14,519 research outputs found
Optimal distillation of a GHZ state
We present the optimal local protocol to distill a
Greenberger-Horne-Zeilinger (GHZ) state from a single copy of any pure state of
three qubits.Comment: RevTex, 4 pages, 2 figures. Published version, some references adde
Interaction cost of non-local gates
We introduce the interaction cost of a non-local gate as the minimal time of
interaction required to perform the gate when assisting the process with fast
local unitaries. This cost, of interest both in the areas of quantum control
and quantum information, depends on the specific interaction, and allows to
compare in an operationally meaningful manner any two non-local gates. In the
case of a two-qubit system, an analytical expression for the interaction cost
of any unitary operation given any coupling Hamiltonian is obtained. One gate
may be more time-consuming than another for any possible interaction. This
defines a partial order structure in the set of non-local gates, that compares
their degree of non-locality. We analytically characterize this partial order
in a region of the set of two-qubit gates.Comment: revtex, 4 pages, no pictures, typos corrected, small changes in
nomenclatur
Three qubits can be entangled in two inequivalent ways
Invertible local transformations of a multipartite system are used to define
equivalence classes in the set of entangled states. This classification
concerns the entanglement properties of a single copy of the state.
Accordingly, we say that two states have the same kind of entanglement if both
of them can be obtained from the other by means of local operations and
classical communcication (LOCC) with nonzero probability. When applied to pure
states of a three-qubit system, this approach reveals the existence of two
inequivalent kinds of genuine tripartite entanglement, for which the GHZ state
and a W state appear as remarkable representatives. In particular, we show that
the W state retains maximally bipartite entanglement when any one of the three
qubits is traced out. We generalize our results both to the case of higher
dimensional subsystems and also to more than three subsystems, for all of which
we show that, typically, two randomly chosen pure states cannot be converted
into each other by means of LOCC, not even with a small probability of success.Comment: 12 pages, 1 figure; replaced with revised version; terminology
adapted to earlier work; reference added; results unchange
Variational quantum Monte Carlo simulations with tensor-network states
We show that the formalism of tensor-network states, such as the matrix
product states (MPS), can be used as a basis for variational quantum Monte
Carlo simulations. Using a stochastic optimization method, we demonstrate the
potential of this approach by explicit MPS calculations for the transverse
Ising chain with up to N=256 spins at criticality, using periodic boundary
conditions and D*D matrices with D up to 48. The computational cost of our
scheme formally scales as ND^3, whereas standard MPS approaches and the related
density matrix renromalization group method scale as ND^5 and ND^6,
respectively, for periodic systems.Comment: 4+ pages, 2 figures. v2: improved data, comparisons with exact
results, to appear in Phys Rev Let
Characterization of non-local gates
A non-local unitary transformation of two qubits occurs when some Hamiltonian
interaction couples them. Here we characterize the amount, as measured by time,
of interaction required to perform two--qubit gates, when also arbitrarily
fast, local unitary transformations can be applied on each qubit. The minimal
required time of interaction, or interaction cost, defines an operational
notion of the degree of non--locality of gates. We characterize a partial order
structure based on this notion. We also investigate the interaction cost of
several communication tasks, and determine which gates are able to accomplish
them. This classifies two--qubit gates into four categories, differing in their
capability to transmit classical, as well as quantum, bits of information.Comment: revtex, 14 pages, no pictures; proof of result 1 simplified
significantl
Optimal simulation of two-qubit Hamiltonians using general local operations
We consider the simulation of the dynamics of one nonlocal Hamiltonian by
another, allowing arbitrary local resources but no entanglement nor classical
communication. We characterize notions of simulation, and proceed to focus on
deterministic simulation involving one copy of the system. More specifically,
two otherwise isolated systems and interact by a nonlocal Hamiltonian
. We consider the achievable space of Hamiltonians such
that the evolution can be simulated by the interaction
interspersed with local operations. For any dimensions of and , and any
nonlocal Hamiltonians and , there exists a scale factor such that
for all times the evolution can be simulated by acting for
time interspersed with local operations. For 2-qubit Hamiltonians and
, we calculate the optimal and give protocols achieving it. The optimal
protocols do not require local ancillas, and can be understood geometrically in
terms of a polyhedron defined by a partial order on the set of 2-qubit
Hamiltonians.Comment: (1) References to related work, (2) protocol to simulate one
two-qudit Hamiltonian with another, and (3) other related results added. Some
proofs are simplifie
Entanglement capabilities of non-local Hamiltonians
We quantify the capability of creating entanglement for a general physical
interaction acting on two qubits. We give a procedure for optimizing the
generation of entanglement. We also show that a Hamiltonian can create more
entanglement if one uses auxiliary systems.Comment: replaced with published version, 4 pages, no figure
Reversible combination of inequivalent kinds of multipartite entanglement
We present a family of tri-partite entangled states that, in an asymptotical sense, can be reversibly converted into EPR states shared by only two of parties (say B and C), and tripartite GHZ states. Thus we show that bipartite and genuine tripartite entanglement can be reversibly combined in several copies of a single tripartite state. For such states the corresponding fractions of GHZ and of EPR states represent a complete quantification of their (asymptotical) entanglement resources. More generally, we show that the three different kinds of bipartite entanglement (AB, AC and BC EPR states) and tripartite GHZ entanglement can be reversibly combined in a single state of three parties. Finally, we generalize this result to any number of parties
Properties of Entanglement Monotones for Three-Qubit Pure States
Various parameterizations for the orbits under local unitary transformations
of three-qubit pure states are analyzed. The interconvertibility, symmetry
properties, parameter ranges, calculability and behavior under measurement are
looked at. It is shown that the entanglement monotones of any multipartite pure
state uniquely determine the orbit of that state under local unitary
transformations. It follows that there must be an entanglement monotone for
three-qubit pure states which depends on the Kempe invariant defined in [Phys.
Rev. A 60, 910 (1999)]. A form for such an entanglement monotone is proposed. A
theorem is proved that significantly reduces the number of entanglement
monotones that must be looked at to find the maximal probability of
transforming one multipartite state to another.Comment: 14 pages, REVTe
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