Quantum coherence between subspaces: State transformation, Cohering Power, -coherence and other properties
arXiv:2302.13148 · doi:10.1103/PhysRevA.109.012435
Abstract
The concept of bock-coherence, first introduced in [1] and developed in [2,3] encompasses the case where experimental capabilities are not so delicate to perform arbitrary refined measurements on individual atoms. We develop a framework which facilitates further investigation of this resource theory in several respects. Using this framework, we investigate the problem of state conversion by incoherent operations and show that a majorization condition is the necessary and sufficient condition for state transformation by block-incoherent operations. We also determine the form of the maximally coherent state from which all other states and all unitary gates can be constructed by incoherent operations. Thereafter, we define the concept of block-cohering and block-decohering powers of quantum channels and determine these powers for several types of channels. Finally, we explore the relation between block coherence and a previous extension of coherence, known as -coherence.
arXiv commentAccepted for publication in Physical Review A
References in corpus (40)
- Quantum entanglement
- Quantifying Coherence
- Quantifying Entanglement
- Quantum Coherence as a Resource
- Quantum Resource Theories
- Operational Resource Theory of Coherence
- Measuring Quantum Coherence with Entanglement
- Reference frames, superselection rules, and quantum information
- The resource theory of quantum reference frames: manipulations and monotones
- Frozen Quantum Coherence
- How to quantify coherence: Distinguishing speakable and unspeakable notions
- A mathematical theory of resources
- (Quantumness in the context of) Resource Theories
- Spin flips and quantum information for anti-parallel spins
- Measuring the quality of a quantum reference frame: the relative entropy of frameness
- A quantitative theory of coherent delocalization
- Conditions for coherence transformations under incoherent operations
- Converting Nonclassicality into Entanglement
- Cohering and de-cohering power of quantum channels
- A resource theory of superposition
- Tradeoff between extractable mechanical work, accessible entanglement, and ability to act as a reference system, under arbitrary superselection rules
- Quantum processes which do not use coherence
- Structure of the resource theory of quantum coherence
- Resource theory of coherence based on positive-operator-valued measures
- Certification and Quantification of Multilevel Quantum Coherence
- Convex ordering and quantification of quantumness
- Creation of superposition of unknown quantum states
- Coherence generating power of quantum unitary maps and beyond
- Quantifying coherence with respect to general quantum measurements
- Optimal measurements for relative quantum information
- Coherence measures with respect to general quantum measurements
- Some notes on the robustness of k-coherence and k-entanglement
- Scaling of macroscopic superpositions close to a quantum phase transition
- Characterizing coherence with quantum observables
- Converting coherence based on positive-operator-valued measures into entanglement
- Universal superposition of arbitrary orthogonal states
- The block-coherence measures and the coherence measures based on positive-operator-valued measures
- Secure alignment of coordinate systems by using quantum correlation
- Quantum Key Distribution with no Shared Reference Frame
- The power of a shared singlet state, compared with a shared reference frame