Resource theory of quantum coherence with probabilistically non-distinguishable pointers and corresponding wave-particle duality
arXiv:2005.08296 · doi:10.1103/PhysRevA.103.022417
Abstract
One of the fundamental features of quantum mechanics is the superposition principle, a manifestation of which is embodied in quantum coherence. Coherence of a quantum state is invariably defined with respect to a preferred set of pointer states, and there exist quantum coherence measures with respect to deterministically as well as probabilistically distinguishable sets of quantum state vectors. Here we study the resource theory of quantum coherence with respect to an arbitrary set of quantum state vectors, that may not even be probabilistically distinguishable. Geometrically, a probabilistically indistinguishable set of quantum state vectors forms a linearly dependent set. We find the free states of the resource theory, and analyze the corresponding free operations, obtaining a necessary condition for an arbitrary quantum operation to be free. We identify a class of measures of the quantum coherence, and in particular establish a monotonicity property of the measures. We find a connection of an arbitrary set of quantum state vectors with positive operator valued measurements with respect to the resource theory being considered, which paves the way for an alternate definition of the free states. We notice that the resource theory of magic can be looked upon as a resource theory of quantum coherence with respect to a set of quantum state vectors that are probabilistically indistinguishable. We subsequently examine the wave-particle duality in a double-slit set-up in which superposition of probabilistically indistinguishable quantum state vectors is possible. Specifically, we report a complementary relation between quantum coherence and path distinguishability in such a set-up.
arXiv comment10 pages and 2 figures
References in corpus (61)
- Quantum entanglement
- Quantifying Coherence
- Entanglement detection
- Quantum Coherence as a Resource
- Device-independent security of quantum cryptography against collective attacks
- Universal Quantum Computation with ideal Clifford gates and noisy ancillas
- Quantum Nonlocality without Entanglement
- Operational Resource Theory of Coherence
- Measuring Quantum Coherence with Entanglement
- Unextendible Product Bases and Bound Entanglement
- Contextuality supplies the magic for quantum computation
- The Resource Theory of Stabilizer Computation
- Probabilistic cloning and identification of linearly independent quantum states
- Converting Coherence to Quantum Correlations
- Application of a resource theory for magic states to fault-tolerant quantum computing
- Quantum coherence in multipartite systems
- Unextendible Product Bases, Uncompletable Product Bases and Bound Entanglement
- A computable measure of nonclassicality for light
- The extraction of work from quantum coherence
- Optimum Unambiguous Discrimination Between Linearly Independent Symmetric States
- Duality of Quantum Coherence and Path Distinguishability
- Converting Nonclassicality into Entanglement
- Coherence and measurement in quantum thermodynamics
- Quantifying Superposition
- Coherence-assisted single-shot cooling by quantum absorption refrigerators
- Measuring Coherence with Entanglement Concurrence
- Unambiguous discrimination of mixed states
- Non-Local Advantage of Quantum Coherence
- Operational one-to-one mapping between coherence and entanglement measures
- Entanglement and coherence in quantum state merging
- A resource theory of superposition
- Optimal distinction between non-orthogonal quantum states
- Quantum State Separation, Unambiguous Discrimination and Exact Cloning
- Resource theory of coherence based on positive-operator-valued measures
- Optimum unambiguous discrimination among linearly-independent non-orthogonal quantum states and its optical realization
- Reduction Theorems for Optimal Unambiguous State Discrimination of Density Matrices
- Delineating incoherent non-Markovian dynamics using quantum coherence
- Comparison of two unknown pure quantum states
- Quantum state filtering and discrimination between sets of Boolean functions
- Optimal unambiguous discrimination between subsets of non-orthogonal quantum states
- General Strategies for Discrimination of Quantum States
- Non-Markovianity, coherence and system-environment correlations in a long-range collision model
- Axiomatic and operational connections between the -norm of coherence and negativity
- Quantification and manipulation of magic states
- Entanglement purification via separable superoperators
- Quantifying coherence with respect to general quantum measurements
- Basis-independent quantum coherence and its distribution
- Coherence number as a discrete quantum resource
- Dynamics and thermodynamics of a central spin immersed in a spin bath
- Discordlike correlation of bipartite coherence
- Non-Markovianity and coherence of a moving qubit inside a leaky cavity
- Measuring coherence of quantum measurements
- Quantum coherence and correlation measures based on affinity
- Coherence and complementarity based on modified generalized skew information
- Wave-particle duality employing quantum coherence in superposition with non-orthogonal pointers
- Wave-particle duality in multi-path interferometers: General concepts and three-path interferometers
- Estimating quantum coherence by noncommutativity of any observable and its incoherent part
- Bell-type inequality in quantum coherence theory as an entanglement witness
- Tripartite Bell-type inequalities for measures of quantum coherence and skew information
- Noncommutative coherence and quantum phase estimation algorithm
- Robustness of interferometric complementarity under Decoherence
Cited by in corpus (10)
- Quantum speed limits for information and coherence
- Converting coherence based on positive-operator-valued measures into entanglement
- Exclusion principle for nonlocal advantage of quantum coherence
- Quantifying the particle aspect of quantum systems
- Quantum coherence with incomplete set of pointers and corresponding wave-particle duality
- Spread and asymmetry of typical quantum coherence and their inhibition in response to glassy disorder
- Correlation between resource-generating capacities of quantum gates
- Interconversion between block coherence and multipartite entanglement in many-body systems
- Quantum Coherence and Distinguishability as Complementary Resources: A Resource-Theoretic Perspective from Wave-Particle Duality
- Response to glassy disorder in coin on spread of quantum walker