Detecting continuous variable entanglement in phase space with the -distribution
arXiv:2211.17165 · doi:10.1103/PhysRevA.108.042410
Abstract
We prove a general class of continuous variable entanglement criteria based on the Husimi -distribution, which represents a quantum state in canonical phase space, by employing a theorem by Lieb and Solovej. We discuss their generality, which roots in the possibility to optimize over the set of concave functions, from the perspective of continuous majorization theory and show that with this approach families of entropic as well as second moment criteria follow as special cases. All derived criteria are compared to corresponding marginal based criteria and the strength of the phase space approach is demonstrated for a family of prototypical example states where only our criteria flag entanglement. Further, we explore their optimization prospects in two experimentally relevant scenarios characterized by sparse data: finite detector resolution and finite statistics. In both scenarios optimization leads to clear improvements enlarging the class of detected states and the signal-to-noise ratio of the detection, respectively.
arXiv comment23 pages, 11 figures, published version
References in corpus (63)
- Quantum entanglement
- Separability Criterion for Density Matrices
- Estimating Mutual Information
- Quantum information with continuous variables
- Gaussian Quantum Information
- Separability of Mixed States: Necessary and Sufficient Conditions
- Entanglement detection
- Peres-Horodecki separability criterion for continuous variable systems
- Inseparability criterion for continuous variable systems
- Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
- Conditions for a class of entanglement transformations
- Entropic Uncertainty Relations and their Applications
- Entangling macroscopic oscillators exploiting radiation pressure
- Measuring out-of-time-order correlations and multiple quantum spectra in a trapped ion quantum magnet
- Observation of quantum state collapse and revival due to the single-photon Kerr effect
- Inseparability criteria for bipartite quantum states
- A Schrodinger Cat Living in Two Boxes
- Spin-Nematic Squeezed Vacuum in a Quantum Gas
- Genuine multipartite Einstein-Podolsky-Rosen steering
- Spatially distributed multipartite entanglement enables Einstein-Podolsky-Rosen steering of atomic clouds
- Characterizing the entanglement of bipartite quantum systems
- Entropic uncertainty relations and entanglement
- Inseparability inequalities for higher-order moments for bipartite systems
- Deterministic generation of multiparticle entanglement by quantum Zeno dynamics
- Entropic Entanglement Criteria for Continuous Variables
- Non-equilibrium dynamics of an unstable quantum pendulum
- Density Matrix From Photon Number Tomography
- Continuous-variable entropic uncertainty relations
- Uncertainty inequalities as entanglement criteria for negative partial-transpose states
- Gaussian entanglement revisited
- Some results concerning maximum Renyi entropy distributions
- Proof of an entropy conjecture for Bloch coherent spin states and its generalizations
- Quantifying entanglement in a 68-billion dimensional quantum state space
- Quantifying high-dimensional entanglement with Einstein-Podolsky-Rosen correlations
- Simultaneous Readout of Noncommuting Collective Spin Observables beyond the Standard Quantum Limit
- Einstein-Podolsky-Rosen-steering using quantum correlations in non-Gaussian entangled states
- A Family of Continuous Variable Entanglement Criteria using General Entropy Functions
- Reliable Entanglement Detection Under Coarse--Grained Measurements
- Experimental Observation of Quantum Correlations in Modular Variables
- Detecting entanglement in spatial interference
- Generation of a two-photon singlet beam
- Characterizing the multipartite continuous-variable entanglement structure from squeezing coefficients and the Fisher information
- Wehrl entropy, entropic uncertainty relations and entanglement
- Quantum Wigner entropy
- On Lieb's conjecture for the Wehrl entropy of Bloch coherent states
- Quantitative tomography for continuous variable quantum systems
- Detecting entanglement structure in continuous many-body quantum systems
- Entanglement detection in quantum many-body systems using entropic uncertainty relations
- Entropic entanglement criteria in phase space
- Evading Vacuum Noise: Wigner Projections or Husimi Samples?
- Entanglement and squeezing in continuous-variable systems
- Optimized Tomography of Continuous Variable Systems Using Excitation Counting
- Experimentally accessible bounds on distillable entanglement from entropic uncertainty relations
- Proof of the Wehrl-type Entropy Conjecture for Symmmetric SU(N) Coherent States
- Heisenberg Uncertainty Relation for Coarse-grained Observables
- Relative entropic uncertainty relation
- Continuous majorization in quantum phase space
- General class of continuous variable entanglement criteria
- Lieb's permanental dominance conjecture
- Relative entropic uncertainty relation for scalar quantum fields
- On the spectral properties of the Bloch-Torrey equation in infinite periodically perforated domains
- Accessing continuous-variable entanglement witnesses with multimode spin observables
- Uncertainty relations with quantum memory for the Wehrl entropy
Cited by in corpus (9)
- General class of continuous variable entanglement criteria
- Entropic distinguishability of quantum fields in phase space
- Wigner non-negative states that verify the Wigner entropy conjecture
- Interferometric detection of continuous-variable entanglement using two states
- Entropy estimation in a spin-1 Bose-Einstein condensate
- Quantum-limited generalized measurement for tunnel-coupled condensates
- Information and majorization theory for fermionic phase-space distributions
- Detecting strongly non-Gaussian entanglement
- Upper bounds on the purity of Wigner positive quantum states that verify the Wigner entropy conjecture