1,853 research outputs found
Generating topological order: no speedup by dissipation
We consider the problem of preparing topologically ordered states using
unitary and non-unitary circuits, as well as local time-dependent Hamiltonian
and Liouvillian evolutions. We prove that for any topological code in
dimensions, the time required to encode logical information into the ground
space is at least , where is the code distance. This
result is tight for the toric code, giving a scaling with the linear system
size. More generally, we show that the linear scaling is necessary even when
dropping the requirement of encoding: preparing any state close to the ground
space using dissipation takes an amount of time proportional to the diameter of
the system in typical 2D topologically ordered systems, as well as for example
the 3D and 4D toric codes.Comment: 7 pages, 1 figur
Anyonic entanglement renormalization
We introduce a family of variational ansatz states for chains of anyons which
optimally exploits the structure of the anyonic Hilbert space. This ansatz is
the natural analog of the multi-scale entanglement renormalization ansatz for
spin chains. In particular, it has the same interpretation as a coarse-graining
procedure and is expected to accurately describe critical systems with
algebraically decaying correlations. We numerically investigate the validity of
this ansatz using the anyonic golden chain and its relatives as a testbed. This
demonstrates the power of entanglement renormalization in a setting with
non-abelian exchange statistics, extending previous work on qudits, bosons and
fermions in two dimensions.Comment: 19 pages, 10 figures, v2: extended, updated to match published
versio
Universal Uhrig dynamical decoupling for bosonic systems
We construct efficient deterministic dynamical decoupling schemes protecting
continuous variable degrees of freedom. Our schemes target decoherence induced
by quadratic system-bath interactions with analytic time-dependence. We show
how to suppress such interactions to -th order using only pulses.
Furthermore, we show to homogenize a -mode bosonic system using only
pulses, yielding - up to -th order - an effective evolution
described by non-interacting harmonic oscillators with identical frequencies.
The decoupled and homogenized system provides natural decoherence-free
subspaces for encoding quantum information. Our schemes only require pulses
which are tensor products of single-mode passive Gaussian unitaries and SWAP
gates between pairs of modes.Comment: 17 pages, 2 figures
Sampling of min-entropy relative to quantum knowledge
Let X_1, ..., X_n be a sequence of n classical random variables and consider
a sample of r positions selected at random. Then, except with (exponentially in
r) small probability, the min-entropy of the sample is not smaller than,
roughly, a fraction r/n of the total min-entropy of all positions X_1, ...,
X_n, which is optimal. Here, we show that this statement, originally proven by
Vadhan [LNCS, vol. 2729, Springer, 2003] for the purely classical case, is
still true if the min-entropy is measured relative to a quantum system. Because
min-entropy quantifies the amount of randomness that can be extracted from a
given random variable, our result can be used to prove the soundness of locally
computable extractors in a context where side information might be
quantum-mechanical. In particular, it implies that key agreement in the
bounded-storage model (using a standard sample-and-hash protocol) is fully
secure against quantum adversaries, thus solving a long-standing open problem.Comment: 48 pages, late
The Bounded Storage Model in The Presence of a Quantum Adversary
An extractor is a function E that is used to extract randomness. Given an
imperfect random source X and a uniform seed Y, the output E(X,Y) is close to
uniform. We study properties of such functions in the presence of prior quantum
information about X, with a particular focus on cryptographic applications. We
prove that certain extractors are suitable for key expansion in the bounded
storage model where the adversary has a limited amount of quantum memory. For
extractors with one-bit output we show that the extracted bit is essentially
equally secure as in the case where the adversary has classical resources. We
prove the security of certain constructions that output multiple bits in the
bounded storage model.Comment: 13 pages Latex, v3: discussion of independent randomizers adde
Matrix product approximations to multipoint functions in two-dimensional conformal field theory
Matrix product states (MPS) illustrate the suitability of tensor networks for
the description of interacting many-body systems: ground states of gapped -D
systems are approximable by MPS as shown by Hastings [J. Stat. Mech. Theor.
Exp., P08024 (2007)]. In contrast, whether MPS and more general tensor networks
can accurately reproduce correlations in critical quantum systems, respectively
quantum field theories, has not been established rigorously. Ample evidence
exists: entropic considerations provide restrictions on the form of suitable
Ansatz states, and numerical studies show that certain tensor networks can
indeed approximate the associated correlation functions. Here we provide a
complete positive answer to this question in the case of MPS and conformal
field theory: we give quantitative estimates for the approximation error when
approximating correlation functions by MPS. Our work is constructive and yields
an explicit MPS, thus providing both suitable initial values as well as a
rigorous justification of variational methods.Comment: 5 pages, 1 figure. See long companion paper arXiv:1509.07414 for full
technical detail
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