5,170 research outputs found
A monomial matrix formalism to describe quantum many-body states
We propose a framework to describe and simulate a class of many-body quantum
states. We do so by considering joint eigenspaces of sets of monomial unitary
matrices, called here "M-spaces"; a unitary matrix is monomial if precisely one
entry per row and column is nonzero. We show that M-spaces encompass various
important state families, such as all Pauli stabilizer states and codes, the
AKLT model, Kitaev's (abelian and non-abelian) anyon models, group coset
states, W states and the locally maximally entanglable states. We furthermore
show how basic properties of M-spaces can transparently be understood by
manipulating their monomial stabilizer groups. In particular we derive a
unified procedure to construct an eigenbasis of any M-space, yielding an
explicit formula for each of the eigenstates. We also discuss the computational
complexity of M-spaces and show that basic problems, such as estimating local
expectation values, are NP-hard. Finally we prove that a large subclass of
M-spaces---containing in particular most of the aforementioned examples---can
be simulated efficiently classically with a unified method.Comment: 11 pages + appendice
Improvement of stabilizer based entanglement distillation protocols by encoding operators
This paper presents a method for enumerating all encoding operators in the
Clifford group for a given stabilizer. Furthermore, we classify encoding
operators into the equivalence classes such that EDPs (Entanglement
Distillation Protocol) constructed from encoding operators in the same
equivalence class have the same performance. By this classification, for a
given parameter, the number of candidates for good EDPs is significantly
reduced. As a result, we find the best EDP among EDPs constructed from [[4,2]]
stabilizer codes. This EDP has a better performance than previously known EDPs
over wide range of fidelity.Comment: 22 pages, 2 figures, In version 2, we enumerate all encoding
operators in the Clifford group, and fix the wrong classification of encoding
operators in version
From qubits to black holes: entropy, entanglement and all that
Entropy plays a crucial role in characterization of information and
entanglement, but it is not a scalar quantity and for many systems it is
different for different relativistic observers. Loop quantum gravity predicts
the Bekenstein-Hawking term for black hole entropy and logarithmic correction
to it. The latter originates in the entanglement between the pieces of spin
networks that describe black hole horizon. Entanglement between gravity and
matter may restore the unitarity in the black hole evaporation process. If the
collapsing matter is assumed to be initially in a pure state, then entropy of
the Hawking radiation is exactly the created entanglement between matter and
gravity.Comment: Honorable Mention in the 2005 Gravity Research Foundation Essay
Competitio
A state variable for crumpled thin sheets
Despite the apparent ease with which a sheet of paper is crumpled and tossed
away, crumpling dynamics are often considered a paradigm of complexity. This
complexity arises from the infinite number of configurations a disordered
crumpled sheet can take. Here we experimentally show that key aspects of
crumpling have a very simple description; the evolution of the damage in
crumpling dynamics can largely be described by a single global quantity, the
total length of all creases. We follow the evolution of the damage network in
repetitively crumpled elastoplastic sheets, and show that the dynamics of this
quantity are deterministic, and depend only on the instantaneous state of the
crease network and not at all on the crumpling history. We also show that this
global quantity captures the crumpling dynamics of a sheet crumpled for the
first time. This leads to a remarkable reduction in complexity, allowing a
description of a highly disordered system by a single state parameter. Similar
strategies may also be useful in analyzing other systems that evolve under
geometric and mechanical constraints, from faulting of tectonic plates to the
evolution of proteins
Encoding a qubit in an oscillator
Quantum error-correcting codes are constructed that embed a
finite-dimensional code space in the infinite-dimensional Hilbert space of a
system described by continuous quantum variables. These codes exploit the
noncommutative geometry of phase space to protect against errors that shift the
values of the canonical variables q and p. In the setting of quantum optics,
fault-tolerant universal quantum computation can be executed on the protected
code subspace using linear optical operations, squeezing, homodyne detection,
and photon counting; however, nonlinear mode coupling is required for the
preparation of the encoded states. Finite-dimensional versions of these codes
can be constructed that protect encoded quantum information against shifts in
the amplitude or phase of a d-state system. Continuous-variable codes can be
invoked to establish lower bounds on the quantum capacity of Gaussian quantum
channels.Comment: 22 pages, 8 figures, REVTeX, title change (qudit -> qubit) requested
by Phys. Rev. A, minor correction
Developing the Deutsch-Hayden approach to quantum mechanics
The formalism of Deutsch and Hayden is a useful tool for describing quantum
mechanics explicitly as local and unitary, and therefore quantum information
theory as concerning a "flow" of information between systems. In this paper we
show that these physical descriptions of flow are unique, and develop the
approach further to include the measurement interaction and mixed states. We
then give an analysis of entanglement swapping in this approach, showing that
it does not in fact contain non-local effects or some form of superluminal
signalling.Comment: 14 pages. Added section on entanglement swappin
Three-intensity decoy state method for device independent quantum key distribution with basis dependent errors
We study the measurement device independent quantum key distribution (MDIQKD)
in practice with limited resource, when there are only 3 different states in
implementing the decoy-state method and when there are basis dependent coding
errors. We present general formulas for the decoy-state method for two-pulse
sources with 3 different states, which can be applied to the recently proposed
MDIQKD with imperfect single-photon source such as the coherent states or the
heralded states from the parametric down conversion. We point out that the
existing result for secure QKD with source coding errors does not always hold.
We find that very accurate source coding is not necessary. In particular, we
loosen the precision of existing result by several magnitude orders for secure
QKD.Comment: Published version with Eq.(17) corrected. We emphasize that our major
result (Eq.16) for the decoy-state part can be applied to generate a key rate
very close to the ideal case of using infinite different coherent states, as
was numerically demonstrated in Ref.[21]. Published in PRA, 2013, Ja
Robust randomized benchmarking of quantum processes
We describe a simple randomized benchmarking protocol for quantum information
processors and obtain a sequence of models for the observable fidelity decay as
a function of a perturbative expansion of the errors. We are able to prove that
the protocol provides an efficient and reliable estimate of an average
error-rate for a set operations (gates) under a general noise model that allows
for both time and gate-dependent errors. We determine the conditions under
which this estimate remains valid and illustrate the protocol through numerical
examples.Comment: 4+ pages, 1 figure, and 1 tabl
A Note on Linear Optics Gates by Post-Selection
Recently it was realized that linear optics and photo-detectors with feedback
can be used for theoretically efficient quantum information processing. The
first of three steps toward efficient linear optics quantum computation (eLOQC)
was to design a simple non-deterministic gate, which upon post-selection based
on a measurement result implements a non-linear phase shift on one mode. Here a
computational strategy is given for finding non-deterministic gates for bosonic
qubits with helper photons. A more efficient conditional sign flip gate is
obtained.Comment: 14 pages. Minor changes for clarit
- …