Optimal Decompositions of Barely Separable States

Abstract

Two families of bipartite mixed quantum states are studied for which it is proved that the number of members in the optimal-decomposition ensemble --- the ensemble realizing the entanglement of formation --- is greater than the rank of the mixed state. We find examples for which the number of states in this optimal ensemble can be larger than the rank by an arbitrarily large factor. In one case the proof relies on the fact that the partial transpose of the mixed state has zero eigenvalues; in the other case the result arises from the properties of product bases that are completable only by embedding in a larger Hilbert space.

14 Pages (RevTeX), 1 figure (eps). Submitted to the special issue of the J. Mod. Opt. V2: Change in terminology from "ensemble length" to "ensemble cardinality"

References in corpus (2)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Quantifying Entanglement

Cited by in corpus (16)

• Quantum entanglement
• General Entanglement Breaking Channels
• The Entanglement of Formation for Isotropic States
• Evidence for Bound Entangled States with Negative Partial Transpose
• Detecting Multipartite Classical States and their Resemblances
• Correlations in quantum states and the local creation of quantum discord
• Unique decompositions, faces, and automorphisms of separable states
• Qubit-qudit states with positive partial transpose
• Separability problem for multipartite states of rank at most four
• Classical extension of quantum-correlated separable states
• Entanglement Breaking Rank and the existence of SIC POVMs
• The role of phases in detecting three-qubit entanglement
• $C^{\ast }$-extreme points of entanglement breaking maps
• Length filtration of the separable states
• Classical simulation of noisy quantum circuits via locally entanglement-optimal unravelings
• Ancilla-Assisted Process Tomography with Bipartiete Mixed Separable States