649 research outputs found
Efficient measurements, purification, and bounds on the mutual information
When a measurement is made on a quantum system in which classical information
is encoded, the measurement reduces the observers average Shannon entropy for
the encoding ensemble. This reduction, being the {\em mutual information}, is
always non-negative. For efficient measurements the state is also purified;
that is, on average, the observers von Neumann entropy for the state of the
system is also reduced by a non-negative amount. Here we point out that by
re-writing a bound derived by Hall [Phys. Rev. A {\bf 55}, 100 (1997)], which
is dual to the Holevo bound, one finds that for efficient measurements, the
mutual information is bounded by the reduction in the von Neumann entropy. We
also show that this result, which provides a physical interpretation for Hall's
bound, may be derived directly from the Schumacher-Westmoreland-Wootters
theorem [Phys. Rev. Lett. {\bf 76}, 3452 (1996)]. We discuss these bounds, and
their relationship to another bound, valid for efficient measurements on pure
state ensembles, which involves the subentropy.Comment: 4 pages, Revtex4. v3: rewritten and reinterpreted somewha
Universality of optimal measurements
We present optimal and minimal measurements on identical copies of an unknown
state of a qubit when the quality of measuring strategies is quantified with
the gain of information (Kullback of probability distributions). We also show
that the maximal gain of information occurs, among isotropic priors, when the
state is known to be pure. Universality of optimal measurements follows from
our results: using the fidelity or the gain of information, two different
figures of merits, leads to exactly the same conclusions. We finally
investigate the optimal capacity of copies of an unknown state as a quantum
channel of information.Comment: Revtex, 5 pages, no figure
Experimental Proposal for Achieving Superadditive Communication Capacities with a Binary Quantum Alphabet
We demonstrate superadditivity in the communication capacity of a binary
alphabet consisting of two nonorthogonal quantum states. For this scheme,
collective decoding is performed two transmissions at a time. This improves
upon the previous schemes of Sasaki et al. [Phys. Rev. A 58, 146 (1998)] where
superadditivity was not achieved until a decoding of three or more
transmissions at a time. This places superadditivity within the regime of a
near-term laboratory demonstration. We propose an experimental test based upon
an alphabet of low photon-number coherent states where the signal decoding is
done with atomic state measurements on a single atom in a high-finesse optical
cavity.Comment: 7 pages, 5 figure
Phase covariant quantum cloning
We consider an N -> M quantum cloning transformation acting on pure two-level
states lying on the equator of the Bloch sphere. An upper bound for its
fidelity is presented, by establishing a connection between optimal phase
covariant cloning and phase estimation. We give the explicit form of a cloning
transformation that achieves the bound for the case N=1, M=2, and find a link
between this case and optimal eavesdropping in the quantum cryptographic scheme
BB84.Comment: 9 pages, 1 figur
Criteria for flatness and injectivity
Let be a commutative Noetherian ring. We give criteria for flatness of
-modules in terms of associated primes and torsion-freeness of certain
tensor products. This allows us to develop a criterion for regularity if
has characteristic , or more generally if it has a locally contracting
endomorphism. Dualizing, we give criteria for injectivity of -modules in
terms of coassociated primes and (h-)divisibility of certain \Hom-modules.
