One-to-one mapping between steering and joint measurability problems
arXiv:1507.08633 · doi:10.1103/PhysRevLett.115.230402
Abstract
Quantum steering refers to the possibility for Alice to remotely steer Bob's state by performing local measurements on her half of a bipartite system. Two necessary ingredients for steering are entanglement and incompatibility of Alice's measurements. In particular, it has been recently proven that for the case of pure states of maximal Schmidt rank the problem of steerability for Bob's assemblage is equivalent to the problem of joint measurability for Alice's observables. We show that such an equivalence holds in general, namely, the steerability of any assemblage can always be formulated as a joint measurability problem, and vice versa. We use this connection to introduce steering inequalities from joint measurability criteria and develop quantifiers for the incompatibility of measurements.
Definition of the SDP in Eq. (31) corrected, thanks to a comment by Marco Piani and Benjamin A. Ross
References in corpus (13)
- Steering, Entanglement, Nonlocality, and the EPR Paradox
- Heisenberg's Uncertainty Principle
- Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
- Semi-device-independent security of one-way quantum key distribution
- Quantifying Entanglement with Witness Operators
- Joint measurability of generalized measurements implies classicality
- Disproving the Peres conjecture: Bell nonlocality from bipartite bound entanglement
- Steering bound entangled states: A counterexample to the stronger Peres conjecture
- Quantum steering ellipsoids, extremal physical states and monogamy
- Noise Robustness of the Incompatibility of Quantum Measurements
- Verifying the quantumness of a channel with an untrusted device
- Commutative POVMs and Fuzzy Observables
- Connecting the generalized robustness and the geometric measure of entanglement
Cited by in corpus (140)
- Quantum Steering
- Quantum steering: a review with focus on semidefinite programming
- An Invitation to Quantum Incompatibility
- Quantifying quantum resources with conic programming
- Sufficient criterion for guaranteeing that a two-qubit state is unsteerable
- All sets of incompatible measurements give an advantage in quantum state discrimination
- Incompatible measurements in quantum information science
- Quantatitive relations between measurement incompatibility, quantum steering, and nonlocality
- Quantum Incompatibility Witnesses
- Natural Framework for Device-Independent Quantification of Quantum Steerability, Measurement Incompatibility, and Self-Testing
- Genuine high-dimensional quantum steering
- Quantifying measurement incompatibility of mutually unbiased bases
- Steering criteria from general entropic uncertainty relations
- Incompatibility robustness of quantum measurements: a unified framework
- Quantum measurement incompatibility does not imply Bell nonlocality
- All quantum resources provide an advantage in exclusion tasks
- Unbounded sequence of observers exhibiting Einstein-Podolsky-Rosen steering
- Set coherence: basis-independent quantification of quantum coherence
- Universal steering inequalities
- Measurement incompatibility and steering are necessary and sufficient for operational contextuality
- Tight steering inequalities from generalized entropic uncertainty relations
- Semidefinite programming relaxations for quantum correlations
- Steering Bell-diagonal states
- Continuous variable steering and incompatibility via state-channel duality
- 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
- Adaptive strategy for joint measurements
- Quantum random access codes and incompatibility of measurements
- Einstein-Podolsky-Rosen steering: Its geometric quantification and witness
- The geometry of the Einstein--Podolsky--Rosen correlations
- Entanglement and superposition are equivalent concepts in any physical theory
- Leggett-Garg macrorealism and the quantum nondisturbance conditions
- Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems
- Temporal Steering in Four Dimensions with applications to coupled qubits and magnetoreception
- Hierarchy in temporal quantum correlations
- One-Shot Manipulation of Dynamical Quantum Resources
- Spatio-Temporal Steering for Testing Nonclassical Correlations in Quantum Networks
- Operational characterization of incompatibility of quantum channels with quantum state discrimination
- Incompatible quantum measurements admitting a local hidden variable model
- Randomness Certification from Multipartite Quantum Steering for Arbitrary Dimensional Systems
- Robust self-testing of steerable quantum assemblages and its applications on device-independent quantum certification
- Entropic uncertainty relations from quantum designs
- Steering-enhanced quantum metrology using superpositions of noisy phase shifts
- Unified picture for spatial, temporal and channel steering
- Quantum marginal problem and incompatibility
- Joint measurability of quantum effects and the matrix diamond
- Device-independent tests of structures of measurement incompatibility
- Measurement incompatibility and quantum advantage in communication
- Simultaneous Measurement of Two Quantum Observables: Compatibility, Broadcasting, and In-between
- Simulability of high-dimensional quantum measurements
- Some quantum measurements with three outcomes can reveal nonclassicality where all two-outcome measurements fail to do so
- Einstein-Podolsky-Rosen correlations and Bell correlations in the simplest scenario
- Certification of incompatible measurements using quantum steering
- Algorithmic construction of local models for entangled quantum states: optimization for two-qubit states
- Incompatibility in general probabilistic theories, generalized spectrahedra, and tensor norms
- Exploring the framework of assemblage moment matrices and its applications in device-independent characterizations
- Quantifying the incompatibility of quantum measurements relative to a basis
- Complete hierarchy for high-dimensional steering certification
