Bipartite Mixed States of Infinite-Dimensional Systems are Generically Nonseparable
arXiv:quant-ph/9908028 · doi:10.1103/PhysRevA.61.012108
Abstract
Given a bipartite quantum system represented by a tensor product of two Hilbert spaces, we give an elementary argument showing that if either component space is infinite-dimensional, then the set of nonseparable density operators is trace-norm dense in the set of all density operators (and the separable density operators nowhere dense). This result complements recent detailed investigations of separability, which show that when both component Hilbert spaces are finite-dimensional, there is a separable neighborhood (perhaps very small for large dimensions) of the maximally mixed state.
5 pages, RevTeX
Cited by in corpus (26)
- Quantum entanglement
- Optimal entanglement witnesses for continuous-variable systems
- Inseparability inequalities for higher-order moments for bipartite systems
- Entanglement and the Thermodynamic Arrow of Time
- On the quantification of entanglement in infinite-dimensional quantum systems
- Generic Bell correlation between arbitrary local algebras in quantum field theory
- On entanglement capabilities in infinite dimensions or multi-dimensional entangled coherent states
- Entanglement and Open Systems in Algebraic Quantum Field Theory
- An Introduction to Quantum Entanglement: a Geometric Approach
- Boosting entanglement generation in down-conversion with incoherent illumination
- Entanglement, Haag-duality and type properties of infinite quantum spin chains
- Decoherence of multi-dimensional entangled coherent states
- Nonclassical distance in multimode bosonic systems
- Geometry of sets of quantum maps: a generic positive map acting on a high-dimensional system is not completely positive
- On the lattice structure of probability spaces in quantum mechanics
- Non-local Correlations are Generic in Infinite-Dimensional Bipartite Systems
- Towards a definition of the Quantum Ergodic Hierarchy: Kolmogorov and Bernoulli systems
- Entanglement in bipartite generalized coherent states
- Entanglement in bipartite quantum systems: Euclidean volume ratios and detectability by Bell inequalities
- Nonexistence of entangled continuous-variable Werner states with positive partial transpose
- Generic Incomparability of Infinite-Dimensional Entangled States
- Integral representations of separable states
- Generating random Gaussian states
- Entanglement, Complexity, and Causal Asymmetry in Quantum Theories
- Universality of finite time disentanglement
- Entanglement in bipartite X-states: Analytical results for the volume of states with positive partial transpose