1,457 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
On Protected Realizations of Quantum Information
There are two complementary approaches to realizing quantum information so
that it is protected from a given set of error operators. Both involve encoding
information by means of subsystems. One is initialization-based error
protection, which involves a quantum operation that is applied before error
events occur. The other is operator quantum error correction, which uses a
recovery operation applied after the errors. Together, the two approaches make
it clear how quantum information can be stored at all stages of a process
involving alternating error and quantum operations. In particular, there is
always a subsystem that faithfully represents the desired quantum information.
We give a definition of faithful realization of quantum information and show
that it always involves subsystems. This justifies the "subsystems principle"
for realizing quantum information. In the presence of errors, one can make use
of noiseless, (initialization) protectable, or error-correcting subsystems. We
give an explicit algorithm for finding optimal noiseless subsystems. Finding
optimal protectable or error-correcting subsystems is in general difficult.
Verifying that a subsystem is error-correcting involves only linear algebra. We
discuss the verification problem for protectable subsystems and reduce it to a
simpler version of the problem of finding error-detecting codes.Comment: 17 page
Quantum criticality as a resource for quantum estimation
We address quantum critical systems as a resource in quantum estimation and
derive the ultimate quantum limits to the precision of any estimator of the
coupling parameters. In particular, if L denotes the size of a system and
\lambda is the relevant coupling parameters driving a quantum phase transition,
we show that a precision improvement of order 1/L may be achieved in the
estimation of \lambda at the critical point compared to the non-critical case.
We show that analogue results hold for temperature estimation in classical
phase transitions. Results are illustrated by means of a specific example
involving a fermion tight-binding model with pair creation (BCS model).Comment: 7 pages. Revised and extended version. Gained one author and a
specific exampl
Quantum Entanglement in Fermionic Lattices
The Fock space of a system of indistinguishable particles is isomorphic (in a
non-unique way) to the state-space of a composite i.e., many-modes, quantum
system. One can then discuss quantum entanglement for fermionic as well as
bosonic systems. We exemplify the use of this notion -central in quantum
information - by studying some e.g., Hubbard,lattice fermionic models relevant
to condensed matter physics.Comment: 4 Pages LaTeX, 1 TeX Figure. Presentation improved, title changed. To
appear in PR
Spin network setting of topological quantum computation
The spin network simulator model represents a bridge between (generalised)
circuit schemes for standard quantum computation and approaches based on
notions from Topological Quantum Field Theories (TQFTs). The key tool is
provided by the fiber space structure underlying the model which exhibits
combinatorial properties closely related to SU(2) state sum models, widely
employed in discretizing TQFTs and quantum gravity in low spacetime dimensions.Comment: Proc. "Foundations of Quantum Information", Camerino (Italy), 16-19
April 2004, to be published in Int. J. of Quantum Informatio
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
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
Dynamical Generation of Noiseless Quantum Subsystems
We present control schemes for open quantum systems that combine decoupling
and universal control methods with coding procedures. By exploiting a general
algebraic approach, we show how appropriate encodings of quantum states result
in obtaining universal control over dynamically-generated noise-protected
subsystems with limited control resources. In particular, we provide an
efficient scheme for performing universal encoded quantum computation in a wide
class of systems subjected to linear non-Markovian quantum noise and supporting
Heisenberg-type internal Hamiltonians.Comment: 4 pages, no figures; REVTeX styl
Strictly contractive quantum channels and physically realizable quantum computers
We study the robustness of quantum computers under the influence of errors
modelled by strictly contractive channels. A channel is defined to be
strictly contractive if, for any pair of density operators in its
domain, for some (here denotes the trace norm). In other words, strictly
contractive channels render the states of the computer less distinguishable in
the sense of quantum detection theory. Starting from the premise that all
experimental procedures can be carried out with finite precision, we argue that
there exists a physically meaningful connection between strictly contractive
channels and errors in physically realizable quantum computers. We show that,
in the absence of error correction, sensitivity of quantum memories and
computers to strictly contractive errors grows exponentially with storage time
and computation time respectively, and depends only on the constant and the
measurement precision. We prove that strict contractivity rules out the
possibility of perfect error correction, and give an argument that approximate
error correction, which covers previous work on fault-tolerant quantum
computation as a special case, is possible.Comment: 14 pages; revtex, amsfonts, amssymb; made some changes (recommended
by Phys. Rev. A), updated the reference
Quantum entanglement and the self-trapping transition in polaronic systems
We revisit from a quantum-information perspective a classic problem of polaron theory in one dimension. In the context of the Holstein model we show that a simple analysis of quantum entanglement between excitonic and phononic degrees of freedom allows one to effectively characterize both the small and large polaron regimes as well as the crossover in between. The small (large) polaron regime corresponds to a high (low) degree of bipartite quantum entanglement between the exciton and the phonon cloud that clothes the exciton. Moreover, the self-trapping transition is clearly displayed by a sharp drop of exciton-phonon entanglement.published_or_final_versio
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