Along the way, we develop tools to achieve such a dual result. These include a
careful analysis of the notions of divisibility and h-divisibility (including a
localization result), a theorem on coassociated primes across a \Hom-module
base change, and a local criterion for injectivity.Comment: 19 page
Universal geometric approach to uncertainty, entropy and information
It is shown that for any ensemble, whether classical or quantum, continuous
or discrete, there is only one measure of the "volume" of the ensemble that is
compatible with several basic geometric postulates. This volume measure is thus
a preferred and universal choice for characterising the inherent spread,
dispersion, localisation, etc, of the ensemble. Remarkably, this unique
"ensemble volume" is a simple function of the ensemble entropy, and hence
provides a new geometric characterisation of the latter quantity. Applications
include unified, volume-based derivations of the Holevo and Shannon bounds in
quantum and classical information theory; a precise geometric interpretation of
thermodynamic entropy for equilibrium ensembles; a geometric derivation of
semi-classical uncertainty relations; a new means for defining classical and
quantum localization for arbitrary evolution processes; a geometric
interpretation of relative entropy; and a new proposed definition for the
spot-size of an optical beam. Advantages of the ensemble volume over other
measures of localization (root-mean-square deviation, Renyi entropies, and
inverse participation ratio) are discussed.Comment: Latex, 38 pages + 2 figures; p(\alpha)->1/|T| in Eq. (72) [Eq. (A10)
of published version
Retrodiction of Generalised Measurement Outcomes
If a generalised measurement is performed on a quantum system and we do not
know the outcome, are we able to retrodict it with a second measurement? We
obtain a necessary and sufficient condition for perfect retrodiction of the
outcome of a known generalised measurement, given the final state, for an
arbitrary initial state. From this, we deduce that, when the input and output
Hilbert spaces have equal (finite) dimension, it is impossible to perfectly
retrodict the outcome of any fine-grained measurement (where each POVM element
corresponds to a single Kraus operator) for all initial states unless the
measurement is unitarily equivalent to a projective measurement. It also
enables us to show that every POVM can be realised in such a way that perfect
outcome retrodiction is possible for an arbitrary initial state when the number
of outcomes does not exceed the output Hilbert space dimension. We then
consider the situation where the initial state is not arbitrary, though it may
be entangled, and describe the conditions under which unambiguous outcome
retrodiction is possible for a fine-grained generalised measurement. We find
that this is possible for some state if the Kraus operators are linearly
independent. This condition is also necessary when the Kraus operators are
non-singular. From this, we deduce that every trace-preserving quantum
operation is associated with a generalised measurement whose outcome is
unambiguously retrodictable for some initial state, and also that a set of
unitary operators can be unambiguously discriminated iff they are linearly
independent. We then examine the issue of unambiguous outcome retrodiction
without entanglement. This has important connections with the theory of locally
linearly dependent and locally linearly independent operators.Comment: To appear in Physical Review
Quantum Open-Closed Homotopy Algebra and String Field Theory
We reformulate the algebraic structure of Zwiebach's quantum open-closed
string field theory in terms of homotopy algebras. We call it the quantum
open-closed homotopy algebra (QOCHA) which is the generalization of the
open-closed homotopy algebra (OCHA) of Kajiura and Stasheff. The homotopy
formulation reveals new insights about deformations of open string field theory
by closed string backgrounds. In particular, deformations by Maurer Cartan
elements of the quantum closed homotopy algebra define consistent quantum open
string field theories.Comment: 36 pages, fixed typos and small clarifications adde
Equation of State for Hot and Dense Matter: -- Model with Scaled Hadron Masses and Couplings
The proposed earlier relativistic mean-field model with hadron masses and
coupling constants depending on the -meson field is generalized to
finite temperatures. Within this approach we simulate the in-medium behavior of
the hadron masses motivated by the Brown-Rho scaling. The high-lying baryon
resonances and boson excitations as well as excitations of the ,
and fields interacting via mean fields are incorporated into
this scheme. Thermodynamic properties of hot and dense hadronic matter are
elaborated with the constructed equation of state. Even at zero baryon density,
effective masses of --- excitations abruptly drop down
for T\gsim 170 MeV and reach zero at a critical temperature
MeV. Below (at MeV) the
specific heat gets a peak like at crossover. We demonstrate that our EoS can be
matched with that computed on the lattice for high temperatures provided the
baryon resonance couplings with nucleon are partially suppressed. In this case
the quark liquid would masquerade as the hadron one. The model is applied to
description of heavy ion collisions in a broad collision energy range. It might
be especially helpful for studying phase diagram in the region near possible
phase transitions.Comment: 53 pages, 16 figures; minor changes made, references adde
Magnetic Oscillations in Dense Cold Quark Matter with Four-Fermion Interactions
The phase structures of Nambu-Jona-Lasinio models with one or two flavours
have been investigated at non-zero values of and , where is an
external magnetic field and is the chemical potential. In the phase
portraits of both models there arise infinitely many massless chirally
symmetric phases, as well as massive ones with spontaneously broken chiral
invariance, reflecting the existence of infinitely many Landau levels. Phase
transitions of first and second orders and a lot of tricritical points have
been shown to exist in phase diagrams. In the massless case, such a phase
structure leads unavoidably to the standard van Alphen-de Haas magnetic
oscillations of some thermodynamical quantities, including magnetization,
pressure and particle density. In the massive case we have found an oscillating
behaviour not only for thermodynamical quantities, but also for a dynamical
quantity as the quark mass. Besides, in this case we have non-standard, i.e.
non-periodic, magnetic oscillations, since the frequency of oscillations is an
-dependent quantity.Comment: latex, 29 pages, 8 figure
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