302 research outputs found
Compatibility of quantum states
We introduce a measure of the compatibility between quantum states--the
likelihood that two density matrices describe the same object. Our measure is
motivated by two elementary requirements, which lead to a natural definition.
We list some properties of this measure, and discuss its relation to the
problem of combining two observers' states of knowledge.Comment: 4 pages, no figure
Conditions for compatibility of quantum state assignments
Suppose N parties describe the state of a quantum system by N possibly
different density operators. These N state assignments represent the beliefs of
the parties about the system. We examine conditions for determining whether the
N state assignments are compatible. We distinguish two kinds of procedures for
assessing compatibility, the first based on the compatibility of the prior
beliefs on which the N state assignments are based and the second based on the
compatibility of predictive measurement probabilities they define. The first
procedure leads to a compatibility criterion proposed by Brun, Finkelstein, and
Mermin [BFM, Phys. Rev. A 65, 032315 (2002)]. The second procedure leads to a
hierarchy of measurement-based compatibility criteria which is fundamentally
different from the corresponding classical situation. Quantum mechanically none
of the measurement-based compatibility criteria is equivalent to the BFM
criterion.Comment: REVTEX 4, 19 pages, 1 postscript figur
Perfect state distinguishability and computational speedups with postselected closed timelike curves
Bennett and Schumacher's postselected quantum teleportation is a model of
closed timelike curves (CTCs) that leads to results physically different from
Deutsch's model. We show that even a single qubit passing through a
postselected CTC (P-CTC) is sufficient to do any postselected quantum
measurement, and we discuss an important difference between "Deutschian" CTCs
(D-CTCs) and P-CTCs in which the future existence of a P-CTC might affect the
present outcome of an experiment. Then, based on a suggestion of Bennett and
Smith, we explicitly show how a party assisted by P-CTCs can distinguish a set
of linearly independent quantum states, and we prove that it is not possible
for such a party to distinguish a set of linearly dependent states. The power
of P-CTCs is thus weaker than that of D-CTCs because the Holevo bound still
applies to circuits using them regardless of their ability to conspire in
violating the uncertainty principle. We then discuss how different notions of a
quantum mixture that are indistinguishable in linear quantum mechanics lead to
dramatically differing conclusions in a nonlinear quantum mechanics involving
P-CTCs. Finally, we give explicit circuit constructions that can efficiently
factor integers, efficiently solve any decision problem in the intersection of
NP and coNP, and probabilistically solve any decision problem in NP. These
circuits accomplish these tasks with just one qubit traveling back in time, and
they exploit the ability of postselected closed timelike curves to create
grandfather paradoxes for invalid answers.Comment: 15 pages, 4 figures; Foundations of Physics (2011
Decoherence can be useful in quantum walks
We present a study of the effects of decoherence in the operation of a
discrete quantum walk on a line, cycle and hypercube. We find high sensitivity
to decoherence, increasing with the number of steps in the walk, as the
particle is becoming more delocalised with each step. However, the effect of a
small amount of decoherence is to enhance the properties of the quantum walk
that are desirable for the development of quantum algorithms. Specifically, we
observe a highly uniform distribution on the line, a very fast mixing time on
the cycle, and more reliable hitting times across the hypercube.Comment: (Imperial College London) 6 (+epsilon) pages, 6 embedded eps figures,
RevTex4. v2 minor changes to correct typos and refs, submitted version. v3
expanded into article format, extra figure, updated refs, Note on "glued
trees" adde
From quantum trajectories to classical orbits
Recently it has been shown that the evolution of open quantum systems may be
``unraveled'' into individual ``trajectories,'' providing powerful numerical
and conceptual tools. In this letter we use quantum trajectories to study
mesoscopic systems and their classical limit. We show that in this limit,
Quantum Jump (QJ) trajectories approach a diffusive limit very similar to the
Quantum State Diffusion (QSD) unraveling. The latter follows classical
trajectories in the classical limit. Hence, both unravelings show the rise of
classical orbits. This is true for both regular and chaotic systems (which
exhibit strange attractors).Comment: 7 pages RevTeX 3.0 + 2 figures (postscript). Submitted to Physical
Review Letter
Discrete-time quantum walks on one-dimensional lattices
In this paper, we study discrete-time quantum walks on one-dimensional
lattices. We find that the coherent dynamics depends on the initial states and
coin parameters. For infinite size of lattice, we derive an explicit expression
for the return probability, which shows scaling behavior
and does not depends on the initial states of the walk. In the long-time limit,
the probability distribution shows various patterns, depending on the initial
states, coin parameters and the lattice size. The average mixing time
closes to the limiting probability in linear (size of the
lattice) for large values of thresholds . Finally, we introduce
another kind of quantum walk on infinite or even-numbered size of lattices, and
show that the walk is equivalent to the traditional quantum walk with
symmetrical initial state and coin parameter.Comment: 17 pages research not
Simulation of quantum random walks using interference of classical field
We suggest a theoretical scheme for the simulation of quantum random walks on
a line using beam splitters, phase shifters and photodetectors. Our model
enables us to simulate a quantum random walk with use of the wave nature of
classical light fields. Furthermore, the proposed set-up allows the analysis of
the effects of decoherence. The transition from a pure mean photon-number
distribution to a classical one is studied varying the decoherence parameters.Comment: extensively revised version; title changed; to appear on Phys. Rev.
Irreversible Quantum Baker Map
We propose a generalization of the model of classical baker map on the torus,
in which the images of two parts of the phase space do overlap. This
transformation is irreversible and cannot be quantized by means of a unitary
Floquet operator. A corresponding quantum system is constructed as a completely
positive map acting in the space of density matrices. We investigate spectral
properties of this super-operator and their link with the increase of the
entropy of initially pure states.Comment: 4 pages, 3 figures include
One-and-a-half quantum de Finetti theorems
We prove a new kind of quantum de Finetti theorem for representations of the
unitary group U(d). Consider a pure state that lies in the irreducible
representation U_{mu+nu} for Young diagrams mu and nu. U_{mu+nu} is contained
in the tensor product of U_mu and U_nu; let xi be the state obtained by tracing
out U_nu. We show that xi is close to a convex combination of states Uv, where
U is in U(d) and v is the highest weight vector in U_mu. When U_{mu+nu} is the
symmetric representation, this yields the conventional quantum de Finetti
theorem for symmetric states, and our method of proof gives near-optimal bounds
for the approximation of xi by a convex combination of product states. For the
class of symmetric Werner states, we give a second de Finetti-style theorem
(our 'half' theorem); the de Finetti-approximation in this case takes a
particularly simple form, involving only product states with a fixed spectrum.
Our proof uses purely group theoretic methods, and makes a link with the
shifted Schur functions. It also provides some useful examples, and gives some
insight into the structure of the set of convex combinations of product states.Comment: 14 pages, 3 figures, v4: minor additions (including figures),
published versio
Protecting Quantum Information with Entanglement and Noisy Optical Modes
We incorporate active and passive quantum error-correcting techniques to
protect a set of optical information modes of a continuous-variable quantum
information system. Our method uses ancilla modes, entangled modes, and gauge
modes (modes in a mixed state) to help correct errors on a set of information
modes. A linear-optical encoding circuit consisting of offline squeezers,
passive optical devices, feedforward control, conditional modulation, and
homodyne measurements performs the encoding. The result is that we extend the
entanglement-assisted operator stabilizer formalism for discrete variables to
continuous-variable quantum information processing.Comment: 7 pages, 1 figur
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