Positive tensor products of maps and<i>n</i>-tensor-stable positive qubit maps

Filippov, S.; Magadov, Kamil Yu.

doi:10.1088/1751-8121/aa5301

Cited by 14 publications

(22 citation statements)

References 74 publications

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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%

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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Section: Local Unital Qubit Maps and Channelsmentioning

confidence: 99%

Absolutely separating quantum maps and channels

2017

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“…Such a map is easily seen to be decomposable, and reversing the scaling operation shows that the original map is decomposable as well. Recently, S. Fillipov and K. Magadov [14] analyzed when tensor squares of qubit maps are positive. Specifically, they showed that for the Pauli diagonal map with |µ = (1, x, y, z) T ∈ R 4 its tensor square Π µ ⊗ Π µ is positive if and only if the following inequalities hold:…”

Section: Motivation and Summary Of Main Resultsmentioning

confidence: 99%

Decomposable Pauli diagonal maps and Tensor Squares of Qubit Maps

Müller-Hermes

2020

Preprint

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It is a well-known result due to E. Størmer that every positive qubit map is decomposable into a sum of a completely positive map and a completely copositive map. Here, we generalize this result to tensor squares of qubit maps. Specifically, we show that any positive tensor product of a qubit map with itself is decomposable. This solves a recent conjecture by S. Fillipov and K. Magadov. We contrast this result with examples of non-decomposable positive maps arising as the tensor product of two distinct qubit maps or as the tensor square of a decomposable map from a qubit to a ququart. To show our main result, we reduce the problem to Pauli diagonal maps. We then characterize the cone of decomposable ququart Pauli diagonal maps by determining all 252 extremal rays of ququart Pauli diagonal maps that are both completely positive and completely copositive. These extremal rays split into three disjoint orbits under a natural symmetry group, and two of these orbits contain only entanglement breaking maps. Finally, we develop a general combinatorial method to determine the extremal rays of Pauli diagonal maps that are both completely positive and completely copositive between multiqubit systems using the ordered spectra of their Choi matrices. Classifying these extremal rays beyond ququarts is left as an open problem.

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“…Further, a result in [ 25 ] ensures that, for trace preserving qubit maps

, the Positivity of the tensor product maps,

, on two qubits is equivalent to the Complete Positivity of the squares,

, of the 1-qubit maps. Since from (27) it follows that

acts as

by changing α into

is Positive for

.…”

Section: Open Quantum Dynamicsmentioning

confidence: 99%

Quasi-Entropies and Non-Markovianity

Benatti

Brancati

2019

Entropy

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We address an informational puzzle that appears with a non-Markovian open qubit dynamics: namely the fact that, while, according to the existing witnesses of information flows, a single qubit affected by that dissipative dynamics does not show information returning to it from its environment, instead two qubits do show such information when evolving independently under the same dynamics. We solve the puzzle by adding the so-called quasi-entropies to the possible witnesses of information flows.

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Positive tensor products of maps andn-tensor-stable positive qubit maps

Cited by 14 publications

References 74 publications

Absolutely separating quantum maps and channels

Absolutely separating quantum maps and channels

Decomposable Pauli diagonal maps and Tensor Squares of Qubit Maps

Quasi-Entropies and Non-Markovianity

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