801 research outputs found
Virtual Quantum Subsystems
The physical resources available to access and manipulate the degrees of
freedom of a quantum system define the set of operationally relevant
observables. The algebraic structure of selects a preferred tensor
product structure i.e., a partition into subsystems. The notion of compoundness
for quantum system is accordingly relativized. Universal control over virtual
subsystems can be achieved by using quantum noncommutative holonomiesComment: Presentation improved, to appear in PRL. 4 Pages, RevTe
Ground-State Entanglement in Interacting Bosonic Graphs
We consider a collection of bosonic modes corresponding to the vertices of a
graph Quantum tunneling can occur only along the edges of
and a local self-interaction term is present. Quantum entanglement of one
vertex with respect the rest of the graph is analyzed in the ground-state of
the system as a function of the tunneling amplitude The topology of
plays a major role in determining the tunneling amplitude
which leads to the maximum ground-state entanglement. Whereas in most of the
cases one finds the intuitively expected result we show that it
there exists a family of graphs for which the optimal value of is pushed
down to a finite value. We also show that, for complete graphs, our bi-partite
entanglement provides useful insights in the analysis of the cross-over between
insulating and superfluid ground statesComment: 5 pages (LaTeX) 5 eps figures include
Refocusing schemes for holonomic quantum computation in presence of dissipation
The effects of dissipation on a holonomic quantum computation scheme are
analyzed within the quantum-jump approach. We extend to the non-Abelian case
the refocusing strategies formerly introduced for (Abelian) geometric
computation. We show how double loop symmetrization schemes allow one to get
rid of the unwanted influence of dissipation in the no-jump trajectory.Comment: 4 pages, revtex
Universal control of quantum subspaces and subsystems
We describe a broad dynamical-algebraic framework for analyzing the quantum
control properties of a set of naturally available interactions. General
conditions under which universal control is achieved over a set of
subspaces/subsystems are found. All known physical examples of universal
control on subspaces/systems are related to the framework developed here.Comment: 4 Pages RevTeX, Some typos fixed, references adde
Subdecoherent Information Encoding in a Quantum-Dot Array
A potential implementation of quantum-information schemes in semiconductor
nanostructures is studied. To this end, the formal theory of quantum encoding
for avoiding errors is recalled and the existence of noiseless states for model
systems is discussed. Based on this theoretical framework, we analyze the
possibility of designing noiseless quantum codes in realistic semiconductor
structures. In the specific implementation considered, information is encoded
in the lowest energy sector of charge excitations of a linear array of quantum
dots. The decoherence channel considered is electron-phonon coupling We show
that besides the well-known phonon bottleneck, reducing single-qubit
decoherence, suitable many-qubit initial preparation as well as register design
may enhance the decoherence time by several orders of magnitude. This behaviour
stems from the effective one-dimensional character of the phononic environment
in the relevant region of physical parameters.Comment: 12 pages LaTeX, 5 postscript figures. Final version accepted by PR
A generalization of Schur-Weyl duality with applications in quantum estimation
Schur-Weyl duality is a powerful tool in representation theory which has many
applications to quantum information theory. We provide a generalization of this
duality and demonstrate some of its applications. In particular, we use it to
develop a general framework for the study of a family of quantum estimation
problems wherein one is given n copies of an unknown quantum state according to
some prior and the goal is to estimate certain parameters of the given state.
In particular, we are interested to know whether collective measurements are
useful and if so to find an upper bound on the amount of entanglement which is
required to achieve the optimal estimation. In the case of pure states, we show
that commutativity of the set of observables that define the estimation problem
implies the sufficiency of unentangled measurements.Comment: The published version, Typos corrected, 40 pages, 2 figure
Internal Consistency of Fault-Tolerant Quantum Error Correction in Light of Rigorous Derivations of the Quantum Markovian Limit
We critically examine the internal consistency of a set of minimal
assumptions entering the theory of fault-tolerant quantum error correction for
Markovian noise. These assumptions are: fast gates, a constant supply of fresh
and cold ancillas, and a Markovian bath. We point out that these assumptions
may not be mutually consistent in light of rigorous formulations of the
Markovian approximation. Namely, Markovian dynamics requires either the
singular coupling limit (high temperature), or the weak coupling limit (weak
system-bath interaction). The former is incompatible with the assumption of a
constant and fresh supply of cold ancillas, while the latter is inconsistent
with fast gates. We discuss ways to resolve these inconsistencies. As part of
our discussion we derive, in the weak coupling limit, a new master equation for
a system subject to periodic driving.Comment: 19 pages. v2: Significantly expanded version. New title. Includes a
debate section in response to comments on the previous version, many of which
appeared here http://dabacon.org/pontiff/?p=959 and here
http://dabacon.org/pontiff/?p=1028. Contains a new derivation of the
Markovian master equation with periodic drivin
Theory of Decoherence-Free Fault-Tolerant Universal Quantum Computation
Universal quantum computation on decoherence-free subspaces and subsystems
(DFSs) is examined with particular emphasis on using only physically relevant
interactions. A necessary and sufficient condition for the existence of
decoherence-free (noiseless) subsystems in the Markovian regime is derived here
for the first time. A stabilizer formalism for DFSs is then developed which
allows for the explicit understanding of these in their dual role as quantum
error correcting codes. Conditions for the existence of Hamiltonians whose
induced evolution always preserves a DFS are derived within this stabilizer
formalism. Two possible collective decoherence mechanisms arising from
permutation symmetries of the system-bath coupling are examined within this
framework. It is shown that in both cases universal quantum computation which
always preserves the DFS (*natural fault-tolerant computation*) can be
performed using only two-body interactions. This is in marked contrast to
standard error correcting codes, where all known constructions using one or
two-body interactions must leave the codespace during the on-time of the
fault-tolerant gates. A further consequence of our universality construction is
that a single exchange Hamiltonian can be used to perform universal quantum
computation on an encoded space whose asymptotic coding efficiency is unity.
The exchange Hamiltonian, which is naturally present in many quantum systems,
is thus *asymptotically universal*.Comment: 40 pages (body: 30, appendices: 3, figures: 5, references: 2). Fixed
problem with non-printing figures. New references added, minor typos
correcte
Thermal entanglement in three-qubit Heisenberg models
We study pairwise thermal entanglement in three-qubit Heisenberg models and
obtain analytic expressions for the concurrence. We find that thermal
entanglement is absent from both the antiferromagnetic model, and the
ferromagnetic model with anisotropy parameter . Conditions
for the existence of thermal entanglement are discussed in detail, as is the
role of degeneracy and the effects of magnetic fields on thermal entanglement
and the quantum phase transition. Specifically, we find that the magnetic field
can induce entanglement in the antiferromagnetic model, but cannot induce
entanglement in the ferromagnetic model.Comment: 9 pages, 6 figures, minor revisions, resubmitted to J. Phys.
Quantum entanglement in states generated by bilocal group algebras
Given a finite group G with a bilocal representation, we investigate the
bipartite entanglement in the state constructed from the group algebra of G
acting on a separable reference state. We find an upper bound for the von
Neumann entropy for a bipartition (A,B) of a quantum system and conditions to
saturate it. We show that these states can be interpreted as ground states of
generic Hamiltonians or as the physical states in a quantum gauge theory and
that under specific conditions their geometric entropy satisfies the entropic
area law. If G is a group of spin flips acting on a set of qubits, these states
are locally equivalent to 2-colorable (i.e., bipartite) graph states and they
include GHZ, cluster states etc. Examples include an application to qudits and
a calculation of the n-tangle for 2-colorable graph states.Comment: 9 pages, no figs; updated to the published versio
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