13 research outputs found
Asymptotic Entanglement and Lindblad Dynamics: a Perturbative Approach
We consider an open bipartite quantum system with dissipative Lindblad type
dynamics. In order to study the entanglement of the stationary states, we
develop a perturbative approach and apply it to the physically significant case
when a purely dissipative perturbation is added to the unperturbed generator
which by itself would produce reversible unitary dynamics.Comment: 15 page
Entanglement or separability: The choice of how to factorize the algebra of a density matrix
We discuss the concept of how entanglement changes with respect to different
factorizations of the total algebra which describes the quantum states.
Depending on the considered factorization a quantum state appears either
entangled or separable. For pure states we always can switch unitarily between
separability and entanglement, however, for mixed states a minimal amount of
mixedness is needed. We discuss our general statements in detail for the
familiar case of qubits, the GHZ states, Werner states and Gisin states,
emphasizing their geometric features. As theorists we use and play with this
free choice of factorization, which is naturally fixed for an experimentalist.
For theorists it offers an extension of the interpretations and is adequate to
generalizations, as we point out in the examples of quantum teleportation and
entanglement swapping.Comment: 29 pages, 9 figures. Introduction, Conclusion and References have
been extended in v
Pauli Diagonal Channels Constant on Axes
We define and study the properties of channels which are analogous to unital
qubit channels in several ways. A full treatment can be given only when the
dimension d is a prime power, in which case each of the (d+1) mutually unbiased
bases (MUB) defines an axis. Along each axis the channel looks like a
depolarizing channel, but the degree of depolarization depends on the axis.
When d is not a prime power, some of our results still hold, particularly in
the case of channels with one symmetry axis. We describe the convex structure
of this class of channels and the subclass of entanglement breaking channels.
We find new bound entangled states for d = 3.
For these channels, we show that the multiplicativity conjecture for maximal
output p-norm holds for p=2. We also find channels with behavior not exhibited
by unital qubit channels, including two pairs of orthogonal bases with equal
output entropy in the absence of symmetry. This provides new numerical evidence
for the additivity of minimal output entropy
Asymptotic properties of quantum Markov chains
The asymptotic dynamics of quantum Markov chains generated by the most
general physically relevant quantum operations is investigated. It is shown
that it is confined to an attractor space on which the resulting quantum Markov
chain is diagonalizable. A construction procedure of a basis of this attractor
space and its associated dual basis is presented. It applies whenever a
strictly positive quantum state exists which is contracted or left invariant by
the generating quantum operation. Moreover, algebraic relations between the
attractor space and Kraus operators involved in the definition of a quantum
Markov chain are derived. This construction is not only expected to offer
significant computational advantages in cases in which the dimension of the
Hilbert space is large and the dimension of the attractor space is small but it
also sheds new light onto the relation between the asymptotic dynamics of
quantum Markov chains and fixed points of their generating quantum operations.Comment: 10 page