5,120 research outputs found
Neighbours of Einstein's Equations: Connections and Curvatures
Once the action for Einstein's equations is rewritten as a functional of an
SO(3,C) connection and a conformal factor of the metric, it admits a family of
``neighbours'' having the same number of degrees of freedom and a precisely
defined metric tensor. This paper analyzes the relation between the Riemann
tensor of that metric and the curvature tensor of the SO(3) connection. The
relation is in general very complicated. The Einstein case is distinguished by
the fact that two natural SO(3) metrics on the GL(3) fibers coincide. In the
general case the theory is bimetric on the fibers.Comment: 16 pages, LaTe
Galois Unitaries, Mutually Unbiased Bases, and MUB-balanced states
A Galois unitary is a generalization of the notion of anti-unitary operators.
They act only on those vectors in Hilbert space whose entries belong to some
chosen number field. For Mutually Unbiased Bases the relevant number field is a
cyclotomic field. By including Galois unitaries we are able to remove a
mismatch between the finite projective group acting on the bases on the one
hand, and the set of those permutations of the bases that can be implemented as
transformations in Hilbert space on the other hand. In particular we show that
there exist transformations that cycle through all the bases in every dimension
which is an odd power of an odd prime. (For even primes unitary MUB-cyclers
exist.) These transformations have eigenvectors, which are MUB-balanced states
(i.e. rotationally symmetric states in the original terminology of Wootters and
Sussman) if and only if d = 3 modulo 4. We conjecture that this construction
yields all such states in odd prime power dimension.Comment: 32 pages, 2 figures, AMS Latex. Version 2: minor improvements plus a
few additional reference
A trick for passing degenerate points in Ashtekar formulation
We examine one of the advantages of Ashtekar's formulation of general
relativity: a tractability of degenerate points from the point of view of
following the dynamics of classical spacetime. Assuming that all dynamical
variables are finite, we conclude that an essential trick for such a continuous
evolution is in complexifying variables. In order to restrict the complex
region locally, we propose some `reality recovering' conditions on spacetime.
Using a degenerate solution derived by pull-back technique, and integrating the
dynamical equations numerically, we show that this idea works in an actual
dynamical problem. We also discuss some features of these applications.Comment: 9 pages by RevTeX or 16 pages by LaTeX, 3 eps figures and epsf-style
file are include
Spectra of phase point operators in odd prime dimensions and the extended Clifford group
We analyse the role of the Extended Clifford group in classifying the spectra
of phase point operators within the framework laid out by Gibbons et al for
setting up Wigner distributions on discrete phase spaces based on finite
fields. To do so we regard the set of all the discrete phase spaces as a
symplectic vector space over the finite field. Auxiliary results include a
derivation of the conjugacy classes of .Comment: Latex, 19page
Manifest Duality in Born-Infeld Theory
Born-Infeld theory is formulated using an infinite set of gauge fields, along
the lines of McClain, Wu and Yu. In this formulation electromagnetic duality is
generated by a fully local functional. The resulting consistency problems are
analyzed and the formulation is shown to be consistent.Comment: 15 pages, Late
The monomial representations of the Clifford group
We show that the Clifford group - the normaliser of the Weyl-Heisenberg group
- can be represented by monomial phase-permutation matrices if and only if the
dimension is a square number. This simplifies expressions for SIC vectors, and
has other applications to SICs and to Mutually Unbiased Bases. Exact solutions
for SICs in dimension 16 are presented for the first time.Comment: Additional author and exact solutions to the SIC problem in dimension
16 adde
Ancilla-assisted sequential approximation of nonlocal unitary operations
We consider the recently proposed "no-go" theorem of Lamata et al [Phys. Rev.
Lett. 101, 180506 (2008)] on the impossibility of sequential implementation of
global unitary operations with the aid of an itinerant ancillary system and
view the claim within the language of Kraus representation. By virtue of an
extremely useful tool for analyzing entanglement properties of quantum
operations, namely, operator-Schmidt decomposition, we provide alternative
proof to the "no-go" theorem and also study the role of initial correlations
between the qubits and ancilla in sequential preparation of unitary entanglers.
Despite the negative response from the "no-go" theorem, we demonstrate
explicitly how the matrix-product operator(MPO) formalism provides a flexible
structure to develop protocols for sequential implementation of such entanglers
with an optimal fidelity. The proposed numerical technique, that we call
variational matrix-product operator (VMPO), offers a computationally efficient
tool for characterizing the "globalness" and entangling capabilities of
nonlocal unitary operations.Comment: Slightly improved version as published in Phys. Rev.
Analysis of complete positivity conditions for quantum qutrit channels
We present an analysis of complete positivity (CP) constraints on qutrit
quantum channels that have a form of affine transformations of generalized
Bloch vector. For diagonal (damping) channels we derive conditions analogous to
the ones that in qubit case produce tetrahedron structure in the channel
parameter space.Comment: 12 pages, 8 figures (.eps), minor changes in the text and formula
Disentanglement of two harmonic oscillators in relativistic motion
We study the dynamics of quantum entanglement between two Unruh-DeWitt
detectors, one stationary (Alice), and another uniformly accelerating (Rob),
with no direct interaction but coupled to a common quantum field in (3+1)D
Minkowski space. We find that for all cases studied the initial entanglement
between the detectors disappears in a finite time ("sudden death"). After the
moment of total disentanglement the correlations between the two detectors
remain nonzero until late times. The relation between the disentanglement time
and Rob's proper acceleration is observer dependent. The larger the
acceleration is, the longer the disentanglement time in Alice's coordinate, but
the shorter in Rob's coordinate.Comment: 16 pages, 8 figures; typos added, minor changes in Secs. I and
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