Restricted numerical range: A versatile tool in the theory of quantum information

DOI10.1063/1.3496901zbMath1314.81045arXiv0905.3646OpenAlexW2015936613WikidataQ62582401 ScholiaQ62582401MaRDI QIDQ5253948

Łukasz Skowronek, Zbigniew Puchała, Jarosław Adam Miszczak, Karol Życzkowski, Piotr Gawron

Publication date: 5 June 2015

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0905.3646

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Quantum measurement theory, state operations, state preparations (81P15) Positive linear operators and order-bounded operators (47B65) Quantum coherence, entanglement, quantum correlations (81P40) Quantum information, communication, networks (quantum-theoretic aspects) (81P45) Quantum state estimation, approximate cloning (81P50)

Related Items (16)

Determination of locally perfect discrimination for two-qubit unitary operations ⋮ Numerical ranges of tensors ⋮ On the determinantal range of matrix products ⋮ Preservers of restricted unitary orbits of projections ⋮ Nuclear numerical range and quantum error correction codes for non-unitary noise models ⋮ An approach to constructing genuinely entangled subspaces of maximal dimension ⋮ Joint numerical ranges, quantum maps, and joint numerical shadows ⋮ Convex geometry of quantum resource quantification ⋮ Numerical range and compressions of the shift ⋮ On the \(C\)-determinantal range for special classes of matrices ⋮ Energy as an Entanglement Indicator ⋮ Geometry of the Set of Mixed Quantum States: An Apophatic Approach ⋮ Local Numerical Range for a Class of 2 ⊗ d Hermitian Operators ⋮ Kippenhahn's Theorem for Joint Numerical Ranges and Quantum States ⋮ Real numerical shadow and generalized B-splines ⋮ Joint separable numerical range and bipartite ultrafine entanglement witnessing

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Higher-rank numerical ranges and compression problems
• Protected subspaces in quantum information
• Completely positive linear maps on complex matrices
• The transition probability in the state space of a \(^*\)-algebra
• Exact Minkowski products of \(N\) complex disks
• A quantum computing primer for operator theorists
• Separability of mixed states: necessary and sufficient conditions.
• Quantum information theory and quantum statistics.
• Linear transformations which preserve trace and positive semidefiniteness of operators
• Cones of positive maps and their duality relations
• Characterization of distillability of entanglement in terms of positive maps
• Spectral properties of entanglement witnesses
• On the dimension of subspaces with bounded Schmidt rank
• The geometric measure of entanglement for a symmetric pure state with non-negative amplitudes
• GRADIENT FLOWS FOR OPTIMIZATION IN QUANTUM INFORMATION AND QUANTUM DYNAMICS: FOUNDATIONS AND APPLICATIONS
• Positive maps, positive polynomials and entanglement witnesses
• Matrix Analysis
• Some variations on the numerical range^†
• The numerical range and decomposable numerical range of matrices
• C-numerical ranges andC-numerical radii
• Concurrence in arbitrary dimensions
• Fidelity for Mixed Quantum States
• Minimal entropy of states emerging from noisy quantum channels
• Statistical properties of random density matrices
• Additivity for unital qubit channels
• Matrix permanent and quantum entanglement of permutation invariant states
• A family of norms with applications in quantum information theory
• A Few Steps More Towards NPT Bound Entanglement
• Research problems on numerical ranges in quantum computing
• Mixed-state entanglement and quantum error correction
• Geometry of Quantum States
• The Jamiołkowski Isomorphism and a Simplified Proof for the Correspondence Between Vectors Having Schmidt Number k and k-Positive Maps
• The significance of theC-numerical range and the localC-numerical range in quantum control and quantum information
• RelativeC-numerical ranges for applications in quantum control and quantum information
• Induced operators on symmetry classes of tensors
• A new concept for block operator matrices: The quadratic numerical range
• Minkowski geometric algebra of complex sets

This page was built for publication: Restricted numerical range: A versatile tool in the theory of quantum information