70 research outputs found
Parameter estimation with mixed quantum states
We consider quantum enhanced measurements with initially mixed states. We
show very generally that for any linear propagation of the initial state that
depends smoothly on the parameter to be estimated, the sensitivity is bound by
the maximal sensitivity that can be achieved for any of the pure states from
which the initial density matrix is mixed. This provides a very general proof
that purely classical correlations cannot improve the sensitivity of parameter
estimation schemes in quantum enhanced measurement schemes.Comment: 6 page
Perfect quantum error correction coding in 24 laser pulses
An efficient coding circuit is given for the perfect quantum error correction
of a single qubit against arbitrary 1-qubit errors within a 5 qubit code. The
circuit presented employs a double `classical' code, i.e., one for bit flips
and one for phase shifts. An implementation of this coding circuit on an
ion-trap quantum computer is described that requires 26 laser pulses. A further
circuit is presented requiring only 24 laser pulses, making it an efficient
protection scheme against arbitrary 1-qubit errors. In addition, the
performance of two error correction schemes, one based on the quantum Zeno
effect and the other using standard methods, is compared. The quantum Zeno
error correction scheme is found to fail completely for a model of noise based
on phase-diffusion.Comment: Replacement paper: Lost two laser pulses gained one author; added
appendix with circuits easily implementable on an ion-trap compute
Implementation of a Deutsch-like quantum algorithm utilizing entanglement at the two-qubit level, on an NMR quantum information processor
We describe the experimental implementation of a recently proposed quantum
algorithm involving quantum entanglement at the level of two qubits using NMR.
The algorithm solves a generalisation of the Deutsch problem and distinguishes
between even and odd functions using fewer function calls than is possible
classically. The manipulation of entangled states of the two qubits is
essential here, unlike the Deutsch-Jozsa algorithm and the Grover's search
algorithm for two bits.Comment: 4 pages, two eps figure
Removal of a single photon by adaptive absorption
We present a method to remove, using only linear optics, exactly one photon
from a field-mode. This is achieved by putting the system in contact with an
absorbing environment which is under continuous monitoring. A feedback
mechanism then decouples the system from the environment as soon as the first
photon is absorbed. We propose a possible scheme to implement this process and
provide the theoretical tools to describe it
The elusive source of quantum effectiveness
We discuss two qualities of quantum systems: various correlations existing
between their subsystems and the distingushability of different quantum states.
This is then applied to analysing quantum information processing. While quantum
correlations, or entanglement, are clearly of paramount importance for
efficient pure state manipulations, mixed states present a much richer arena
and reveal a more subtle interplay between correlations and distinguishability.
The current work explores a number of issues related with identifying the
important ingredients needed for quantum information processing. We discuss the
Deutsch-Jozsa algorithm, the Shor algorithm, the Grover algorithm and the power
of a single qubit class of algorithms. One section is dedicated to cluster
states where entanglement is crucial, but its precise role is highly
counter-intuitive. Here we see that distinguishability becomes a more useful
concept.Comment: 8 pages, no figure
Uhlmann's geometric phase in presence of isotropic decoherence
Uhlmann's mixed state geometric phase [Rep. Math. Phys. {\bf 24}, 229 (1986)]
is analyzed in the case of a qubit affected by isotropic decoherence treated in
the Markovian approximation. It is demonstrated that this phase decreases
rapidly with increasing decoherence rate and that it is most fragile to weak
decoherence for pure or nearly pure initial states. In the unitary case, we
compare Uhlmann's geometric phase for mixed states with that occurring in
standard Mach-Zehnder interferometry [Phys. Rev. Lett. {\bf 85}, 2845 (2000)]
and show that the latter is more robust to reduction in the length of the Bloch
vector. We also describe how Uhlmann's geometric phase in the present case
could in principle be realized experimentally.Comment: New ref added, refs updated, journal ref adde
Toward scalable quantum computation with cavity QED systems
We propose a scheme for quantum computing using high-Q cavities in which the
qubits are represented by single cavity modes restricted in the space spanned
by the two lowest Fock states. We show that single qubit operations and
universal multiple qubit gates can be implemented using atoms sequentially
crossing the cavities.Comment: 14 pages, 8 figure
Homodyne Bell's inequalities for entangled mesoscopic superpositions
We present a scheme for demonstrating violation of Bell's inequalities using
a spin-1/2 system entangled with a pair of classically distinguishable wave
packets in a harmonic potential. In the optical domain, such wave packets can
be represented by coherent states of a single light mode. The proposed scheme
involves standard spin-1/2 projections and measurements of the position and the
momentum of the harmonic oscillator system, which for a light mode can be
realized by means of homodyne detection. We discuss effects of imperfections,
including non-unit efficiency of the homodyne detector, and point out a close
link between the visibility of interference and violation of Bell's
inequalities in the described scheme.Comment: 6 pages, 3 figures. Extended version, journal reference adde
G\"odel Incompleteness and the Black Hole Information Paradox
Semiclassical reasoning suggests that the process by which an object
collapses into a black hole and then evaporates by emitting Hawking radiation
may destroy information, a problem often referred to as the black hole
information paradox. Further, there seems to be no unique prediction of where
the information about the collapsing body is localized. We propose that the
latter aspect of the paradox may be a manifestation of an inconsistent
self-reference in the semiclassical theory of black hole evolution. This
suggests the inadequacy of the semiclassical approach or, at worst, that
standard quantum mechanics and general relavity are fundamentally incompatible.
One option for the resolution for the paradox in the localization is to
identify the G\"odel-like incompleteness that corresponds to an imposition of
consistency, and introduce possibly new physics that supplies this
incompleteness. Another option is to modify the theory in such a way as to
prohibit self-reference. We discuss various possible scenarios to implement
these options, including eternally collapsing objects, black hole remnants,
black hole final states, and simple variants of semiclassical quantum gravity.Comment: 14 pages, 2 figures; revised according to journal requirement
Contribution to understanding the mathematical structure of quantum mechanics
Probabilistic description of results of measurements and its consequences for
understanding quantum mechanics are discussed. It is shown that the basic
mathematical structure of quantum mechanics like the probability amplitudes,
Born rule, commutation and uncertainty relations, probability density current,
momentum operator, rules for including the scalar and vector potentials and
antiparticles can be obtained from the probabilistic description of results of
measurement of the space coordinates and time. Equations of motion of quantum
mechanics, the Klein-Gordon equation, Schrodinger equation and Dirac equation
are obtained from the requirement of the relativistic invariance of the
space-time Fisher information. The limit case of the delta-like probability
densities leads to the Hamilton-Jacobi equation of classical mechanics. Many
particle systems and the postulates of quantum mechanics are also discussed.Comment: 21 page
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