Hierarchy of continuous-variable quantum resource theories
arXiv:2106.11334 · doi:10.1088/1367-2630/ac2f90
Abstract
Connections between the resource theories of coherence and purity (or non-uniformity) are well known for discrete-variable, finite-dimensional, quantum systems. We establish analogous results for continuous-variable systems, in particular Gaussian systems. To this end, we define the concept of maximal coherence at fixed energy, which is achievable with energy-preserving unitaries. We show that the maximal Gaussian coherence (where states and operations are required to be Gaussian) can be quantified analytically by the relative entropy. We then propose a resource theory of non-uniformity, by considering the purity of a quantum state at fixed energy as resource, and by defining non-uniformity monotones. In the Gaussian case, we prove the equality of Gaussian non-uniformity and maximal Gaussian coherence. Finally, we show a hierarchy for non-uniformity, coherence, discord and entanglement in continuous-variable systems.
arXiv comment22 pages, 3 figures
References in corpus (36)
- Quantum information with continuous variables
- Gaussian Quantum Information
- Quantifying Coherence
- Quantum Coherence as a Resource
- The classical-quantum boundary for correlations: discord and related measures
- Entanglement Measures and Purification Procedures
- Quantum Resource Theories
- Unified View of Quantum and Classical Correlations
- Continuous variable quantum information: Gaussian states and beyond
- The Resource Theory of Quantum States Out of Thermal Equilibrium
- Quantum versus classical correlations in Gaussian states
- Gaussian quantum discord
- The Real Symplectic Groups in Quantum Mechanics and Optics
- Quantum optics in the phase space - A tutorial on Gaussian states
- The resource theory of informational nonequilibrium in thermodynamics
- How to quantify coherence: Distinguishing speakable and unspeakable notions
- Modes and states in Quantum Optics
- Reversible transformations from pure to mixed states, and the unique measure of information
- Quantifying the non-Gaussian character of a quantum state by quantum relative entropy
- An introductory review of the resource theory approach to thermodynamics
- The entangling power of passive optical elements
- Maximal Coherence and the Resource Theory of Purity
- Quantifying Superposition
- Maximally coherent mixed states: Complementarity between maximal coherence and mixedness
- On the quantification of entanglement in infinite-dimensional quantum systems
- Quantifying coherence of Gaussian states
- Quantifying Coherence in Infinite Dimensional Systems
- Gaussian quantum resource theories
- Continuity bounds on the quantum relative entropy
- Continuity bounds on the quantum relative entropy - II
- Gaussian entanglement revisited
- Maximal coherence in generic basis
- Gaussian Thermal Operations and the Limits of Algorithmic Cooling
- Quantum thermodynamics in a multipartite setting: A resource theory of local Gaussian work extraction for multimode bosonic systems
- Thermodynamic resources in continuous-variable quantum systems
- Gaussian multipartite quantum discord from classical mutual information