstract

Einstein-Podolsky-Rosen steering is a form of inseparability in quantum theory commonly acknowledged to be intermediate between entanglement and Bell nonlocality. However, this statement has so far only been proven for a restricted class of measurements, namely projective measurements. Here we prove that entanglement, one-way steering, two-way steering and nonlocality are genuinely different considering general measurements, i.e. single round positive-operator-valued-measures. Finally, we show that the use of sequences of measurements is relevant for steering tests, as they can be used to reveal "hidden steering".

Typo in equation 13 corrected (noticed by Jessica Bavaresco)

References in corpus (14)

• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox
• Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
• Observation of one-way Einstein-Podolsky-Rosen steering
• Joint measurability of generalized measurements implies classicality
• Disproving the Peres conjecture: Bell nonlocality from bipartite bound entanglement
• All bipartite entangled states display some hidden nonlocality
• Noise robustness of the nonlocality of entangled quantum states
• Steering bound entangled states: A counterexample to the stronger Peres conjecture
• Einstein-Podolsky-Rosen steering and the steering ellipsoid
• Local hidden--variable models for entangled quantum states
• Geometric Bell-like inequalities for steering
• Quantifying the nonlocality of GHZ quantum correlations by a bounded communication simulation protocol
• Einstein-Podolsky-Rosen steering measure for two-mode continuous variable states

Cited by in corpus (131)

