Eventually Entanglement Breaking Maps

Abstract

We analyze certain class of linear maps on matrix algebras that become entanglement breaking after composing a finite or infinite number of times with themselves. This means that the Choi matrix of the iterated linear map becomes separable in the tensor product space. If a linear map is entanglement breaking after finite iterations, we say the map has a finite index of separability. In particular we show that every unital PPT-channel becomes entanglement breaking after a finite number of iterations. It turns out that the class of unital channels that have finite index of separability is a dense subset of the unital channels. We construct concrete examples of maps which are not PPT but have finite index of separability. We prove that there is a large class of unital channels that are asymptotically entanglement breaking. This analysis is motivated by the PPT-squared conjecture made by M. Christandl that says every PPT channel, when composed with itself, becomes entanglement breaking.

A simple proof of Theorem 5.2, suggested by the referee, has been added. Some references are updated

References in corpus (3)

• Minimal and Maximal Operator Spaces and Operator Systems in Entanglement Theory
• Spectral Properties of Tensor Products of Channels
• An Uncertainty Principle For Completely Positive Maps

Cited by in corpus (19)

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• Mapping cone of $k$-Entanglement Breaking Maps
• Asymptotic Properties for Markovian Dynamics in Quantum Theory and General Probabilistic Theories
• Truncated moment sequences and a solution to the channel separability problem
• Asymptotic Dynamics of Open Quantum Systems and Modular Theory
• Roots of Completely Positive Maps
• Random covariant quantum channels
• Decomposable Pauli diagonal maps and Tensor Squares of Qubit Maps
• Entanglement-breaking channels with general outcome operator algebras
• $k$-Positive Maps: New Characterizations and a Generation Method
• Nullspaces of Entanglement Breaking Channels and Applications
• A Multiplicative Ergodic Theorem for Bistochastic Ergodic Quantum Processes with Applications to Entanglement
• Quantum information theory and Fourier multipliers on quantum groups