37,264 research outputs found
Why Nature has made a choice of one time and three space coordinates?
We propose a possible answer to one of the most exciting open questions in
physics and cosmology, that is the question why we seem to experience four-
dimensional space-time with three ordinary and one time dimensions. We have
known for more than 70 years that (elementary) particles have spin degrees of
freedom, we also know that besides spin they also have charge degrees of
freedom, both degrees of freedom in addition to the position and momentum
degrees of freedom. We may call these ''internal degrees of freedom '' the
''internal space'' and we can think of all the different particles, like quarks
and leptons, as being different internal states of the same particle. The
question then naturally arises: Is the choice of the Minkowski metric and the
four-dimensional space-time influenced by the ''internal space''?
Making assumptions (such as particles being in first approximation massless)
about the equations of motion, we argue for restrictions on the number of space
and time dimensions. (Actually the Standard model predicts and experiments
confirm that elementary particles are massless until interactions switch on
masses.)
Accepting our explanation of the space-time signature and the number of
dimensions would be a point supporting (further) the importance of the
''internal space''.Comment: 13 pages, LaTe
Optimal purification of a generic n-qudit state
We propose a quantum algorithm for the purification of a generic mixed state
of a -qudit system by using an ancillary -qudit system. The
algorithm is optimal in that (i) the number of ancillary qudits cannot be
reduced, (ii) the number of parameters which determine the purification state
exactly equals the number of degrees of freedom of , and (iii)
is easily determined from the density matrix . Moreover, we
introduce a quantum circuit in which the quantum gates are unitary
transformations acting on a -qudit system. These transformations are
determined by parameters that can be tuned to generate, once the ancillary
qudits are disregarded, any given mixed -qudit state.Comment: 8 pages, 9 figures, remarks adde
Correlations in optically-controlled quantum emitters
We address the problem of optically controlling and quantifying the
dissipative dynamics of quantum and classical correlations in a set-up of
individual quantum emitters under external laser excitation. We show that both
types of correlations, the former measured by the quantum discord, are present
in the system's evolution even though the emitters may exhibit an early stage
disentanglement. In the absence of external laser pumping,we demonstrate
analytically, for a set of suitable initial states, that there is an entropy
bound for which quantum discord and entanglement of the emitters are always
greater than classical correlations, thus disproving an early conjecture that
classical correlations are greater than quantum correlations. Furthermore, we
show that quantum correlations can also be greater than classical correlations
when the system is driven by a laser field. For scenarios where the emitters'
quantum correlations are below their classical counterparts, an optimization of
the evolution of the quantum correlations can be carried out by appropriately
tailoring the amplitude of the laser field and the emitters' dipole-dipole
interaction. We stress the importance of using the entanglement of formation,
rather than the concurrence, as the entanglement measure, since the latter can
grow beyond the total correlations and thus give incorrect results on the
actual system's degree of entanglement.Comment: 11 pages, 10 figures, this version contains minor modifications; to
appear in Phys. Rev.
Operator-Schmidt decompositions and the Fourier transform, with applications to the operator-Schmidt numbers of unitaries
The operator-Schmidt decomposition is useful in quantum information theory
for quantifying the nonlocality of bipartite unitary operations. We construct a
family of unitary operators on C^n tensor C^n whose operator-Schmidt
decompositions are computed using the discrete Fourier transform. As a
corollary, we produce unitaries on C^3 tensor C^3 with operator-Schmidt number
S for every S in {1,...,9}. This corollary was unexpected, since it
contradicted reasonable conjectures of Nielsen et al [Phys. Rev. A 67 (2003)
052301] based on intuition from a striking result in the two-qubit case. By the
results of Dur, Vidal, and Cirac [Phys. Rev. Lett. 89 (2002) 057901
quant-ph/0112124], who also considered the two-qubit case, our result implies
that there are nine equivalence classes of unitaries on C^3 tensor C^3 which
are probabilistically interconvertible by (stochastic) local operations and
classical communication. As another corollary, a prescription is produced for
constructing maximally-entangled operators from biunimodular functions.
