Maximal violation of steering inequalities and the matrix cube
arXiv:2105.11302 · doi:10.22331/q-2022-02-21-656
Abstract
In this work, we characterize the amount of steerability present in quantum theory by connecting the maximal violation of a steering inequality to an inclusion problem of free spectrahedra. In particular, we show that the maximal violation of an arbitrary unbiased dichotomic steering inequality is given by the inclusion constants of the matrix cube, which is a well-studied object in convex optimization theory. This allows us to find new upper bounds on the maximal violation of steering inequalities and to show that previously obtained violations are optimal. In order to do this, we prove lower bounds on the inclusion constants of the complex matrix cube, which might be of independent interest. Finally, we show that the inclusion constants of the matrix cube and the matrix diamond are the same. This allows us to derive new bounds on the amount of incompatibility available in dichotomic quantum measurements in fixed dimension.
arXiv commentFinal version: 30 pages, 2 figures
References in corpus (35)
- Steering, Entanglement, Nonlocality, and the EPR Paradox
- One-sided Device-Independent Quantum Key Distribution: Security, feasibility, and the connection with steering
- Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox
- Quantum Steering
- Entanglement, EPR-correlations, Bell-nonlocality, and Steering
- Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
- Quantum steering: a review with focus on semidefinite programming
- Experimental EPR-Steering of Bell-local States
- Quantifying Einstein-Podolsky-Rosen steering
- Testing the Hilbert space dimension
- Joint Measurability, Einstein-Podolsky-Rosen Steering, and Bell Nonlocality
- Genuine multipartite Einstein-Podolsky-Rosen steering
- An Invitation to Quantum Incompatibility
- Joint measurability of generalized measurements implies classicality
- One-to-one mapping between steering and joint measurability problems
- Negativity and steering: a stronger Peres conjecture
- Quantatitive relations between measurement incompatibility, quantum steering, and nonlocality
- Genuine high-dimensional quantum steering
- Comparing the degrees of incompatibility inherent in probabilistic physical theories
- Unbounded violation of quantum steering inequalities
- Witnessing irreducible dimension
- The matricial relaxation of a linear matrix inequality
- Dilations, inclusions of matrix convex sets, and completely positive maps
- Optimal Measurements for Tests of EPR-Steering with No Detection Loophole using Two-Qubit Werner States
- Most incompatible measurements for robust steering tests
- Loss-tolerant EPR steering for arbitrary dimensional states: joint measurability and unbounded violations under losses
- Einstein-Podolsky-Rosen steering: Its geometric quantification and witness
- Quantum steerability: characterization, quantification, superactivation and unbounded amplification
- Minimal and maximal matrix convex sets
- Conditions on the existence of maximally incompatible two-outcome measurements in General Probabilistic Theory
- Incompatible measurements in a class of general probabilistic theories
- Quantum steering inequality with tolerance for measurement-setting-errors: experimentally feasible signature of unbounded violation
- Joint measurability of quantum effects and the matrix diamond
- Incompatibility in general probabilistic theories, generalized spectrahedra, and tensor norms
- Compatibility of quantum measurements and inclusion constants for the matrix jewel