- Conditions for the compatibility of channels in general probabilistic theory and their connection to steering and Bell nonlocality
- Device-independent quantification of measurement incompatibility
- Estimating Quantum Hamiltonians via Joint Measurements of Noisy Non-Commuting Observables
- Detecting genuine multipartite entanglement in steering scenarios
- Quantum Incompatibility of a Physical Context
- Robust genuine high-dimensional steering with many measurements
- Deep learning the hierarchy of steering measurement settings of qubit-pair states
- Unlimited One-Way Steering
- Compatibility of Generalized Noisy Qubit Measurements
- General Method for Classicality Certification in the Prepare and Measure Scenario
- Incompatibility as a resource for programmable quantum instruments
- Quantum measurement incompatibility in subspaces
- On the compatibility of quantum instruments
- Collision model approach to steering of an open driven qubit
- Characterizing and quantifying the incompatibility of quantum instruments
- Quantum Measurements in the Light of Quantum State Estimation
- Benchmarking Quantum State Transfer on Quantum Devices using Spatio-Temporal Steering
- Optimal joint measurements of complementary observables by a single trapped ion
- Necessary and sufficient condition for joint measurability
- Amount of quantum coherence needed for measurement incompatibility
- Measurement-device-independent and arbitrarily loss-tolerant verification of quantum steering
- Quantifying necessary quantum resources for nonlocality
- Thermodynamic Approach to Quantifying Incompatible Instruments
- Dynamics of incompatibility of quantum measurements in open systems
- Layers of classicality in the compatibility of measurements
- Necessary conditions for steerability of two qubits, from consideration of local operations
- Zero Uncertainty States in the Presence of Quantum Memory
- Distance-based resource quantification for sets of quantum measurements
- Equivalence between simulability of high-dimensional measurements and high-dimensional steering
- Necessary and sufficient conditions for multipartite Bell violations with only one trusted device
- Entropic uncertainty relations for multiple measurements assigned with biased weights
- Unveiling quantum steering by quantum-classical uncertainty complementarity
- On the pure state outcomes of Einstein-Podolsky-Rosen steering
- Uniform Quantification of Correlations for Bipartite Systems
- Incompatibility of local measurements provide advantage in local quantum state discrimination
- Quantum Resource Control for noisy EPR-steering with qubit measurements
- Single-particle entanglement gives rise to truly nonlocal effects like single-particle steering
- Quantum thermodynamic advantage in work extraction from steerable quantum correlations
- Adjusting inequalities for detection-loophole-free steering experiments
- Assemblages and steering in general probabilistic theories
- Interplay of nonlocality and incompatibility breaking qubit channels
- On the power of one pure steered state for EPR-steering with a pair of qubits
- Incompatibility probability of random quantum measurements
- Single-particle steering and nonlocality: The consecutive Stern-Gerlach Experiments
- All incompatible measurements on qubits lead to multiparticle Bell nonlocality
- Detecting the genuine multipartite two-way steerability with linear steering inequalities
- Maximal violation of steering inequalities and the matrix cube
- Constrained Measurement Incompatibility from Generalised Contextuality of Steered Preparation
- Constructing extremal compatible quantum observables by means of two mutually unbiased bases
- Naimark dilations of qubit POVMs and joint measurements
- N term pairwise correlation inequalities, steering and joint measurability
- Averaged fidelity-based steering criteria
- Measurement-device-independent verification of channel steering
- Diagnosing steerability of a bipartite state with the nonsteering threshold
- Revealing the quantitative relation between simultaneous correlations in complementary bases and quantum steering for two-qubit Bell diagonal states
- Binarisation of multi-outcome measurements in high-dimensional quantum correlation experiments
- Certifying measurement incompatibility in prepare-and-measure and Bell scenarios
- Necessary and Sufficient Condition for Randomness Certification from Incompatibility
- Experimentally determining the incompatibility of two qubit measurements
- Experimentally ruling out joint reality based on operational completeness
- Mirrored Entanglement Witnesses for Multipartite and High-Dimensional Quantum Systems
- A Fisher information-based incompatibility criterion for quantum channels
- Entanglement Cost for Steering Assemblages
- Optimal Fermionic Joint Measurements for Estimating Non-Commuting Majorana Observables
- A Note on Hierarchy of Quantum Measurement Incompatibilities
- Operational simultaneous correlations in complementary bases of bipartite states via one-sided semi-device-independent steering
- Measurement-device-independent measure of steerability and witnesses for all steerable resources
- Compressing continuous variable quantum measurements
- Resource theory of interactive quantum instruments
- An operational characterization of infinite-dimensional quantum resources
- Information leak and incompatibility of physical context: A modified approach
- Classifying Measurement Incompatibility under Classical Pre- and Post-Processing Operations
- Quantum steerability based on joint measurability
- Semi-device-independent certification of number of measurements
- Barycentric decomposition for quantum instruments
- Theory-Independent Context Incompatibility: Quantification and Experimental Demonstration
- Witness High-Dimensional Quantum Steering via Majorization Lattice
- A physical noise model for quantum measurements
- Operational Coherent Measurements with Steering and Randomness
- Protection of quantum steering ellipsoids in non-Markovian environments
- On compatibility of binary qubit measurements