1,535 research outputs found
A comparison of the entanglement measures negativity and concurrence
In this paper we investigate two different entanglement measures in the case
of mixed states of two qubits. We prove that the negativity of a state can
never exceed its concurrence and is always larger then
where is the concurrence of the state.
Furthermore we derive an explicit expression for the states for which the upper
or lower bound is satisfied. Finally we show that similar results hold if the
relative entropy of entanglement and the entanglement of formation are
compared
Multipartite entanglement in 2 x 2 x n quantum systems
We classify multipartite entangled states in the 2 x 2 x n (n >= 4) quantum
system, for example the 4-qubit system distributed over 3 parties, under local
filtering operations. We show that there exist nine essentially different
classes of states, and they give rise to a five-graded partially ordered
structure, including the celebrated Greenberger-Horne-Zeilinger (GHZ) and W
classes of 3 qubits. In particular, all 2 x 2 x n-states can be
deterministically prepared from one maximally entangled state, and some
applications like entanglement swapping are discussed.Comment: 9 pages, 3 eps figure
Asymptotic entanglement capacity of the Ising and anisotropic Heisenberg interactions
We compute the asymptotic entanglement capacity of the Ising interaction ZZ,
the anisotropic Heisenberg interaction XX + YY, and more generally, any
two-qubit Hamiltonian with canonical form K = a XX + b YY. We also describe an
entanglement assisted classical communication protocol using the Hamiltonian K
with rate equal to the asymptotic entanglement capacity.Comment: 5 pages, 1 figure; minor corrections, conjecture adde
Quantum Metropolis Sampling
The original motivation to build a quantum computer came from Feynman who
envisaged a machine capable of simulating generic quantum mechanical systems, a
task that is believed to be intractable for classical computers. Such a machine
would have a wide range of applications in the simulation of many-body quantum
physics, including condensed matter physics, chemistry, and high energy
physics. Part of Feynman's challenge was met by Lloyd who showed how to
approximately decompose the time-evolution operator of interacting quantum
particles into a short sequence of elementary gates, suitable for operation on
a quantum computer. However, this left open the problem of how to simulate the
equilibrium and static properties of quantum systems. This requires the
preparation of ground and Gibbs states on a quantum computer. For classical
systems, this problem is solved by the ubiquitous Metropolis algorithm, a
method that basically acquired a monopoly for the simulation of interacting
particles. Here, we demonstrate how to implement a quantum version of the
Metropolis algorithm on a quantum computer. This algorithm permits to sample
directly from the eigenstates of the Hamiltonian and thus evades the sign
problem present in classical simulations. A small scale implementation of this
algorithm can already be achieved with today's technologyComment: revised versio
Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
We present an algorithm to simulate two-dimensional quantum lattice systems
in the thermodynamic limit. Our approach builds on the {\em projected
entangled-pair state} algorithm for finite lattice systems [F. Verstraete and
J.I. Cirac, cond-mat/0407066] and the infinite {\em time-evolving block
decimation} algorithm for infinite one-dimensional lattice systems [G. Vidal,
Phys. Rev. Lett. 98, 070201 (2007)]. The present algorithm allows for the
computation of the ground state and the simulation of time evolution in
infinite two-dimensional systems that are invariant under translations. We
demonstrate its performance by obtaining the ground state of the quantum Ising
model and analysing its second order quantum phase transition.Comment: 4 pages, 6 figures, 1 table. Revised version, with new diagrams and
plots. The results on classical systems can now be found at arXiv:0711.396
Separable states can be used to distribute entanglement
We show that no entanglement is necessary to distribute entanglement; that
is, two distant particles can be entangled by sending a third particle that is
never entangled with the other two. Similarly, two particles can become
entangled by continuous interaction with a highly mixed mediating particle that
never itself becomes entangled. We also consider analogous properties of
completely positive maps, in which the composition of two separable maps can
create entanglement.Comment: 4 pages, 2 figures. Slight modification
Normal forms and entanglement measures for multipartite quantum states
A general mathematical framework is presented to describe local equivalence
classes of multipartite quantum states under the action of local unitary and
local filtering operations. This yields multipartite generalizations of the
singular value decomposition. The analysis naturally leads to the introduction
of entanglement measures quantifying the multipartite entanglement (as
generalizations of the concurrence and the 3-tangle), and the optimal local
filtering operations maximizing these entanglement monotones are obtained.
Moreover a natural extension of the definition of GHZ-states to e.g. systems is obtained.Comment: Proof of uniqueness of normal form adde
Thermal States as Convex Combinations of Matrix Product States
We study thermal states of strongly interacting quantum spin chains and prove
that those can be represented in terms of convex combinations of matrix product
states. Apart from revealing new features of the entanglement structure of
Gibbs states our results provide a theoretical justification for the use of
White's algorithm of minimally entangled typical thermal states. Furthermore,
we shed new light on time dependent matrix product state algorithms which yield
hydrodynamical descriptions of the underlying dynamics.Comment: v3: 10 pages, 2 figures, final published versio
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