Separability of mixed states: necessary and sufficient conditions

  title={Separability of mixed states: necessary and sufficient conditions},
  author={Michal Horodecki and Paweł Horodecki and Ryszard Horodecki},
  journal={Physics Letters A},

Small quantum networks in the qudit stabilizer formalism

How much noise can a given quantum state tolerate without losing its entanglement? For qudits of arbitrary dimension, I investigate this question for two noise models: Global white noise, where a

Generation and Detection of Quantum Correlations and Entanglement on a Spin-Based Quantum Information Processor

This thesis focuses on the experimental creation and detection of a variety of quantum correlations using nuclear magnetic resonance hardware. Quantum entanglement, being most common and

Quantum correlations and distinguishability of quantum states

A survey of various concepts in quantum information is given, with a main emphasis on the distinguishability of quantum states and quantum correlations. Covered topics include generalized and least


We present a survey on mathematical topics relating to separable states and entanglement witnesses. The convex cone duality between separable states and entanglement witnesses is discussed and later

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On a class of $k$-entanglement witnesses

Recently, Yang et al. [14] showed that each 2-positive map acting from M3(C) into itself is decomposable. It is equivalent to the statement that each PPT state on C3 ⊗ C3 has Schmidt number at most

Quantum Entanglement: a Study of Recent Separability Criteria

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We study the non-equilibrium dynamics of two coupled oscillators interacting with their own heat baths of quantum scalar fields at different temperature T 1 and T 2 with bilinear couplings between

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Information-theoretic aspects of inseparability of mixed states.

  • Horodecki
  • Psychology
    Physical review. A, Atomic, molecular, and optical physics
  • 1996
Information-theoretic aspects of quantum inseparability of mixed states are investigated in terms of the {alpha} entropy inequalities and teleportation fidelity and a complete characterization of the inseparable 2{times}2 systems with maximally disordered subsystems is presented within the Hilbert-Schmidt space formalism.

Separability Criterion for Density Matrices.

  • Pérès
  • Physics
    Physical review letters
  • 1996
It is proved that a necessary condition for separability is that a matrix, obtained by partial transposition of {rho}, has only non-negative eigenvalues.

General properties of entropy

This paper discusses properties of entropy, as well as related concepts such as relative entropy, skew entropy, dynamical entropy, etc, in detail with reference to their implications in statistical mechanics, to get a glimpse of systems with infinitely many degrees of freedom.