Einstein-Podolsky-Rosen steering: Its geometric quantification and witness

Abstract

We propose a measure of quantum steerability, namely a convex steering monotone, based on the trace distance between a given assemblage and its corresponding closest assemblage admitting a local-hidden-state (LHS) model. We provide methods to estimate such a quantity, via lower and upper bounds, based on semidefinite programming. One of these upper bounds has a clear geometrical interpretation as a linear function of rescaled Euclidean distances in the Bloch sphere between the normalized quantum states of: (i) a given assemblage and (ii) an LHS assemblage. For a qubit-qubit quantum state, the above ideas also allow us to visualize various steerability properties of the state in the Bloch sphere via the so-called LHS surface. In particular, some steerability properties can be obtained by comparing such an LHS surface with a corresponding quantum steering ellipsoid. Thus, we propose a witness of steerability corresponding to the difference of the volumes enclosed by these two surfaces. This witness (which reveals the steerability of a quantum state) enables finding an optimal measurement basis, which can then be used to determine the proposed steering monotone (which describes the steerability of an assemblage) optimized over all mutually-unbiased bases.

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• Quantum Steering
• 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
• Robust self-testing of steerable quantum assemblages and its applications on device-independent quantum certification
• Nonlocality, quantum correlations, and violations of classical realism in the dynamics of two noninteracting quantum walkers
• Experimental hierarchy and optimal robustness of quantum correlations of two-qubit states with controllable white noise
• Exploring the framework of assemblage moment matrices and its applications in device-independent characterizations
• Deep learning the hierarchy of steering measurement settings of qubit-pair states
• Thermodynamic Approach to Quantifying Incompatible Instruments
• Unveiling quantum steering by quantum-classical uncertainty complementarity
• Distance-based resource quantification for sets of quantum measurements
• Distributed quantum incompatibility
• Accelerating multipartite entanglement generation in non-Hermitian superconducting qubits
• Measuring network quantum steerability utilizing artificial neural networks
• Role of maximally entangled states in the context of linear steering inequalities
• Maximal violation of steering inequalities and the matrix cube
• Entanglement balance of quantum $(e,2e)$ scattering processes
• Quantifying Quantum Steering with Limited Resources: A Semi-supervised Machine Learning Approach
• Locally inaccessible hidden quantum correlations
• 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
• Comparing coherence measures for X states: Can quantum states be ordered based on quantum coherence?
• Operational Coherent Measurements with Steering and Randomness
• Protection of quantum steering ellipsoids in non-Markovian environments
• Asymmetric steerability of quantum equilibrium and nonequilibrium steady states through entanglement detection