Reversing tact, we state a generalized operator-Schmidt decomposition of the
quantum Fourier transform considered as an operator C^M_1 tensor C^M_2 -->
C^N_1 tensor C^N_2, with M_1 x M_2 = N_1 x N_2. This decomposition shows (by
Nielsen's bound) that the communication cost of the QFT remains maximal when a
net transfer of qudits is permitted. In an appendix, a canonical procedure is
given for removing basis-dependence for results and proofs depending on the
"magic basis" introduced in [S. Hill and W. Wootters, "Entanglement of a pair
of quantum bits," Phys Rev. Lett 78 (1997) 5022-5025, quant-ph/9703041 (and
quant-ph/9709029)].Comment: More formal version of my talk at the Simons Conference on Quantum
and Reversible Computation at Stony Brook May 31, 2003. The talk slides and
audio are available at
http://www.physics.sunysb.edu/itp/conf/simons-qcomputation.html. Fixed typos
and minor cosmetic
Gravi-Weak Unification and the Black-Hole-Hedgehog's Solution with Magnetic Field Contribution
In the present paper, we investigated the gravitational black-hole-hedgehog's
solution with magnetic field contribution in the framework of the f(R)--gravity
described by the Gravi-Weak unification model. Assuming the Multiple Point
Principle (MPP), we considered the existence of the two degenerate vacua of the
Universe: the first Electroweak (EW) vacuum with GeV ("true
vacuum"), and the second Planck scale ("false vacuum") with
GeV. In these vacua, we investigated different topological defects. The main
aim of this paper is an investigation of the black-hole-hedgehog configurations
as defects of the "false vacuum". We have obtained the solution which
corresponds to a global monopole, that has been "swallowed" by the black-hole
with core mass and radius
We investigated the metric in
the vicinity of the black-hole-hedgehog and estimated its horizon radius:
. We have considered the phase transition from the
"false vacuum" to the "true vacuum" and confirmed the stability of the
EW--vacuum.Comment: 22 pages. arXiv admin note: text overlap with arXiv:1703.05594,
arXiv:1801.06979, arXiv:1605.01169; text overlap with arXiv:1002.4275 by
other author
Quantum state engineering, purification, and number resolved photon detection with high finesse optical cavities
We propose and analyze a multi-functional setup consisting of high finesse
optical cavities, beam splitters, and phase shifters. The basic scheme projects
arbitrary photonic two-mode input states onto the subspace spanned by the
product of Fock states |n>|n> with n=0,1,2,.... This protocol does not only
provide the possibility to conditionally generate highly entangled photon
number states as resource for quantum information protocols but also allows one
to test and hence purify this type of quantum states in a communication
scenario, which is of great practical importance. The scheme is especially
attractive as a generalization to many modes allows for distribution and
purification of entanglement in networks. In an alternative working mode, the
setup allows of quantum non demolition number resolved photodetection in the
optical domain.Comment: 14 pages, 10 figure
Unstable Modes in Three-Dimensional SU(2) Gauge Theory
We investigate SU(2) gauge theory in a constant chromomagnetic field in three
dimensions both in the continuum and on the lattice. Using a variational method
to stabilize the unstable modes, we evaluate the vacuum energy density in the
one-loop approximation. We compare our theoretical results with the outcomes of
the numerical simulations.Comment: 24 pages, REVTEX 3.0, 3 Postscript figures included. (the whole
postscript file (text+figures) is available on request from
[email protected]
Decoherence-free quantum-information processing using dipole-coupled qubits
We propose a quantum-information processor that consists of decoherence-free
logical qubits encoded into arrays of dipole-coupled qubits. High-fidelity
single-qubit operations are performed deterministically within a
decoherence-free subsystem without leakage via global addressing of bichromatic
laser fields. Two-qubit operations are realized locally with four physical
qubits, and between separated logical qubits using linear optics. We show how
to prepare cluster states using this method. We include all
non-nearest-neighbor effects in our calculations, and we assume the qubits are
not located in the Dicke limit. Although our proposal is general to any system
of dipole-coupled qubits, throughout the paper we use nitrogen-vacancy (NV)
centers in diamond as an experimental context for our theoretical results.Comment: 7 pages, 5 figure
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