111 research outputs found
Why and how to use a differential equation method to calculate multi-loop integrals
A short pedagogical introduction to a differential method used to calculate
multi-loop scalar integrals is presented. As an example it is shown how to
obtain, using the method, large mass expansion of the two loop sunrise master
integrals.Comment: 9 p., presented at XXV International Conference on Theoretical
Physics "Particle Physics and Astrophysics in the Standard Models and
Beyond", Ustron, Poland, September 200
Correlation experiments in nonlinear quantum mechanics
We show how one can compute multiple-time multi-particle correlation
functions in nonlinear quantum mechanics in a way which guarantees locality of
the formalism.Comment: Section on causally related corelation experiments is added (Russian
roulette with a cheating player as an analogue of nonlinear EPR problem); to
be published in Phys. Lett. A 301 (2002) 139-15
Relativistic BB84, relativistic errors, and how to correct them
The Bennett-Brassard cryptographic scheme (BB84) needs two bases, at least
one of them linearly polarized. The problem is that linear polarization
formulated in terms of helicities is not a relativistically covariant notion:
State which is linearly polarized in one reference frame becomes depolarized in
another one. We show that a relativistically moving receiver of information
should define linear polarization with respect to projection of
Pauli-Lubanski's vector in a principal null direction of the Lorentz
transformation which defines the motion, and not with respect to the helicity
basis. Such qubits do not depolarize.Comment: revtex
Quantum feedback with weak measurements
The problem of feedback control of quantum systems by means of weak
measurements is investigated in detail. When weak measurements are made on a
set of identical quantum systems, the single-system density matrix can be
determined to a high degree of accuracy while affecting each system only
slightly. If this information is fed back into the systems by coherent
operations, the single-system density matrix can be made to undergo an
arbitrary nonlinear dynamics, including for example a dynamics governed by a
nonlinear Schr\"odinger equation. We investigate the implications of such
nonlinear quantum dynamics for various problems in quantum control and quantum
information theory, including quantum computation. The nonlinear dynamics
induced by weak quantum feedback could be used to create a novel form of
quantum chaos in which the time evolution of the single-system wave function
depends sensitively on initial conditions.Comment: 11 pages, TeX, replaced to incorporate suggestions of Asher Pere
Complete positivity of nonlinear evolution: A case study
Simple Hartree-type equations lead to dynamics of a subsystem that is not
completely positive in the sense accepted in mathematical literature. In the
linear case this would imply that negative probabilities have to appear for
some system that contains the subsystem in question. In the nonlinear case this
does not happen because the mathematical definition is physically unfitting as
shown on a concrete example.Comment: extended version, 3 appendices added (on mixed states, projection
postulate, nonlocality), to be published in Phys. Rev.
Nonlocal looking equations can make nonlinear quantum dynamics local
A general method for extending a non-dissipative nonlinear Schr\"odinger and
Liouville-von Neumann 1-particle dynamics to an arbitrary number of particles
is described. It is shown at a general level that the dynamics so obtained is
completely separable, which is the strongest condition one can impose on
dynamics of composite systems. It requires that for all initial states
(entangled or not) a subsystem not only cannot be influenced by any action
undertaken by an observer in a separated system (strong separability), but
additionally that the self-consistency condition is fulfilled. It is shown that a correct
extension to particles involves integro-differential equations which, in
spite of their nonlocal appearance, make the theory fully local. As a
consequence a much larger class of nonlinearities satisfying the complete
separability condition is allowed than has been assumed so far. In particular
all nonlinearities of the form are acceptable. This shows that
the locality condition does not single out logarithmic or 1-homeogeneous
nonlinearities.Comment: revtex, final version, accepted in Phys.Rev.A (June 1998
Bell's inequality with Dirac particles
We study Bell's inequality using the Bell states constructed from four
component Dirac spinors. Spin operator is related to the Pauli-Lubanski pseudo
vector which is relativistic invariant operator. By using Lorentz
transformation, in both Bell states and spin operator, we obtain an observer
independent Bell's inequality, so that it is maximally violated as long as it
is violated maximally in the rest frame.Comment: 7 pages. arXiv admin note: text overlap with arXiv:quant-ph/0308156
by other author
Entangled-state cryptographic protocol that remains secure even if nonlocal hidden variables exist and can be measured with arbitrary precision
Standard quantum cryptographic protocols are not secure if one assumes that
nonlocal hidden variables exist and can be measured with arbitrary precision.
The security can be restored if one of the communicating parties randomly
switches between two standard protocols.Comment: Shortened version, accepted in Phys. Rev.
Photon polarization and Wigner's little group
To discuss one-photon polarization states we find an explicit form of the
Wigner's little group element in the massless case for arbitrary Lorentz
transformation. As is well known, when analyzing the transformation properties
of the physical states, only the value of the phase factor is relevant. We show
that this phase factor depends only on the direction of the momentum
and does not depend on the frequency . Finally, we use
this observation to discuss the transformation properties of the linearly
polarized photons and the corresponding reduced density matrix. We find that
they transform properly under Lorentz group.Comment: Version published in Phys. Rev. A, few typos correcte
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