Measures of imaginarity and quantum state order

Abstract

Complex numbers are widely used in both classical and quantum physics, and play an important role in describing quantum systems and their dynamical behavior. In this paper we study several measures of imaginarity of quantum states in the framework of resource theory, such as the measures based on $l_1$ norm, and convex function, etc. We also investigate the influence of the quantum channels on quantum state order for a single-qubit.

arXiv comment11 pages

References in corpus (33)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Quantum secret sharing
• Quantifying Coherence
• Theoretical efficient high capacity Quantum Key Distribution Scheme
• Quantum Resource Theories
• Operational Resource Theory of Coherence
• The role of quantum information in thermodynamics --- a topical review
• Intrinsic randomness as a measure of quantum coherence
• The general structure of quantum resource theories
• Secure direct communication using Einstein-Podolsky-Rosen pairs and teleportation
• Making the decoy-state measurement-device-independent quantum key distribution practically useful
• Measuring the quality of a quantum reference frame: the relative entropy of frameness
• Deterministic secure direct communication using GHZ states and swapping quantum entanglement
• Quantifying entanglement resources
• Operational Resource Theory of Imaginarity
• Security proof for cryptographic protocols based only on the monogamy of Bell's inequality violations
• Universally-composable privacy amplification from causality constraints
• A resource theory of superposition
• Quantifying the Imaginarity of Quantum Mechanics
• Optimal Controlled Teleportation
• Resource theory of imaginarity: Quantification and state conversion
• On nonlocality as a resource theory and nonlocality measures
• On the permutationally invariant part of a density matrix and nonseparability of N-qubit states
• Measure of multipartite entanglement with computable lower bounds
• Quantum correlations and distinguishability of quantum states
• Real-Vector-Space Quantum Theory with a Universal Quantum Bit
• Detection of genuinely entangled and non-separable $n$-partite quantum states
• Generalized decoding, effective channels, and simplified security proofs in quantum key distribution
• Ordering states with coherence measures
• Quantum secret sharing between m-party and n-party with six states
• Maximum Relative Entropy of Coherence for Quantum Channels
• Deterministic transformations of multilevel coherent states under incoherence-preserving operations
• Dynamics of coherence-induced state ordering under Markovian channels

Cited by in corpus (13)

• Resource Theory of Imaginarity: New Distributed Scenarios
• Nonlocal Advantages of Quantum Imaginarity
• Quantifying imaginarity in terms of pure-state imaginarity
• Imaginarity of quantum channels: Refinement and Alternative
• Geometric-Like imaginarity: quantification and state conversion
• Two imaginarity monotones induced by unified $(\alpha ,\beta )$-relative entropy
• Quantifying the imaginarity via different distance measures
• Coherence and Imaginarity as Resources in Quantum Circuit Complexity
• Quantum-imaginarity-based quantum speed limit
• Imaginarity measures induced by relative entropy
• Quantifying imaginarity of quantum operations
• The detection power of real entanglement witnesses under local unitary equivalence
• Imaginarity as a Resource within Quantum Coherence: Geometric Decomposition and Operational Conversion