46,954 research outputs found
The trumping relation and the structure of the bipartite entangled states
The majorization relation has been shown to be useful in classifying which
transformations of jointly held quantum states are possible using local
operations and classical communication. In some cases, a direct transformation
between two states is not possible, but it becomes possible in the presence of
another state (known as a catalyst); this situation is described mathematically
by the trumping relation, an extension of majorization. The structure of the
trumping relation is not nearly as well understood as that of majorization. We
give an introduction to this subject and derive some new results. Most notably,
we show that the dimension of the required catalyst is in general unbounded;
there is no integer such that it suffices to consider catalysts of
dimension or less in determining which states can be catalyzed into a given
state. We also show that almost all bipartite entangled states are potentially
useful as catalysts.Comment: 7 pages, RevTe
Monotonicity of quantum relative entropy revisited
Monotonicity under coarse-graining is a crucial property of the quantum
relative entropy. The aim of this paper is to investigate the condition of
equality in the monotonicity theorem and in its consequences such as the strong
sub-additivity of the von Neumann entropy, the Golden-Thompson trace inequality
and the monotonicity of the Holevo quantity.The relation to quantum Markovian
states is briefly indicated.Comment: 13 pages, LATEX fil
Entanlement-Assisted Classical Capacity of Quantum Channels with Correlated Noise
We calculate the entanglement-assisted classical capacity of symmetric and
asymmetric Pauli channels where two consecutive uses of the channels are
correlated. It is evident from our study that in the presence of memory, a
higher amount of classical information is transmitted over quantum channels if
there exists prior entanglement as compared to product and entangled state
coding.Comment: 8 Pages, 2 Figure
The Global Anomaly Through Level Circling
We discuss a novel manifestation of the global anomaly in an
gauge theory with an odd number of chiral quark doublets and arbitrary Yukawa
couplings. We argue that the massive 4-dim.() Euclidean Dirac operator is
nonhermitean with its spectrum of eigenvalues lying in
pairs in the complex plane. Consequently the existence of an odd number of
normalizable zero modes of the 5-dim.() massive Dirac operator is
equivalent to a fermionic level exchange phenomenon, level ``circling'', under
continuous topologically nontrivial deformations of the external gauge field.
More generally global anomalies are a manifestation of fermionic level
``circling'' in any gauge theory with an odd number of massive
fermions in the spinor representation and arbitrary Yukawa couplings.Comment: 14 pages, NBI-HE-93-5
On sphaleron deformations induced by Yukawa interactions
Due to the presence of the chiral anomaly sphalerons with Chern-Simons number
a half (CS=1/2) are the only static configurations that allow for a fermion
level crossing in the two-dimensional Abelian-Higgs model with massless
fermions, i.e. in the absence of Yukawa interactions. In the presence of
fermion-Higgs interactions we demonstrate the existence of zero energy
solutions to the one-dimensional Dirac equation at deformed sphalerons with
CS Induced level crossing due to Yukawa interactions illustrates a
non-trivial generalization of the Atiyah-Patodi-Singer index theorem and of the
equivalence between parity anomaly in odd and the chiral anomaly in even
dimensions. We discuss a subtle manifestation of this effect in the standard
electroweak theory at finite temperatures.Comment: 14 pages, Latex, NBI-HE-93-7
Standard Model and Graviweak Unification with (Super)Renormalizable Gravity. Part I: Visible and Invisible Sectors of the Universe
We develop a self-consistent -invariant model of the unification
of gravity with weak gauge and Higgs fields in the visible and
invisible sectors of our Universe. We consider a general case of the graviweak
unification, including the higher-derivative super-renormalizable theory of
gravity, which is a unitary, asymptotically-free and perturbatively consistent
theory of the quantum gravity.Comment: 27 page
Six-qubit permutation-based decoherence-free orthogonal basis
There is a natural orthogonal basis of the 6-qubit decoherence-free (DF)
space robust against collective noise. Interestingly, most of the basis states
can be obtained from one another just permuting qubits. This property: (a) is
useful for encoding qubits in DF subspaces, (b) allows the implementation of
the Bennett-Brassard 1984 (BB84) protocol in DF subspaces just permuting
qubits, which completes a the method for quantum key distribution using DF
states proposed by Boileau et al. [Phys. Rev. Lett. 92, 017901 (2004)], and (c)
points out that there is only one 6-qubit DF state which is essentially new
(not obtained by permutations) and therefore constitutes an interesting
experimental challenge.Comment: REVTeX4, 5 page
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