Absolutely $k$-Incoherent Quantum States and Spectral Inequalities for Factor Width of a Matrix

Abstract

We investigate the set of quantum states that can be shown to be $k$-incoherent based only on their eigenvalues (equivalently, we explore which Hermitian matrices can be shown to have small factor width based only on their eigenvalues). In analogy with the absolute separability problem in quantum resource theory, we call these states "absolutely $k$-incoherent", and we derive several necessary and sufficient conditions for membership in this set. We obtain many of our results by making use of recent results concerning hyperbolicity cones associated with elementary symmetric polynomials.

arXiv comment21 pages, 2 figures

References in corpus (29)

• Quantum Resource Theories
• Measuring Quantum Coherence with Entanglement
• Bell Inequalities and the Separability Criterion
• Entanglement monotones
• Robustness of coherence: An operational and observable measure of quantum coherence
• Direct estimations of linear and non-linear functionals of a quantum state
• Universal Quantum Estimator
• Witnessing Quantum Coherence: from solid-state to biological systems
• Largest separable balls around the maximally mixed bipartite quantum state
• Maximally entangled mixed states of two qubits
• Geometry of entangled states
• A quantitative theory of coherent delocalization
• All entangled states are useful for channel discrimination
• Efficient and coherent excitation transfer across disordered molecular networks
• One-Shot Operational Quantum Resource Theory
• On the dimension of subspaces with bounded Schmidt rank
• Certification and Quantification of Multilevel Quantum Coherence
• Experimental progress on quantum coherence: detection, quantification, and manipulation
• Separability from Spectrum for Qubit-Qudit States
• PPT from spectra
• Contrast in Multipath Interference and Quantum Coherence
• Detecting coherence via spectrum estimation
• Determining eigenvalues of a density matrix with minimal information in a single experimental setting
• Circulants and critical points of polynomials
• Positive reduction from spectra
• Polynomial-sized Semidefinite Representations of Derivative Relaxations of Spectrahedral Cones
• Spectral Properties of Symmetric Quantum States and Symmetric Entanglement Witnesses
• Deterministic transformations of multilevel coherent states under incoherence-preserving operations
• Modern compressive tomography for quantum information science

Cited by in corpus (4)

• Tight bounds for antidistinguishability and circulant sets of pure quantum states
• Coherence and Imaginarity as Resources in Quantum Circuit Complexity
• Quantum channels and some absolute properties of quantum states
• The Factor Width Rank of a Matrix