Hierarchy of Steering Criteria Based on Moments for All Bipartite Quantum Systems
arXiv:1507.04164 · doi:10.1103/PhysRevLett.115.210401
Abstract
Einstein-Podolsky-Rosen steering is a manifestation of quantum correlations exhibited by quantum systems, that allows for entanglement certification when one of the subsystems is not characterized. Detecting steerability of quantum states is essential to assess their suitability for quantum information protocols with partially trusted devices. We provide a hierarchy of sufficient conditions for the steerability of bipartite quantum states of any dimension, including continuous variable states. Previously known steering criteria are recovered as special cases of our approach. The proposed method allows us to derive optimal steering witnesses for arbitrary families of quantum states, and provides a systematic framework to analytically derive non-linear steering criteria. We discuss relevant examples and, in particular, provide an optimal steering witness for a lossy single-photon Bell state; the witness can be implemented just by linear optics and homodyne detection, and detects steering with a higher loss tolerance than any other known method. Our approach is readily applicable to multipartite steering detection and to the characterization of joint measurability.
5+4 pages; Close to published version. Comments are welcome
References in corpus (23)
- Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km
- Entanglement detection
- Device-independent security of quantum cryptography against collective attacks
- Steering, Entanglement, Nonlocality, and the EPR Paradox
- A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
- Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox
- Entanglement, EPR-correlations, Bell-nonlocality, and Steering
- Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
- Quantification of Gaussian quantum steering
- Observation of one-way 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
- Joint measurability of generalized measurements implies classicality
- Inequivalence of entanglement, steering, and Bell nonlocality for general measurements
- Detection of entanglement in asymmetric quantum networks and multipartite quantum steering
- Imperfect measurements settings: implications on quantum state tomography and entanglement witnesses
- Experimental Proof of Nonlocal Wavefunction Collapse for a Single Particle Using Homodyne Measurement
- Fine-grained EPR-steering inequalities
- Analog of the Clauser-Horne-Shimony-Holt inequality for steering
- Nonlocality of a single photon: paths to an EPR-steering experiment
- Loss-tolerant EPR steering for arbitrary dimensional states: joint measurability and unbounded violations under losses
- Einstein-Podolsky-Rosen steering measure for two-mode continuous variable states
- Stronger steerability criterion for more uncertain continuous variable systems
Cited by in corpus (73)
- Quantum Steering
- Quantum steering: a review with focus on semidefinite programming
- Bell nonlocality in networks
- Experimental quantification of asymmetric 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
- Natural Framework for Device-Independent Quantification of Quantum Steerability, Measurement Incompatibility, and Self-Testing
- Genuine high-dimensional quantum steering
- Steering criteria from general entropic uncertainty relations
- Exploration quantum steering, nonlocality and entanglement of two-qubit X-state in structured reservoirs
- Necessary and sufficient condition for steerability of two-qubit states by the geometry of steering outcomes
- Self-testing through EPR-steering
- Universal steering inequalities
- Network Quantum Steering
- Semidefinite programming relaxations for quantum correlations
- Steering Bell-diagonal states
- Continuous variable steering and incompatibility via state-channel duality
- Non-asymptotic entanglement distillation
- Efficient device-independent entanglement detection for multipartite systems
- Generating high-order quantum exceptional points in synthetic dimensions
- Multipartite steering inequalities based on entropic uncertainty relations
- Controlling Stationary One-Way Steering via Thermal Effects in Optomechanics
- Steerability detection of arbitrary 2-qubit state via machine learning
- Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems
- Non-separability and steerability of two-qubit states from the geometry of steering outcomes
- Einstein-Podolsky-Rosen Steering and Quantum Steering Ellipsoids: Optimal Two-Qubit States and Projective Measurements
- Nonadditivity of Rains' bound for distillable entanglement
- Shareability of Quantum Steering and its Relation with Entanglement
- Steering Criteria via Covariance Matrices of Local Observables in Arbitrary Dimensional Quantum Systems
- Experimental hierarchy and optimal robustness of quantum correlations of two-qubit states with controllable white noise
- Improving the bidirectional steerability between two accelerated partners via filtering process
- Semi-definite programming and quantum information
- Investigating Einstein-Podolsky-Rosen steering of continuous variable bipartite states by non-Gaussian pseudospin measurements
- How the relativistic motion affects Einstein-Podolsky-Rosen steering
- Uncertainty Relations for coarse-grained measurements: an overview
- Einstein-Podolsky-Rosen correlations and Bell correlations in the simplest scenario
- Simulability of high-dimensional quantum measurements
- Experimental certification of steering criterion based on general entropic uncertainty relation
- Signifying the nonlocality of NOON states using Einstein-Podolsky-Rosen steering inequalities
- EPR Steering inequalities with Communication Assistance
- Cost of Einstein-Podolsky-Rosen steering in the context of extremal boxes
- Exploring the framework of assemblage moment matrices and its applications in device-independent characterizations
- Einstein-Podolsky-Rosen steering based on semi-supervised machine learning
- Detected the steerability bounds of the generalized Werner states via BackPropagation neural network
- Experimental hierarchy of two-qubit quantum correlations without state tomography
- Einstein-Podolsky-Rosen Steering Criterion and Monogamy Relation via Correlation Matrices in Tripartite Systems
- Nonclassical steering and the Gaussian steering triangoloids
- Detecting Einstein-Podolsky-Rosen steering in non-Gaussian spin states from conditional spin-squeezing parameters
- Broadband complex two-mode quadratures for quantum optics
- Experimental detection of steerability in Bell local states with two measurement settings
- Homodyne detection of non-Gaussian quantum steering
- Recovering the lost steerability of quantum states within non-Markovian environments by utilizing quantum partially collapsing measurements
- Necessary and sufficient conditions for multipartite Bell violations with only one trusted device
- Equivalence between simulability of high-dimensional measurements and high-dimensional steering
- Detecting quantum steering in networks
- Certifying steady-state properties of open quantum systems
- Quantum Resource Control for noisy EPR-steering with qubit measurements
- Quantum thermodynamic advantage in work extraction from steerable quantum correlations
- Einstein-Podolsky-Rosen uncertainty limits for bipartite multimode states
- Detecting the genuine multipartite two-way steerability with linear steering inequalities
- On Quantum Steering and Wigner Negativity
- Detecting Tripartite Steering via Quantum Entanglement
- Distributing long-distance trust in optomechanics
- Quantum entanglement in phase space
- Quantifying Quantum Steering with Limited Resources: A Semi-supervised Machine Learning Approach
- Diagnosing steerability of a bipartite state with the nonsteering threshold
- Averaged fidelity-based steering criteria
- Compressing continuous variable quantum measurements
- Entanglement Cost for Steering Assemblages
- Parameterized steering criteria via correlation matrices
- Protection of quantum steering ellipsoids in non-Markovian environments
- Demonstration that Einstein-Podolsky-Rosen steering requires more than one bit of faster-than-light information transmission