Joint measurability of quantum effects and the matrix diamond
arXiv:1807.01508 · doi:10.1063/1.5049125
Abstract
In this work, we investigate the joint measurability of quantum effects and connect it to the study of free spectrahedra. Free spectrahedra typically arise as matricial relaxations of linear matrix inequalities. An example of a free spectrahedron is the matrix diamond, which is a matricial relaxation of the -ball. We find that joint measurability of binary POVMs is equivalent to the inclusion of the matrix diamond into the free spectrahedron defined by the effects under study. This connection allows us to use results about inclusion constants from free spectrahedra to quantify the degree of incompatibility of quantum measurements. In particular, we completely characterize the case in which the dimension is exponential in the number of measurements. Conversely, we use techniques from quantum information theory to obtain new results on spectrahedral inclusion for the matrix diamond.
arXiv comment28 pages, 4 figures. v3: minor revisions
References in corpus (30)
- Bell nonlocality
- On mutually unbiased bases
- Optimal Cloning of Pure States
- Fundamentals of Quantum Information Theory
- SIC-POVMs: A new computer study
- An Invitation to Quantum Incompatibility
- Joint measurability of generalized measurements implies classicality
- Measurements incompatible in Quantum Theory cannot be measured jointly in any other local theory
- One-to-one mapping between steering and joint measurability problems
- Asymmetric quantum cloning machines in any dimension
- Constructing exact symmetric informationally complete measurements from numerical solutions
- Noise Robustness of the Incompatibility of Quantum Measurements
- Comparing the degrees of incompatibility inherent in probabilistic physical theories
- Quantum measurement incompatibility does not imply Bell nonlocality
- Multipartite Asymmetric Quantum Cloning
- Measurement incompatibility does not give rise to Bell violation in general
- Universal steering inequalities
- The matricial relaxation of a linear matrix inequality
- Dilations, inclusions of matrix convex sets, and completely positive maps
- Information complementarity: A new paradigm for decoding quantum incompatibility
- Extending quantum operations
- Maximally incompatible quantum observables
- Minimal and maximal matrix convex sets
- Approximate joint measurement of qubit observables through an Arthur-Kelly type model
- Estimating the expectation values of spin 1/2 observables with finite resources
- Free Convex Algebraic Geometry
- Group representation approach to 1 - N universal quantum cloning machines
- Compatibility for Probabilistic Theories
- Interpolation for completely positive maps: numerical solutions
- Universal Asymmetric Quantum Cloning Revisited
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- Incompatibility robustness of quantum measurements: a unified framework
- Incompatibility in general probabilistic theories, generalized spectrahedra, and tensor norms
- Quantum measurement incompatibility in subspaces
- Compatibility of quantum measurements and inclusion constants for the matrix jewel
- Order preserving maps on quantum measurements
- Dilations of -commuting unitaries
- Incompatibility probability of random quantum measurements
- The compatibility dimension of quantum measurements
- Separability for mixed states with operator Schmidt rank two
- Noncommutative polynomials describing convex sets
- All incompatible measurements on qubits lead to multiparticle Bell nonlocality
- Maximal violation of steering inequalities and the matrix cube
- Quantum Information Theory and Free Semialgebraic Geometry: One Wonderland Through Two Looking Glasses
- Measurement incompatibility vs. Bell non-locality: an approach via tensor norms
- A tensor norm approach to quantum compatibility
- Dilations of unitary tuples
- Magic squares: Latin, Semiclassical and Quantum
- A Fisher information-based incompatibility criterion for quantum channels
- Extreme points of matrix convex sets and their spanning properties
- Optimal Fermionic Joint Measurements for Estimating Non-Commuting Majorana Observables
- Matrix Extreme Points and Free extreme points of Free spectrahedra
- Polytope compatibility -- from quantum measurements to magic squares
- On compatibility of binary qubit measurements
- A physical noise model for quantum measurements