212 research outputs found
Distillability and positivity of partial transposes in general quantum field systems
Criteria for distillability, and the property of having a positive partial
transpose, are introduced for states of general bipartite quantum systems. The
framework is sufficiently general to include systems with an infinite number of
degrees of freedom, including quantum fields. We show that a large number of
states in relativistic quantum field theory, including the vacuum state and
thermal equilibrium states, are distillable over subsystems separated by
arbitrary spacelike distances. These results apply to any quantum field model.
It will also be shown that these results can be generalized to quantum fields
in curved spacetime, leading to the conclusion that there is a large number of
quantum field states which are distillable over subsystems separated by an
event horizon.Comment: 25 pages, 2 figures. v2: Typos removed, references and comments
added. v3: Expanded introduction and reference list. To appear in Rev. Math.
Phy
Multipartite entanglement in three-mode Gaussian states of continuous variable systems: Quantification, sharing structure and decoherence
We present a complete analysis of multipartite entanglement of three-mode
Gaussian states of continuous variable systems. We derive standard forms which
characterize the covariance matrix of pure and mixed three-mode Gaussian states
up to local unitary operations, showing that the local entropies of pure
Gaussian states are bound to fulfill a relationship which is stricter than the
general Araki-Lieb inequality. Quantum correlations will be quantified by a
proper convex roof extension of the squared logarithmic negativity (the
contangle), satisfying a monogamy relation for multimode Gaussian states, whose
proof will be reviewed and elucidated. The residual contangle, emerging from
the monogamy inequality, is an entanglement monotone under Gaussian local
operations and classical communication and defines a measure of genuine
tripartite entanglement. We analytically determine the residual contangle for
arbitrary pure three-mode Gaussian states and study the distribution of quantum
correlations for such states. This will lead us to show that pure, symmetric
states allow for a promiscuous entanglement sharing, having both maximum
tripartite residual entanglement and maximum couplewise entanglement between
any pair of modes. We thus name these states GHZ/ states of continuous
variable systems because they are simultaneous continuous-variable counterparts
of both the GHZ and the states of three qubits. We finally consider the
action of decoherence on tripartite entangled Gaussian states, studying the
decay of the residual contangle. The GHZ/ states are shown to be maximally
robust under both losses and thermal noise.Comment: 20 pages, 5 figures. (v2) References updated, published versio
On the Phase Covariant Quantum Cloning
It is known that in phase covariant quantum cloning the equatorial states on
the Bloch sphere can be cloned with a fidelity higher than the optimal bound
established for universal quantum cloning. We generalize this concept to
include other states on the Bloch sphere with a definite component of spin.
It is shown that once we know the component, we can always clone a state
with a fidelity higher than the universal value and that of equatorial states.
We also make a detailed study of the entanglement properties of the output
copies and show that the equatorial states are the only states which give rise
to separable density matrix for the outputs.Comment: Revtex4, 6 pages, 5 eps figure
Notions of Infinity in Quantum Physics
In this article we will review some notions of infiniteness that appear in
Hilbert space operators and operator algebras. These include proper
infiniteness, Murray von Neumann's classification into type I and type III
factors and the class of F{/o} lner C*-algebras that capture some aspects of
amenability. We will also mention how these notions reappear in the description
of certain mathematical aspects of quantum mechanics, quantum field theory and
the theory of superselection sectors. We also show that the algebra of the
canonical anti-commutation relations (CAR-algebra) is in the class of F{/o}
lner C*-algebras.Comment: 11 page
Quantum cloning machines for equatorial qubits
Quantum cloning machines for equatorial qubits are studied. For the case of 1
to 2 phase-covariant quantum cloning machine, we present the networks
consisting of quantum gates to realize the quantum cloning transformations. The
copied equatorial qubits are shown to be separable by using Peres-Horodecki
criterion. The optimal 1 to M phase-covariant quantum cloning transformations
are given.Comment: Revtex, 9 page
Strong subadditivity inequality for quantum entropies and four-particle entanglement
Strong subadditivity inequality for a three-particle composite system is an
important inequality in quantum information theory which can be studied via a
four-particle entangled state. We use two three-level atoms in
configuration interacting with a two-mode cavity and the Raman adiabatic
passage technique for the production of the four-particle entangled state.
Using this four-particle entanglement, we study for the first time various
aspects of the strong subadditivity inequality.Comment: 5 pages, 3 figures, RevTeX4, submitted to PR
Tema Con Variazioni: Quantum Channel Capacity
Channel capacity describes the size of the nearly ideal channels, which can
be obtained from many uses of a given channel, using an optimal error
correcting code. In this paper we collect and compare minor and major
variations in the mathematically precise statements of this idea which have
been put forward in the literature. We show that all the variations considered
lead to equivalent capacity definitions. In particular, it makes no difference
whether one requires mean or maximal errors to go to zero, and it makes no
difference whether errors are required to vanish for any sequence of block
sizes compatible with the rate, or only for one infinite sequence.Comment: 32 pages, uses iopart.cl
Truncated su(2) moment problem for spin and polarization states
We address the problem whether a given set of expectation values is
compatible with the first and second moments of the generic spin operators of a
system with total spin j. Those operators appear as the Stokes operator in
quantum optics, as well as the total angular momentum operators in the atomic
ensemble literature. We link this problem to a particular extension problem for
bipartite qubit states; this problem is closely related to the symmetric
extension problem that has recently drawn much attention in different contexts
of the quantum information literature. We are able to provide operational,
approximate solutions for every large spin numbers, and in fact the solution
becomes exact in the limiting case of infinite spin numbers. Solutions for low
spin numbers are formulated in terms of a hyperplane characterization, similar
to entanglement witnesses, that can be efficiently solved with semidefinite
programming.Comment: 18 pages, 1 figur
Causal structures and causal boundaries
We give an up-to-date perspective with a general overview of the theory of
causal properties, the derived causal structures, their classification and
applications, and the definition and construction of causal boundaries and of
causal symmetries, mostly for Lorentzian manifolds but also in more abstract
settings.Comment: Final version. To appear in Classical and Quantum Gravit
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