Entanglement or separability: The choice of how to factorize the algebra of a density matrix

Abstract

We discuss the concept of how entanglement changes with respect to different factorizations of the total algebra which describes the quantum states. Depending on the considered factorization a quantum state appears either entangled or separable. For pure states we always can switch unitarily between separability and entanglement, however, for mixed states a minimal amount of mixedness is needed. We discuss our general statements in detail for the familiar case of qubits, the GHZ states, Werner states and Gisin states, emphasizing their geometric features. As theorists we use and play with this free choice of factorization, which is naturally fixed for an experimentalist. For theorists it offers an extension of the interpretations and is adequate to generalizations, as we point out in the examples of quantum teleportation and entanglement swapping.

29 pages, 9 figures. Introduction, Conclusion and References have been extended in v2

References in corpus (9)

• Experimental quantum teleportation
• Entanglement of Dirac fields in non-inertial frames
• Bloch vectors for qudits
• The state space for two qutrits has a phase space structure in its core
• Observables can be tailored to change the entanglement of any pure state
• The geometry of bipartite qutrits including bound entanglement
• Geometric entanglement witnesses and bound entanglement
• Entanglement witnesses and geometry of entanglement of two--qutrit states
• Bound entanglement in the magic simplex of two--qutrits

Cited by in corpus (22)

• Modes and states in Quantum Optics
• Measuring Coherence with Entanglement Concurrence
• Entanglement in indistinguishable particle systems
• A quantum information theoretic analysis of three flavor neutrino oscillations
• Revealing Hidden Coherence in Partially Coherent Light
• Geometry of two-qubit states with negative conditional entropy
• Entangled Entanglement: The Geometry of GHZ States
• Witness of mixed separable states useful for entanglement creation
• Time-ordering Dependence of Measurements in Teleportation
• Building the Observer into the System: Toward a Realistic Description of Human Interaction with the World
• Moment-Based Evidence for Simple Rational-Valued Hilbert-Schmidt Generic 2 x 2 Separability Probabilities
• Role of spatial higher order derivatives in momentum space entanglement
• Separability, Contextuality, and the Quantum Frame Problem
• John Bell and the Nature of the Quantum World
• Absolute separability witnesses for symmetric multiqubit states
• Entanglement beyond tensor product structure: algebraic aspects of quantum non - separability
• Implementation of classical communication in a quantum world
• Locality and entanglement of indistinguishable particles
• Bounds on mixed state entanglement
• Entanglement for any definition of two subsystems
• Quantum entanglement in physical and cognitive systems: a conceptual analysis and a general representation
• Cosmological constant as quantum error correction from generalised gauge invariance in double field theory