Quantification of Einstein-Podolski-Rosen steering for two-qubit states

Abstract

In the last few years, several criteria to identify Eistein-Podolski-Rosen steering have been proposed and experimentally implemented. On the operational side, however, the evaluation of the steerability degree of a given state has shown to be a difficult task and only a few results are known. In this work, we propose a measure of steering that is based on the maximal violation of well established steering inequalities. Applying this approach to two-qubit states, we managed to derive simple closed formulas for steering in the two- and three-measurement scenarios. Among the options investigated, a measure has been found that correctly satisfies the entanglement-steering-nonlocality hierarchy and reproduces results reported so far.

5 pages, published version

References in corpus (11)

• Steering, Entanglement, Nonlocality, and the EPR Paradox
• 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
• Joint measurability of generalized measurements implies classicality
• Analog of the Clauser-Horne-Shimony-Holt inequality for steering
• Geometric Bell-like inequalities for steering
• Relations between entanglement, Bell-inequality violation and teleportation fidelity for the two-qubit X states
• Quantifying the nonlocality of GHZ quantum correlations by a bounded communication simulation protocol

Cited by in corpus (87)

• Quantum Steering
• Multipartite Gaussian steering: monogamy constraints and quantum cryptography applications
• Hierarchy of the nonlocal advantage of quantum coherence and Bell nonlocality
• Demonstration of Einstein-Podolsky-Rosen Steering with Enhanced Subchannel Discrimination
• Steering criteria from general entropic uncertainty relations
• Steering a single system sequentially by multiple observers
• Steering Bell-diagonal states
• Experimental demonstration of measurement-device-independent measure of quantum steering
• All two-qubit states that are steerable via Clauser-Horne-Shimony-Holt-type correlations are Bell nonlocal
• Experimental investigation of nonlocal advantage of quantum coherence
• Einstein-Podolsky-Rosen steering: Its geometric quantification and witness
• Quantum steerability: characterization, quantification, superactivation and unbounded amplification
• Anisotropic invariance and the distribution of quantum correlations
• Complementarity Relations Between Quantum Steering Criteria
• Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems
• Nonanomalous measure of realism-based nonlocality
• Temporal Steering in Four Dimensions with applications to coupled qubits and magnetoreception
• The influence of Unruh effect on quantum steering for accelerated two-level detectors with different measurements
• Detecting Einstein-Podolsky-Rosen steering through entanglement detection
• Demonstrating shareability of multipartite Einstein-Podolsky-Rosen steering
• Spatio-Temporal Steering for Testing Nonclassical Correlations in Quantum Networks
• Nonlocality, quantum correlations, and violations of classical realism in the dynamics of two noninteracting quantum walkers
• Shareability of Quantum Steering and its Relation with Entanglement
• Quantum battery in the Heisenberg spin chain models with Dzyaloshinskii-Moriya interaction
• Complementary relations of entanglement, coherence, steering and Bell nonlocality inequality violation in three-qubit states
• Experimental hierarchy and optimal robustness of quantum correlations of two-qubit states with controllable white noise
• Unification of quantum resources in tripartite systems
• Nonlocal Advantages of Quantum Imaginarity
• A Study on Thermal Quantum Resources and Probabilistic Teleportation in Spin-1/2 Heisenberg XYZ+DM+KSEA Model under Variable Zeeman Splitting
• Quantum Correlation Sharing: A Review On Recent Progress From Nonlocality To Other Non-Classical Correlations
• Hierarchy of quantum correlations under non-Markovian dynamics
• Experimental certification of steering criterion based on general entropic uncertainty relation
• Einstein-Podolsky-Rosen correlations and Bell correlations in the simplest scenario
• Constraint relation between steerability and concurrence for two-qubit states
• Experimental hierarchy of two-qubit quantum correlations without state tomography
• Dynamics and recovery of genuine multipartite Einstein-Podolsky-Rosen steering and genuine multipartite nonlocality for a dissipative Dirac system via Unruh effect
• Geometric Steering Criterion for Two-qubit States
• Deep learning the hierarchy of steering measurement settings of qubit-pair states
• Weak quantum discord
• Absolute Non-Violation of a Three-Setting Steering Inequality by Two-Qubit States
• Collision model approach to steering of an open driven qubit
• Quantum steering as a witness of quantum scrambling
• Preparing tunable Bell-diagonal states on a quantum computer
• Creating quantum correlations in generalized entanglement swapping
• Improvement in quantum communication using quantum switch
• Does conditional entropy squeezing indicate normalized entropic uncertainty relation steering?
• On the pure state outcomes of Einstein-Podolsky-Rosen steering
• Fortran code for generating random probability vectors, unitaries, and quantum states
• Experimental hierarchy of the nonclassicality of single-qubit states via potentials for entanglement, steering, and Bell nonlocality
• Uniform Quantification of Correlations for Bipartite Systems
• Necessary and sufficient conditions for multipartite Bell violations with only one trusted device
• Protecting quantum correlations of negative quantum states using weak measurement under non-Markovian noise
• Single-particle entanglement gives rise to truly nonlocal effects like single-particle steering
• Quantum steering and quantum discord under noisy channels and entanglement swapping
• Detecting EPR steering via two classes of local measurements
• Detecting the genuine multipartite two-way steerability with linear steering inequalities
• Sharing EPR steering between sequential pairs of observers
• Emergence of maximal hidden quantum correlations and its trade-off with the filtering probability in dissipative two-qubit systems
• Quantum conditional entropies and steerability of states with maximally mixed marginals
• Note on Product-Form Monogamy Relations for Nonlocality and Other Correlation Measures
• Analysis of Quantum Steering Measures
• Role of maximally entangled states in the context of linear steering inequalities
• Diagnosing steerability of a bipartite state with the nonsteering threshold
• Averaged fidelity-based steering criteria
• Certifying quantumness beyond steering and nonlocality and its implications on quantum information processing
• Characterizing scalable measures of quantum resources
• Revealing the quantitative relation between simultaneous correlations in complementary bases and quantum steering for two-qubit Bell diagonal states
• Hidden Steering Nonlocality in Quantum Networks
• Several Trade off Features of Quantum Steering in Distributed Scenario
• Trust-free verification of steering: why you can't cheat a quantum referee
• Locally inaccessible hidden quantum correlations
• Secure One-Sided Device-Independent Quantum Key Distribution Under Collective Attacks with Enhanced Robustness
• Decoherence of Dirac-particle quantumness for fermionic fields in a dilatonic black hole
• Steering in Neutrino Oscillations with Non-Standard Interaction
• Measurement-device-independent measure of steerability and witnesses for all steerable resources
• Swapping of quantum correlations and the role of local filtering operations
• Role of Steering Inequality In Quantum Key Distribution Protocol
• Operational simultaneous correlations in complementary bases of bipartite states via one-sided semi-device-independent steering
• From top quarks to enhanced quantum key distribution: A Framework for Optimal Predictability of Quantum Observables
• Asymmetric steerability of quantum equilibrium and nonequilibrium steady states through entanglement detection
• Quantum direct cause across the Cherenkov threshold in circuit QED
• Certifying classes of $d$-outcome measurements with quantum steering
• Experimental demonstration of complementarity relations between quantum steering criteria
• Quantum correlations and coherence in a two-qubit anisotropic $XY$ under magnetic field
• Tripartite entanglement and tripartite steering in three-qubit pure states induced by vacuum--one-photon superpositions
• Broadcasting of non-locality
• Necessary and sufficient criterion of steering for two-qubit T states