• Quantum Steering
• Quantum steering: a review with focus on semidefinite programming
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• Observation of genuine one-way Einstein-Podolsky-Rosen steering
• Quantification of Einstein-Podolski-Rosen steering for two-qubit states
• Multipartite Gaussian steering: monogamy constraints and quantum cryptography applications
• Sufficient criterion for guaranteeing that a two-qubit state is unsteerable
• Hierarchy of Steering Criteria Based on Moments for All Bipartite Quantum Systems
• Optimal randomness certification in the quantum steering and prepare-and-measure scenarios
• Incompatible measurements in quantum information science
• Genuine high-dimensional quantum steering
• Conclusive experimental demonstration of one-way Einstein-Podolsky-Rosen steering
• All entangled states can demonstrate non-classical teleportation
• Tutorial: Nonlinear magnonics
• Demonstration of Einstein-Podolsky-Rosen Steering with Enhanced Subchannel Discrimination
• General method for constructing local-hidden-variable models for entangled quantum states
• Algorithmic construction of local hidden variable models for entangled quantum states
• Perfect Transfer of enhanced entanglement and asymmetric steering in a cavity magnomechanical system
• Necessary and sufficient condition for steerability of two-qubit states by the geometry of steering outcomes
• Unbounded sequence of observers exhibiting Einstein-Podolsky-Rosen steering
• Universal steering inequalities
• Experimental Measurement-Device-Independent Quantum Steering and Randomness Generation Beyond Qubits
• Manipulating the direction of Einstein-Podolsky-Rosen steering
• Incompatibility breaking quantum channels
• Machine Learning meets Quantum Foundations: A Brief Survey
• Network Quantum Steering
• Tight steering inequalities from generalized entropic uncertainty relations
• Steering Bell-diagonal states
• Entanglement without hidden nonlocality
• Most incompatible measurements for robust steering tests
• Manipulation and enhancement of asymmetric steering via interference effects induced by closed-loop coupling
• Experimental demonstration of measurement-device-independent measure of quantum steering
• Quantifying Quantumness of Channels Without Entanglement
• Complete classification of steerability under local filters and its relation with measurement incompatibility
• Quantum steerability: characterization, quantification, superactivation and unbounded amplification
• The geometry of the Einstein--Podolsky--Rosen correlations
• Retrieving High-Dimensional Quantum Steering From a Noisy Environment with N Measurement Settings
• Super-Activation of Quantum Steering
• Revealing of hidden quantum steerability using local filtering operations
• A channel-based framework for steering, non-locality and beyond
• Temporal Steering in Four Dimensions with applications to coupled qubits and magnetoreception
• Measurement incompatibility and Schrödinger-EPR steering in a class of probabilistic theories
• Distillation of quantum steering
• Pearson Correlation Coefficient as a measure for Certifying and Quantifying High Dimensional Entanglement
• Detecting Einstein-Podolsky-Rosen steering through entanglement detection
• Incompatible quantum measurements admitting a local hidden variable model
• Robust self-testing of steerable quantum assemblages and its applications on device-independent quantum certification
• Shareability of Quantum Steering and its Relation with Entanglement
• Unified picture for spatial, temporal and channel steering
• Quantum battery in the Heisenberg spin chain models with Dzyaloshinskii-Moriya interaction
• Distributed sampling, quantum communication witnesses, and measurement incompatibility
• Complementary relations of entanglement, coherence, steering and Bell nonlocality inequality violation in three-qubit states
• Classical communication cost of quantum steering
• Swapping of Gaussian Einstein-Podolsky-Rosen steering
• A formalism for steering with local quantum measurements
• A Study on Thermal Quantum Resources and Probabilistic Teleportation in Spin-1/2 Heisenberg XYZ+DM+KSEA Model under Variable Zeeman Splitting
• Unification of quantum resources in tripartite systems
• Bell nonlocality with a single shot
• Experimental demonstration of one-sided device-independent self-testing of any pure two-qubit entangled state
• Einstein-Podolsky-Rosen correlations and Bell correlations in the simplest scenario
• Exact Steering Bound for Two-Qubit Werner States
• Experimental certification of steering criterion based on general entropic uncertainty relation
• Some quantum measurements with three outcomes can reveal nonclassicality where all two-outcome measurements fail to do so
• Reliable experimental certification of one-way Einstein-Podolsky-Rosen steering
• Algorithmic construction of local models for entangled quantum states: optimization for two-qubit states
• Certification of incompatible measurements using quantum steering
• EPR Steering inequalities with Communication Assistance
• Cost of Einstein-Podolsky-Rosen steering in the context of extremal boxes
• Quantum steering with positive operator valued measures
• Dynamics and recovery of genuine multipartite Einstein-Podolsky-Rosen steering and genuine multipartite nonlocality for a dissipative Dirac system via Unruh effect
• Detecting genuine multipartite entanglement in steering scenarios
• Necessary Condition for Steerability of Arbitrary Two-Qubit States with Loss
• Unlimited One-Way Steering
• Deep learning the hierarchy of steering measurement settings of qubit-pair states
• Experimental observation the Einstein-Podolsky-Rosen Steering based on the detection of entanglement
• Activation of nonlocality in bound entanglement
• Einstein-Podolsky-Rosen steering and Bell nonlocality of two macroscopic mechanical oscillators in optomechanical systems
• Hierarchy of Genuine Multipartite Quantum Correlations
• Compatibility of Generalized Noisy Qubit Measurements
• Quantum uncertainty relation based on the mean deviation
• Device-independent verification of Einstein-Podolsky-Rosen steering
• Engineering asymmetric steady-state Einstein-Podolsky-Rosen steering in macroscopic hybrid systems
• Non-Local Network Coding in Interference Channels
• Constructions of genuinely entangled multipartite states with applications to local hidden variables (LHV) and states (LHS) models
• Creating quantum correlations in generalized entanglement swapping
• One-way Einstein-Podolsky-Rosen steering beyond qubits
• Operational characterization of quantumness of unsteerable bipartite states
• Certification of the maximally entangled state using non-projective measurements
• Does conditional entropy squeezing indicate normalized entropic uncertainty relation steering?
• Quantum Bell Nonlocality is Entanglement
• On the properties of qudits
• Equivalence between simulability of high-dimensional measurements and high-dimensional steering
• Necessary conditions for steerability of two qubits, from consideration of local operations
• Necessary and sufficient conditions for multipartite Bell violations with only one trusted device
• Classical-hidden-variable description for entanglement dynamics of two-qubit pure states
• Local-hidden-state models for Bell diagonal states and beyond
• Interplays between classical and quantum entanglement-assisted communication scenarios
• On the power of one pure steered state for EPR-steering with a pair of qubits
• Quantum Steering on IBMQ
• Hierarchical axioms for quantum mechanics
• Keyring models: an approach to steerability
• Device-independent and semi-device-independent entanglement certification in broadcast Bell scenarios
• Quantification of Quantum Correlations in Two-Beam Gaussian States Using Photon-Number Measurements
• All incompatible measurements on qubits lead to multiparticle Bell nonlocality
• Role of maximally entangled states in the context of linear steering inequalities
• Analysis of Quantum Steering Measures
• Characterization of the quantumness of unsteerable tripartite correlations
• Einstein-Podolsky-Rosen steering paradox "2=1'' for $N$ qubits
• Revealing the quantitative relation between simultaneous correlations in complementary bases and quantum steering for two-qubit Bell diagonal states
• A tighter steering criterion using the Robertson-Schrodinger uncertainty relation
• Persistency of Genuine Correlations Under Particle Loss
• Violation of steering inequality for generalized equiangular measurements
• Locally inaccessible hidden quantum correlations
• Almost device-independent certification of GME states with minimal measurements
• Robust certification of quantum instruments through a sequential communication game
• Quantum resources of the steady-state of three coupled qubits: Microscopic versus Phenomenological model
• Detector dependency of diffusive quantum monitorings
• Steering in Neutrino Oscillations with Non-Standard Interaction
• Measurement-device-independent measure of steerability and witnesses for all steerable resources
• EPR steering in symmetrical Gaussian states
• On compatibility of binary qubit measurements
• Violation of space-time Bell-CHSH inequality beyond Tsirelson bound via post selection and quantum cryptography
• Asymmetric steerability of quantum equilibrium and nonequilibrium steady states through entanglement detection
• Exploiting Gaussian steering to probe non-Markovianity due to the interaction with a structured environment
• Activation of post-quantum steering
• Cyclic Einstein-Podolsky-Rosen Steering
• Violation of Bell Inequalities: Mapping the Conceptual Implications
• Simulation of Quantum Correlation Functions is not Sufficient Resource to Describe Quantum Entanglement
• Certifying the activation of Bell nonlocality with finite data
• Witness High-Dimensional Quantum Steering via Majorization Lattice
• Conditional steering under von-Neumann scenario