Analog of the Clauser-Horne-Shimony-Holt inequality for steering

Abstract

The Clauser-Horne-Shimony-Holt (CHSH) inequality (and its permutations), are necessary and sufficient criteria for Bell nonlocality in the simplest Bell-nonlocality scenario: 2 parties, 2 measurements per party and 2 outcomes per measurement. Here we derive an inequality for EPR-steering that is an analogue of the CHSH, in that it is necessary and sufficient in this same scenario. However, since in the case of steering the device at Bob's site must be specified (as opposed to the Bell case in which it is a black box), the scenario we consider is that where Alice performs two (black-box) dichotomic measurements, and Bob performs two mutually unbiased qubit measurements. We show that this inequality is strictly weaker than the CHSH, as expected, and use it to decide whether a recent experiment [Phys. Rev. Lett. 110, 130401 (2013).] involving a single-photon split between two parties has demonstrated EPR-steering.

arXiv commentExpanded v2, new results, new figure. 9 pages, 2 figures

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Cited by in corpus (61)

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• Quantum steering: a review with focus on semidefinite programming
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• Hierarchy of Steering Criteria Based on Moments for All Bipartite Quantum Systems
• Steering a single system sequentially by multiple observers
• Steering criteria from general entropic uncertainty relations
• Sharing of Non-Local Advantage of Quantum Coherence by sequential observers
• Experimental Measurement-Device-Independent Quantum Steering and Randomness Generation Beyond Qubits
• All two-qubit states that are steerable via Clauser-Horne-Shimony-Holt-type correlations are Bell nonlocal
• Genuine Einstein-Podolsky-Rosen steering of three-qubit states by multiple sequential observers
• Anisotropic invariance and the distribution of quantum correlations
• Steerability detection of arbitrary 2-qubit state via machine learning
• Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems
• One-sided Device-independent Self-testing of any Pure Two-qubit Entangled State
• Detecting Einstein-Podolsky-Rosen steering through entanglement detection
• Shareability of Quantum Steering and its Relation with Entanglement
• Steering Criteria via Covariance Matrices of Local Observables in Arbitrary Dimensional Quantum Systems
• Improving the bidirectional steerability between two accelerated partners via filtering process
• Experimental hierarchy and optimal robustness of quantum correlations of two-qubit states with controllable white noise
• Nonlocality, steering and quantum state tomography in a single experiment
• How the relativistic motion affects Einstein-Podolsky-Rosen steering
• Tighter Einstein-Podolsky-Rosen steering inequality based on the sum uncertainty relation
• Quantum Correlation Sharing: A Review On Recent Progress From Nonlocality To Other Non-Classical Correlations
• Einstein-Podolsky-Rosen correlations and Bell correlations in the simplest scenario
• Robust Semi-Device Independent Certification of All Pure Bipartite Maximally Entangled States via Quantum Steering
• Cost of Einstein-Podolsky-Rosen steering in the context of extremal boxes
• Detected the steerability bounds of the generalized Werner states via BackPropagation neural network
• 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
• Einstein-Podolsky-Rosen Steering Criterion and Monogamy Relation via Correlation Matrices in Tripartite Systems
• Eavesdropping a Quantum Key Distribution network using sequential quantum unsharp measurement attacks
• Preparing tunable Bell-diagonal states on a quantum computer
• Operational characterization of quantumness of unsteerable bipartite states
• Reference frame independent Einstein-Podolsky-Rosen steering
• Experimental detection of steerability in Bell local states with two measurement settings
• Recovering the lost steerability of quantum states within non-Markovian environments by utilizing quantum partially collapsing measurements
• Does conditional entropy squeezing indicate normalized entropic uncertainty relation steering?
• Shareability of steering in 2-producible states
• Optimal quantum violation of Clauser-Horne-Shimony-Holt like steering inequality
• Protecting quantum correlations in presence of generalised amplitude damping channel: the two-qubit case
• Necessary and sufficient conditions for multipartite Bell violations with only one trusted device
• Detecting quantum steering in networks
• On the power of one pure steered state for EPR-steering with a pair of qubits
• Measuring network quantum steerability utilizing artificial neural networks
• Single-particle entanglement gives rise to truly nonlocal effects like single-particle steering
• Detecting EPR steering via two classes of local measurements
• Characterizing quantum correlations in the nonsignaling framework
• Detecting the genuine multipartite two-way steerability with linear steering inequalities
• Role of maximally entangled states in the context of linear steering inequalities
• Quantum steering as a probe of energy transfer in quantum batteries
• Characterization of the quantumness of unsteerable tripartite correlations
• Diagnosing steerability of a bipartite state with the nonsteering threshold
• Averaged fidelity-based steering criteria
• Several Trade off Features of Quantum Steering in Distributed Scenario
• Robust one-sided self-testing of two-qubit states via quantum steering
• Bell correlations between momentum-entangled pairs of ${}^4{\text{He}}^{\ast }$ atoms
• Parameterized steering criteria via correlation matrices
• Imprecise quantum steering inequalities in tripartite systems
• Correcting for finite statistics effects in a quantum steering experiment
• Demonstration that Einstein-Podolsky-Rosen steering requires more than one bit of faster-than-light information transmission