3,687 research outputs found
Reexamination of determinant-based separability test for two qubits
It was shown in [Augusiak et al.,\;Phys. Rev. A \textbf{77}, 030301(R)
(2008)] that discrimination between entanglement and separability in a two
qubit state can be achieved by a measurement of a single observable on four
copies of it. Moreover, a pseudo entanglement monotone was proposed to
quantify entanglement in such states. The main goal of the present paper is to
show that close relationship between and concurrence reported there is a
result of sharing the same underlying construction of a spin flipped matrix. We
also show that monogamy of entanglement can be rephrased in terms of and
prove the factorization law for .Comment: improved v3, journal ref. adde
Universal observable detecting all two-qubit entanglement and determinant based separability tests
We construct a single observable measurement of which mean value on four
copies of an {\it unknown} two-qubit state is sufficient for unambiguous
decision whether the state is separable or entangled. In other words, there
exists a universal collective entanglement witness detecting all two-qubit
entanglement. The test is directly linked to a function which characterizes to
some extent the entanglement quantitatively. This function is an entanglement
monotone under so--called local pure operations and classical communication
(pLOCC) which preserve local dimensions. Moreover it provides tight upper and
lower bounds for negativity and concurrence. Elementary quantum computing
device estimating unknown two-qubit entanglement is designed.Comment: 5 pages, RevTeX, one figure replaced by another, tight bounds on
negativity and concurrence added, function proved to be a monotone under the
pure LOCC, list of authors put in alphabetical orde
Entanglement, Purity, and Information Entropies in Continuous Variable Systems
Quantum entanglement of pure states of a bipartite system is defined as the
amount of local or marginal ({\em i.e.}referring to the subsystems) entropy.
For mixed states this identification vanishes, since the global loss of
information about the state makes it impossible to distinguish between quantum
and classical correlations. Here we show how the joint knowledge of the global
and marginal degrees of information of a quantum state, quantified by the
purities or in general by information entropies, provides an accurate
characterization of its entanglement. In particular, for Gaussian states of
continuous variable systems, we classify the entanglement of two--mode states
according to their degree of total and partial mixedness, comparing the
different roles played by the purity and the generalized entropies in
quantifying the mixedness and bounding the entanglement. We prove the existence
of strict upper and lower bounds on the entanglement and the existence of
extremally (maximally and minimally) entangled states at fixed global and
marginal degrees of information. This results allow for a powerful, operative
method to measure mixed-state entanglement without the full tomographic
reconstruction of the state. Finally, we briefly discuss the ongoing extension
of our analysis to the quantification of multipartite entanglement in highly
symmetric Gaussian states of arbitrary -mode partitions.Comment: 16 pages, 5 low-res figures, OSID style. Presented at the
International Conference ``Entanglement, Information and Noise'', Krzyzowa,
Poland, June 14--20, 200
Group transference techniques for the estimation of the decoherence times and capacities of quantum Markov semigroups
Capacities of quantum channels and decoherence times both quantify the extent
to which quantum information can withstand degradation by interactions with its
environment. However, calculating capacities directly is known to be
intractable in general. Much recent work has focused on upper bounding certain
capacities in terms of more tractable quantities such as specific norms from
operator theory. In the meantime, there has also been substantial recent
progress on estimating decoherence times with techniques from analysis and
geometry, even though many hard questions remain open. In this article, we
introduce a class of continuous-time quantum channels that we called
transferred channels, which are built through representation theory from a
classical Markov kernel defined on a compact group. We study two subclasses of
such kernels: H\"ormander systems on compact Lie-groups and Markov chains on
finite groups. Examples of transferred channels include the depolarizing
channel, the dephasing channel, and collective decoherence channels acting on
qubits. Some of the estimates presented are new, such as those for channels
that randomly swap subsystems. We then extend tools developed in earlier work
by Gao, Junge and LaRacuente to transfer estimates of the classical Markov
kernel to the transferred channels and study in this way different
non-commutative functional inequalities. The main contribution of this article
is the application of this transference principle to the estimation of various
capacities as well as estimation of entanglement breaking times, defined as the
first time for which the channel becomes entanglement breaking. Moreover, our
estimates hold for non-ergodic channels such as the collective decoherence
channels, an important scenario that has been overlooked so far because of a
lack of techniques.Comment: 35 pages, 2 figures. Close to published versio
Optimal estimation of entanglement and discord in two-qubit states
Recently, the fast development of quantum technologies led to the need for
tools allowing the characterization of quantum resources. In particular, the
ability to estimate non-classical aspects, e.g. entanglement and quantum
discord, in two-qubit systems, is relevant to optimise the performance of
quantum information processes. Here we present an experiment in which the
amount of entanglement and discord are measured exploiting different
estimators. Among them, some will prove to be optimal, i.e., able to reach the
ultimate precision bound allowed by quantum mechanics. These estimation
techniques have been tested with a specific family of states ranging from
nearly pure Bell states to completely mixed states. This work represents a
significant step in the development of reliable metrological tools for quantum
technologies
Entanglement susceptibility: Area laws and beyond
Generic quantum states in the Hilbert space of a many body system are nearly
maximally entangled whereas low energy physical states are not; the so-called
area laws for quantum entanglement are widespread. In this paper we introduce
the novel concept of entanglement susceptibility by expanding the 2-Renyi
entropy in the boundary couplings. We show how this concept leads to the
emergence of area laws for bi-partite quantum entanglement in systems ruled by
local gapped Hamiltonians. Entanglement susceptibility also captures
quantitatively which violations one should expect when the system becomes
gapless. We also discuss an exact series expansion of the 2-Renyi entanglement
entropy in terms of connected correlation functions of a boundary term. This is
obtained by identifying Renyi entropy with ground state fidelity in a doubled
and twisted theory.Comment: minor corrections, references adde
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