Locally inaccessible hidden quantum correlations

Abstract

We prove, modulo a conjecture on quantum steering ellipsoids being true, the existence of the phenomenon of locally inaccessible hidden quantum correlations. That is, the existence of two-particle states whose hidden quantum correlations cannot be revealed by local filters implemented exclusively on one side of the experiment, but that can still be revealed when both parties cooperate in applying judiciously chosen local filters. The quantum correlations here considered are the violation of the CHSH-inequality for Bell-nonlocality and the violation of the ${\mathrm{F}}_3$-inequality for EPR-steering. Specifically, we provide a necessary criterion for guaranteeing the presence of such phenomenon for arbitrary two-qubit states. This criterion in turn relies on the conjecture that the maximal violation of CHSH-inequality and ${\mathrm{F}}_3$-inequality are both upper bounded by functions that depend on the magnitude of the quantum steering ellipsoid centre. This latter conjecture, although currently lacking an analytical proof, is supported by numerical results. We use this necessary criterion to explicitly show examples of two-qubit states with locally inaccessible hidden quantum correlations and, furthermore, two-qubit states with locally inaccessible maximal hidden quantum correlations.

9 pages, 4 figures

References in corpus (34)

• Separability Criterion for Density Matrices
• Bell nonlocality
• Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox
• Quantum Steering
• Quantum steering: a review with focus on semidefinite programming
• Bell's inequalities and density matrices. Revealing hidden nonlocality.
• Measures and applications of quantum correlations
• Inequivalence of entanglement, steering, and Bell nonlocality for general measurements
• Entanglement versus Bell violations and their behaviour under local filtering operations
• Local filtering operations on two qubits
• Quantum Steering Ellipsoids
• Quantification of Einstein-Podolski-Rosen steering for two-qubit states
• Genuine hidden quantum nonlocality
• Maximally entangled mixed states: Creation and concentration
• Sufficient criterion for guaranteeing that a two-qubit state is unsteerable
• Purifying noisy entanglement requires collective measurements
• Entangled Mixed States and Local Purification
• General method for constructing local-hidden-variable models for entangled quantum states
• Algorithmic construction of local hidden variable models for entangled quantum states
• Optimal Entanglement Enhancement for Mixed States
• Entanglement without hidden nonlocality
• Experimental Entanglement Distillation of Two-qubit Mixed States Under Local filtering Operations
• Complete classification of steerability under local filters and its relation with measurement incompatibility
• Einstein-Podolsky-Rosen steering: Its geometric quantification and witness
• Tuning quantum channels to maximize polarization entanglement for telecom photon pairs
• Quantum correlations of two-qubit states with one maximally mixed marginal
• Revealing of hidden quantum steerability using local filtering operations
• Nonlocality tests enhanced by a third observer
• Einstein-Podolsky-Rosen Steering and Quantum Steering Ellipsoids: Optimal Two-Qubit States and Projective Measurements
• Nonlocal quantum correlations under amplitude damping decoherence
• Activating Hidden Teleportation Power: Theory and Experiment
• Algorithmic construction of local models for entangled quantum states: optimization for two-qubit states
• Emergence of maximal hidden quantum correlations and its trade-off with the filtering probability in dissipative two-qubit systems
• Hidden Steering Nonlocality in Quantum Networks