Absolutely separating quantum maps and channels

Abstract

Absolutely separable states $\varrho$ remain separable under arbitrary unitary transformations $U\varrho U^{†}$. By example of a three qubit system we show that in 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 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 stability of absolutely separating maps under tensor product and show that ${\Phi }^{\otimes N}$ is absolutely separating for any $N$ if and only if $\Phi$ 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.

28 pages, 7 figures

References in corpus (8)

• Pauli Diagonal Channels Constant on Axes
• Entanglement-annihilating and entanglement-breaking channels
• Tensor power of dynamical maps and P- vs. CP-divisibility
• Quantum evolution in the stroboscopic limit of repeated measurements
• Entangled states close to the maximally mixed state
• Absolutely classical spin states
• Positive reduction from spectra
• PPT-inducing, distillation-prohibiting, and entanglement-binding quantum channels

Cited by in corpus (14)

• Maximal Coherence and the Resource Theory of Purity
• Classical capacity of the generalized Pauli channels
• Characterizing the boundary of the set of absolutely separable states and their generation via noisy environments
• Ultimate entanglement robustness of two-qubit states against general local noises
• Quantum informational properties of the Landau-Streater channel
• Lower and upper bounds on nonunital qubit channel capacities
• Maximum entanglement of mixed symmetric states under unitary transformations
• Geometry of generalized Pauli channels
• Nonequivalence between absolute separability and positive partial transposition in the symmetric subspace
• Sufficient criteria for absolute separability in arbitrary dimensions via linear map inverses
• Quantum channels and some absolute properties of quantum states
• Capacities of a two-parameter family of noisy Werner-Holevo channels
• On the extreme points of sets of absolulely separable and PPT states
• Detection of nonabsolute separability in quantum states and channels through moments