Operational simultaneous correlations in complementary bases of bipartite states via one-sided semi-device-independent steering
arXiv:2407.11755 · doi:10.1103/PhysRevA.111.062403
Abstract
Recently, a different form of quantum steering, i.e., certification of quantum steering in a one-sided semi-device-independent way, has been formulated [Jebarathinam \etal Phys. Rev. A 108, 042211 (2023)]. In this work, we use this phenomenon to provide operational simultaneous correlations in mutually unbiased bases as quantified by the measures in [Wu \etal Scientific Reports 4, 4036 (2014)]. First, we show that for any bipartite state, such measure of simultaneous correlations in two mutually unbiased bases can be operationally identified as exhibiting one-sided semi-device-independent steering in a two-setting scenario. Next, we demonstrate that for two-qubit Bell-diagonal states, quantifying one-sided semi-device-independent steerability provides an operational quantification of information-theoretic quantification of simultaneous correlations in mutually unbiased bases. Then, we provide a different classification of two-qubit separable states with the above-mentioned information-theoretic quantification of simultaneous correlations in mutually unbiased bases and the quantification of one-sided semi-device-independent steerability. Finally, we invoke quantum steering ellipsoid formalism to shed intuitions on the operational characterization of simultaneous correlations in complementary bases of two-qubit states via one-sided semi-device-independent steerability. This provides us with a geometric visualization of the results.
14 pages, 5 figures. Accepted in PRA
References in corpus (44)
- Introducing Quantum Discord
- Quantifying Coherence
- Classical, quantum and total correlations
- Quantum Coherence as a Resource
- Steering, Entanglement, Nonlocality, and the EPR Paradox
- Necessary and sufficient condition for non-zero quantum discord
- Measuring Quantum Coherence with Entanglement
- One-sided Device-Independent Quantum Key Distribution: Security, feasibility, and the connection with steering
- On the quantum, classical and total amount of correlations in a quantum state
- Quantum discord as resource for remote state preparation
- Frozen Quantum Coherence
- Quantum coherence in multipartite systems
- Quantifying Einstein-Podolsky-Rosen steering
- Behavior of Quantum Correlations under Local Noise
- Quantum Steering Ellipsoids
- Quantification of Einstein-Podolski-Rosen steering for two-qubit states
- One-to-one mapping between steering and joint measurability problems
- A Unified View of Quantum Correlations and Quantum Coherence
- The resource theory of steering
- Quantum processes which do not use coherence
- Optimal randomness certification in the quantum steering and prepare-and-measure scenarios
- Mutually unbiased bases and symmetric informationally complete measurements in Bell experiments
- On the optimal measurement for quantum discord of two-qubit states
- Quantum discord of two-qubit rank-two states
- Quantum discord and remote state preparation
- Volume monogamy of quantum steering ellipsoids for multi-qubit systems
- Correlations in quantum states and the local creation of quantum discord
- Complete classification of steerability under local filters and its relation with measurement incompatibility
- Einstein-Podolsky-Rosen steering: Its geometric quantification and witness
- Discordlike correlation of bipartite coherence
- Reveal quantum correlation in complementary bases
- Self-testing of any pure entangled state with minimal number of measurements and optimal randomness certification in one-sided device-independent scenario
- Quantum correlation exists in any non-product state
- Cost of Einstein-Podolsky-Rosen steering in the context of extremal boxes
- Deep learning the hierarchy of steering measurement settings of qubit-pair states
- Classical extension of quantum-correlated separable states
- Quantum steering as a witness of quantum scrambling
- Operational characterization of quantumness of unsteerable bipartite states
- Superunsteerability as a quantifiable resource for random access codes assisted by Bell-diagonal states
- Unveiling quantum steering by quantum-classical uncertainty complementarity
- Characterization of the quantumness of unsteerable tripartite correlations
- Asymmetric One-Sided Semi-Device-Independent Steerability of Quantum Discordant States
- Certifying quantumness beyond steering and nonlocality and its implications on quantum information processing
- Revealing the quantitative relation between simultaneous correlations in complementary bases and quantum steering for two-qubit Bell diagonal states