Absolutely separating quantum maps and channels

Filippov, S.; Magadov, Kamil Yu.; Jivulescu, Maria Anastasia

doi:10.1088/1367-2630/aa7e06

Cited by 13 publications

(14 citation statements)

References 62 publications

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“…We also attempted to further the understanding of absolutely local maps, which render the resultant state useless regarding nonlocality. This is akin to the work already done in entanglement theory where absolute separability maps were considered [48]. In the tables presented, as expected intuitively, we observe that in most of the cases the parameter ranges obtained for a single interaction are subsets of that obtained for double interaction.…”

Section: Discussionsupporting

confidence: 78%

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Environmental Effects on Nonlocal Correlations

Guha

Bhattacharya

Das

et al. 2019

Quanta

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Environmental interactions are ubiquitous in practical instances of any quantum information processing protocol. The interaction results in depletion of various quantum resources and even complete loss in numerous situations. Nonlocality, which is one particular quantum resource marking a significant departure of quantum mechanics from classical mechanics, meets the same fate. In the present work we study the decay in nonlocality to the extent of the output state admitting a local hidden state model. Using some fundamental quantum channels we also demonstrate the complete decay in the resources in the purview of the Bell–Clauser–Horne–Shimony–Holt inequality and a three-settings steering inequality. We also obtain bounds on the parameter of the depolarizing map for which it becomes steerability breaking pertaining to a general class of two qubit states.Quanta 2019; 8: 57–67.

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Section: Discussionsupporting

confidence: 78%

“…These states are termed as absolutely Bell-CHSH local states [46,47]. The question of transforming a separable, but not absolutely separable, state into an absolutely separable one under environmental interactions is important in practical situations and has been investigated recently [48].…”

Section: Introductionmentioning

confidence: 99%

Environmental Effects on Nonlocal Correlations

Guha

Bhattacharya

Das

et al. 2019

Quanta

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“…For instance, the set of maximally entangled mixed states, i.e., states which maximize entanglement for a fixed spectrum, as well as states that maximize entanglement at a fixed value of purity, have been characterized for various quantifiers of entanglement and purity [51][52][53][54]. States satisfying 0 max  r = ( ) are also known as absolutely separable states, and have been studied in [73][74][75]. Similar studies were performed for discord [76,77], based on the original definition [5].…”

Section: Relation To Entanglement and Quantum Discordmentioning

confidence: 99%

Maximal coherence and the resource theory of purity

et al. 2018

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The resource theory of quantum coherence studies the off-diagonal elements of a density matrix in a distinguished basis, whereas the resource theory of purity studies all deviations from the maximally mixed state. We establish a direct connection between the two resource theories, by identifying purity as the maximal coherence which is achievable by unitary operations. The states that saturate this maximum identify a universal family of maximally coherent mixed states. These states are optimal resources under maximally incoherent operations, and thus independent of the way coherence is quantified. For all distance-based coherence quantifiers the maximal coherence can be evaluated exactly, and is shown to coincide with the corresponding distance-based purity quantifier. We further show that purity bounds the maximal amount of entanglement and discord that can be generated by unitary operations, thus demonstrating that purity is the most elementary resource for quantum information processing.

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“…We focus on entanglement-annihilating properties of the map Λ = Φ ⊗ Φ, where Φ is the Landau-Streater channel. As we show below, Φ ⊗ Φ is not entanglement annihilating if j 1, from which it will follow that Φ is not entanglement breaking and Φ ⊗ Φ is not absolutely separating 45 .…”

Section: B Entanglement Assisted Capacitymentioning

confidence: 92%

Quantum informational properties of the Landau–Streater channel

Filippov

Kuzhamuratova

2019

Journal of Mathematical Physics

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We study the Landau-Streater quantum channel Φ : B(H d ) → B(H d ), whose Kraus operators are proportional to the irreducible unitary representation of SU (2) generators of dimension d. We establish SU (2) covariance for all d and U (3) covariance for d = 3. Using the theory of angular momentum, we explicitly find the spectrum and the minimal output entropy of Φ. Negative eigenvalues in the spectrum of Φ indicate that the channel cannot be obtained as a result of Hermitian Markovian quantum dynamics. Degradability and antidegradability of the Landau-Streater channel is fully analyzed. We calculate classical and entanglement-assisted capacities of Φ. Quantum capacity of Φ vanishes if d = 2, 3 and is strictly positive if d 4. We show that the channel Φ ⊗ Φ does not annihilate entanglement and preserves entanglement of some states with Schmidt rank 2 if d 3.

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Absolutely separating quantum maps and channels

Cited by 13 publications

References 62 publications

Environmental Effects on Nonlocal Correlations

Environmental Effects on Nonlocal Correlations

Maximal coherence and the resource theory of purity

Quantum informational properties of the Landau–Streater channel

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