126 research outputs found
A Simple Algorithm for Local Conversion of Pure States
We describe an algorithm for converting one bipartite quantum state into
another using only local operations and classical communication, which is much
simpler than the original algorithm given by Nielsen [Phys. Rev. Lett. 83, 436
(1999)]. Our algorithm uses only a single measurement by one of the parties,
followed by local unitary operations which are permutations in the local
Schmidt bases.Comment: 5 pages, LaTeX, reference adde
A de Finetti Representation Theorem for Quantum Process Tomography
In quantum process tomography, it is possible to express the experimenter's
prior information as a sequence of quantum operations, i.e., trace-preserving
completely positive maps. In analogy to de Finetti's concept of exchangeability
for probability distributions, we give a definition of exchangeability for
sequences of quantum operations. We then state and prove a representation
theorem for such exchangeable sequences. The theorem leads to a simple
characterization of admissible priors for quantum process tomography and solves
to a Bayesian's satisfaction the problem of an unknown quantum operation.Comment: 10 page
Local Realistic Model for the Dynamics of Bulk-Ensemble NMR Information Processing
We construct a local realistic hidden-variable model that describes the
states and dynamics of bulk-ensemble NMR information processing up to about 12
nuclear spins. The existence of such a model rules out violation of any Bell
inequality, temporal or otherwise, in present high-temperature, liquid-state
NMR experiments. The model does not provide an efficient description in that
the number of hidden variables grows exponentially with the number of nuclear
spins.Comment: REVTEX, 7 page
Quantum computers in phase space
We represent both the states and the evolution of a quantum computer in phase
space using the discrete Wigner function. We study properties of the phase
space representation of quantum algorithms: apart from analyzing important
examples, such as the Fourier Transform and Grover's search, we examine the
conditions for the existence of a direct correspondence between quantum and
classical evolutions in phase space. Finally, we describe how to directly
measure the Wigner function in a given phase space point by means of a
tomographic method that, itself, can be interpreted as a simple quantum
algorithm.Comment: 16 pages, 7 figures, to appear in Phys Rev
Separability of very noisy mixed states and implications for NMR quantum computing
We give a constructive proof that all mixed states of N qubits in a
sufficiently small neighborhood of the maximally mixed state are separable. The
construction provides an explicit representation of any such state as a mixture
of product states. We give upper and lower bounds on the size of the
neighborhood, which show that its extent decreases exponentially with the
number of qubits. We also discuss the implications of the bounds for NMR
quantum computing.Comment: 4 pages, extensively revised, references adde
Quasi-probability representations of quantum theory with applications to quantum information science
This article comprises a review of both the quasi-probability representations
of infinite-dimensional quantum theory (including the Wigner function) and the
more recently defined quasi-probability representations of finite-dimensional
quantum theory. We focus on both the characteristics and applications of these
representations with an emphasis toward quantum information theory. We discuss
the recently proposed unification of the set of possible quasi-probability
representations via frame theory and then discuss the practical relevance of
negativity in such representations as a criteria for quantumness.Comment: v3: typos fixed, references adde
Classical model for bulk-ensemble NMR quantum computation
We present a classical model for bulk-ensemble NMR quantum computation: the
quantum state of the NMR sample is described by a probability distribution over
the orientations of classical tops, and quantum gates are described by
classical transition probabilities. All NMR quantum computing experiments
performed so far with three quantum bits can be accounted for in this classical
model. After a few entangling gates, the classical model suffers an exponential
decrease of the measured signal, whereas there is no corresponding decrease in
the quantum description. We suggest that for small numbers of quantum bits, the
quantum nature of NMR quantum computation lies in the ability to avoid an
exponential signal decrease.Comment: 14 pages, no figures, revte
Hypersensitivity and chaos signatures in the quantum baker's maps
Classical chaotic systems are distinguished by their sensitive dependence on
initial conditions. The absence of this property in quantum systems has lead to
a number of proposals for perturbation-based characterizations of quantum
chaos, including linear growth of entropy, exponential decay of fidelity, and
hypersensitivity to perturbation. All of these accurately predict chaos in the
classical limit, but it is not clear that they behave the same far from the
classical realm. We investigate the dynamics of a family of quantizations of
the baker's map, which range from a highly entangling unitary transformation to
an essentially trivial shift map. Linear entropy growth and fidelity decay are
exhibited by this entire family of maps, but hypersensitivity distinguishes
between the simple dynamics of the trivial shift map and the more complicated
dynamics of the other quantizations. This conclusion is supported by an
analytical argument for short times and numerical evidence at later times.Comment: 32 pages, 6 figure
Quantum computing and information extraction for a dynamical quantum system
We discuss the simulation of a complex dynamical system, the so-called
quantum sawtooth map model, on a quantum computer. We show that a quantum
computer can be used to efficiently extract relevant physical information for
this model. It is possible to simulate the dynamical localization of classical
chaos and extract the localization length of the system with quadratic speed up
with respect to any known classical computation. We can also compute with
algebraic speed up the diffusion coefficient and the diffusion exponent both in
the regimes of Brownian and anomalous diffusion. Finally, we show that it is
possible to extract the fidelity of the quantum motion, which measures the
stability of the system under perturbations, with exponential speed up.Comment: 11 pages, 5 figures, submitted to Quantum Information Processing,
Special Issue devoted to the Physics of Quantum Computin
Quantum nonlinear dynamics of continuously measured systems
Classical dynamics is formulated as a Hamiltonian flow on phase space, while
quantum mechanics is formulated as a unitary dynamics in Hilbert space. These
different formulations have made it difficult to directly compare quantum and
classical nonlinear dynamics. Previous solutions have focussed on computing
quantities associated with a statistical ensemble such as variance or entropy.
However a more direct comparison would compare classical predictions to the
quantum for continuous simultaneous measurement of position and momentum of a
single system. In this paper we give a theory of such measurement and show that
chaotic behaviour in classical systems can be reproduced by continuously
measured quantum systems.Comment: 11 pages, REVTEX, 3 figure
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