Local two-qubit entanglement-annihilating channels

Filippov, S.; Rybár, Tomáš; Ziman, Märio

doi:10.1103/physreva.85.012303

Cited by 40 publications

(63 citation statements)

References 34 publications

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“…We continue with a reformulation of the PPT squared conjecture related to so called entanglement annihilating channels [29,31]. A linear map T :…”

Section: B Connection To Local Entanglement Annihilationmentioning

confidence: 99%

“…Trivial examples of such maps are the entanglement breaking maps. However, there are examples [31] of completely positive maps which are 2-locally entanglement annihilating, but not entanglement breaking. The following reformulation shows that such maps could be obtained from any linear map that is both completely positive and completely copositive: Suppose first that Conjecture IV.1 holds true.…”

Section: B Connection To Local Entanglement Annihilationmentioning

confidence: 99%

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When Do Composed Maps Become Entanglement Breaking?

Christandl

Müller-Hermes

Wolf

2019

Ann. Henri Poincaré

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We will call a completely positive map a quantum channel if it preserves the trace, i.e. if Tr [T (X)] = Tr [X] for any X ∈ M d 1 . While quantum channels represent general physical processes in the context of quantum information theory, entanglement breaking quantum channels represent such processes that cannot be used to distribute entanglement, and they are useless for any non-classical communication task [1]. Completely copositive quantum channels represent physical processes which are too noisy to be used for some information processing tasks (e.g. quantum communication [2]). However, unlike entanglement breaking channels they can sometimes be used for certain non-classical information processing tasks (e.g. private communication [3]). * Electronic address: christandl@math.ku.dk † Electronic address: muellerh@posteo.net, muellerh@math.ku.dk ‡ Electronic address: m.wolf@tum.de

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“…We continue with a reformulation of the PPT squared conjecture related to so called entanglement annihilating channels [29,31]. A linear map T :…”

Section: B Connection To Local Entanglement Annihilationmentioning

confidence: 99%

Section: B Connection To Local Entanglement Annihilationmentioning

confidence: 99%

When Do Composed Maps Become Entanglement Breaking?

Christandl

Müller-Hermes

Wolf

2019

Ann. Henri Poincaré

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“…In this subsection we consider unital qubit maps     U  ( ) ( ) : Consider a local unital map acting on two qubits, ¡ Ä ¡¢. General properties of such maps are reviewed in [15,39].…”

Section: Local Unital Qubit Maps and Channelsmentioning

confidence: 99%

“…Suppose a quantum channel Φ is such that its output   = F[ ] out is separable for some initial system state ñ. It may happen either due to entanglement annihilation of the initially entangled state ñ [14,15], or due to the fact that the initial state ñ was separable and Φ preserved its separability. Though the state  out is inapplicable for entanglement-based quantum protocols, there is often a possibility to make it entangled by applying appropriate control operations, e.g.…”

Section: Introductionmentioning

confidence: 99%

Absolutely separating quantum maps and channels

2017

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Absolutely separating quantum maps and channels AbstractAbsolutely separable states ñ remain separable under arbitrary unitary transformations  † U U . By example of a three qubit system we show that in a multipartite scenario neither full separability implies bipartite absolute separability nor the reverse statement holds. The main goal of the paper is to analyze quantum maps resulting in absolutely separable output states. Such absolutely separating maps affect the states in a way, when no Hamiltonian dynamics can make them entangled afterwards. We study the general properties of absolutely separating maps and channels with respect to bipartitions and multipartitions and show that absolutely separating maps are not necessarily entanglement breaking. We examine the stability of absolutely separating maps under a tensor product and show that F ÄN is absolutely separating for any N if and only if Φ is the tracing map. Particular results are obtained for families of local unital multiqubit channels, global generalized Pauli channels, and combination of identity, transposition, and tracing maps acting on states of arbitrary dimension. We also study the interplay between local and global noise components in absolutely separating bipartite depolarizing maps and discuss the input states with high resistance to absolute separability.

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“…To describe the stages of gradual entanglement degradation, the notions of entanglement annihilation [8,9] and entanglement dissociation [10] were introduced recently.…”

Section: Introductionmentioning

confidence: 99%

PPT-Inducing, Distillation-Prohibiting, and Entanglement-Binding Quantum Channels

Filippov

2014

J Russ Laser Res

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Entanglement degradation in open quantum systems is reviewed in the Choi-Jamio lkowski representation of linear maps. In addition to physical processes of entanglement dissociation and entanglement annihilation, we consider quantum dynamics transforming arbitrary input states into those that remain positive under partial transpose (PPT-inducing channels). Such evolutions form a convex subset of distillation-prohibiting channels. A relation between the above channels and entanglement-binding ones is clarified. An example of the distillation-prohibiting map Φ ⊗ Φ is given, where Φ is not entanglement binding.

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Local two-qubit entanglement-annihilating channels

Cited by 40 publications

References 34 publications

When Do Composed Maps Become Entanglement Breaking?

When Do Composed Maps Become Entanglement Breaking?

Absolutely separating quantum maps and channels

PPT-Inducing, Distillation-Prohibiting, and Entanglement-Binding Quantum Channels

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