837 research outputs found
Quantum Probability from Decision Theory?
In a recent paper (quant-ph/9906015), Deutsch claims to derive the
"probabilistic predictions of quantum theory" from the "non-probabilistic
axioms of quantum theory" and the "non-probabilistic part of classical decision
theory." We show that his derivation fails because it includes hidden
probabilistic assumptions.Comment: LaTeX, 8 pages, no figure
Hamiltonian Oracles
Hamiltonian oracles are the continuum limit of the standard unitary quantum
oracles. In this limit, the problem of finding the optimal query algorithm can
be mapped into the problem of finding shortest paths on a manifold. The study
of these shortest paths leads to lower bounds of the original unitary oracle
problem. A number of example Hamiltonian oracles are studied in this paper,
including oracle interrogation and the problem of computing the XOR of the
hidden bits. Both of these problems are related to the study of geodesics on
spheres with non-round metrics. For the case of two hidden bits a complete
description of the geodesics is given. For n hidden bits a simple lower bound
is proven that shows the problems require a query time proportional to n, even
in the continuum limit. Finally, the problem of continuous Grover search is
reexamined leading to a modest improvement to the protocol of Farhi and
Gutmann.Comment: 16 pages, REVTeX 4 (minor corrections in v2
Generalization of entanglement to convex operational theories: Entanglement relative to a subspace of observables
We define what it means for a state in a convex cone of states on a space of
observables to be generalized-entangled relative to a subspace of the
observables, in a general ordered linear spaces framework for operational
theories. This extends the notion of ordinary entanglement in quantum
information theory to a much more general framework. Some important special
cases are described, in which the distinguished observables are subspaces of
the observables of a quantum system, leading to results like the identification
of generalized unentangled states with Lie-group-theoretic coherent states when
the special observables form an irreducibly represented Lie algebra. Some open
problems, including that of generalizing the semigroup of local operations with
classical communication to the convex cones setting, are discussed.Comment: 19 pages, to appear in proceedings of Quantum Structures VII, Int. J.
Theor. Phy
Separable balls around the maximally mixed multipartite quantum states
We show that for an m-partite quantum system, there is a ball of radius
2^{-(m/2-1)} in Frobenius norm, centered at the identity matrix, of separable
(unentangled) positive semidefinite matrices. This can be used to derive an
epsilon below which mixtures of epsilon of any density matrix with 1 - epsilon
of the maximally mixed state will be separable. The epsilon thus obtained is
exponentially better (in the number of systems) than existing results. This
gives a number of qubits below which NMR with standard pseudopure-state
preparation techniques can access only unentangled states; with parameters
realistic for current experiments, this is 23 qubits (compared to 13 qubits via
earlier results). A ball of radius 1 is obtained for multipartite states
separable over the reals.Comment: 8 pages, LaTe
Generalized remote state preparation: Trading cbits, qubits and ebits in quantum communication
We consider the problem of communicating quantum states by simultaneously
making use of a noiseless classical channel, a noiseless quantum channel and
shared entanglement. We specifically study the version of the problem in which
the sender is given knowledge of the state to be communicated. In this setting,
a trade-off arises between the three resources, some portions of which have
been investigated previously in the contexts of the quantum-classical trade-off
in data compression, remote state preparation and superdense coding of quantum
states, each of which amounts to allowing just two out of these three
resources. We present a formula for the triple resource trade-off that reduces
its calculation to evaluating the data compression trade-off formula. In the
process, we also construct protocols achieving all the optimal points. These
turn out to be achievable by trade-off coding and suitable time-sharing between
optimal protocols for cases involving two resources out of the three mentioned
above.Comment: 15 pages, 2 figures, 1 tabl
Indeterminate-length quantum coding
The quantum analogues of classical variable-length codes are
indeterminate-length quantum codes, in which codewords may exist in
superpositions of different lengths. This paper explores some of their
properties. The length observable for such codes is governed by a quantum
version of the Kraft-McMillan inequality. Indeterminate-length quantum codes
also provide an alternate approach to quantum data compression.Comment: 32 page
Direct evaluation of pure graph state entanglement
We address the question of quantifying entanglement in pure graph states.
Evaluation of multipartite entanglement measures is extremely hard for most
pure quantum states. In this paper we demonstrate how solving one problem in
graph theory, namely the identification of maximum independent set, allows us
to evaluate three multipartite entanglement measures for pure graph states. We
construct the minimal linear decomposition into product states for a large
group of pure graph states, allowing us to evaluate the Schmidt measure.
Furthermore we show that computation of distance-like measures such as relative
entropy of entanglement and geometric measure becomes tractable for these
states by explicit construction of closest separable and closest product states
respectively. We show how these separable states can be described using
stabiliser formalism as well as PEPs-like construction. Finally we discuss the
way in which introducing noise to the system can optimally destroy
entanglement.Comment: 23 pages, 9 figure
Linking a distance measure of entanglement to its convex roof
An important problem in quantum information theory is the quantification of
entanglement in multipartite mixed quantum states. In this work, a connection
between the geometric measure of entanglement and a distance measure of
entanglement is established. We present a new expression for the geometric
measure of entanglement in terms of the maximal fidelity with a separable
state. A direct application of this result provides a closed expression for the
Bures measure of entanglement of two qubits. We also prove that the number of
elements in an optimal decomposition w.r.t. the geometric measure of
entanglement is bounded from above by the Caratheodory bound, and we find
necessary conditions for the structure of an optimal decomposition.Comment: 11 pages, 4 figure
The quantum capacity is properly defined without encodings
We show that no source encoding is needed in the definition of the capacity
of a quantum channel for carrying quantum information. This allows us to use
the coherent information maximized over all sources and and block sizes, but
not encodings, to bound the quantum capacity. We perform an explicit
calculation of this maximum coherent information for the quantum erasure
channel and apply the bound in order find the erasure channel's capacity
without relying on an unproven assumption as in an earlier paper.Comment: 19 pages revtex with two eps figures. Submitted to Phys. Rev. A.
Replaced with revised and simplified version, and improved references, etc.
Why can't the last line of the comments field end with a period using this
web submission form
- …