Bipartite entanglement-annihilating maps: necessary and sufficient conditions

Abstract

We fully characterize bipartite entanglement-annihilating (EA) channels that destroy entanglement of any state shared by subsystems and, thus, should be avoided in any entanglement-enabled experiment. Our approach relies on extending the problem to EA positive maps, the cone of which remains invariant under concatenation with partially positive maps. Due to this invariancy, positive EA maps adopt a well characterization and their intersection with completely positive trace-preserving maps results in the set of EA channels. In addition to a general description, we also provide sufficient operational criteria revealing EA channels. They have a clear physical meaning since the processes involved contain stages of classical information transfer for subsystems. We demonstrate the applicability of derived criteria for local and global depolarizing noises, and specify corresponding noise levels beyond which any initial state becomes disentangled after passing the channel. The robustness of some entangled states is discussed.

7 pages, 5 figures

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Cited by in corpus (21)

• The entropy vector formalism and the structure of multidimensional entanglement in multipartite systems
• General no-go theorem for entanglement extraction
• Bipartite depolarizing channels
• Positivity of linear maps under tensor powers
• Dissociation and annihilation of multipartite entanglement structure in dissipative quantum dynamics
• Entanglement sensitivity to signal attenuation and amplification
• Quantum evolution in the stroboscopic limit of repeated measurements
• Lectures on Quantum Tensor Networks
• Robustness of multiparticle entanglement: specific entanglement classes and random states
• Entanglement in dissipative dynamics of identical particles
• Non-classical correlations in quantum mechanics and beyond
• Absolutely separating quantum maps and channels
• Ultimate entanglement robustness of two-qubit states against general local noises
• Positive tensor products of qubit maps and n-tensor-stable positive qubit maps
• PPT-inducing, distillation-prohibiting, and entanglement-binding quantum channels
• Annihilating Entanglement Between Cones
• Truncated moment sequences and a solution to the channel separability problem
• All incompatible measurements on qubits lead to multiparticle Bell nonlocality
• Spin polarization-scaling quantum maps and channels
• Superior resilience of non-Gaussian entanglement against local Gaussian noises
• Some Entanglement Survives Most Measurements