487 research outputs found
Assumptions that imply quantum dynamics is linear
A basic linearity of quantum dynamics, that density matrices are mapped
linearly to density matrices, is proved very simply for a system that does not
interact with anything else. It is assumed that at each time the physical
quantities and states are described by the usual linear structures of quantum
mechanics. Beyond that, the proof assumes only that the dynamics does not
depend on anything outside the system but must allow the system to be described
as part of a larger system. The basic linearity is linked with previously
established results to complete a simple derivation of the linear Schrodinger
equation. For this it is assumed that density matrices are mapped one-to-one
onto density matrices. An alternative is to assume that pure states are mapped
one-to-one onto pure states and that entropy does not decrease.Comment: 10 pages. Added references. Improved discussion of equations of
motion for mean values. Expanded Introductio
Quantum Communication between N partners and Bell's inequalities
We consider a family of quantum communication protocols involving
partners. We demonstrate the existence of a link between the security of these
protocols against individual attacks by the eavesdropper, and the violation of
some Bell's inequalities, generalizing the link that was noticed some years ago
for two-partners quantum cryptography. The arguments are independent of the
local hidden variable debate.Comment: 4 pages, 2 figure
Effective Hamiltonian Approach to the Master Equation
A method of exactly solving the master equation is presented in this letter.
The explicit form of the solution is determined by the time evolution of a
composite system including an auxiliary system and the open system in question.
The effective Hamiltonian governing the time evolution of the composed system
are derived from the master equation. Two examples, the dissipative two-level
system and the damped harmonic oscillator, are presented to illustrate the
solving procedure.
PACS number(s): 05.30.-d, 05.40.+j, 42.50.CtComment: 4 pages, no figure
Generalized quantum measurements and local realism
The structure of a local hidden variable model for experiments involving
sequences of measurements rigorously is analyzed. Constraints imposed by local
realism on the conditional probabilities of the outcomes of such measurement
schemes are explicitly derived. The violation of local realism in the case of
``hidden nonlocality'' is illustrated by an operational example.Comment: Revtex, 12 pages; Some modifications of introduction has been made; a
note stating that part of results had been obtained earlier by other authors,
has been added; one postscript figure available at request from
[email protected]
Coherent pulse implementations of quantum cryptography protocols resistant to photon number splitting attacks
A new class of quantum cryptography (QC) protocols that are robust against
the most general photon number splitting attacks in a weak coherent pulse
implementation has been recently proposed. In this article we give a quite
exhaustive analysis of several eavesdropping attacks on these schemes. The
eavesdropper (Eve) is supposed to have unlimited technological power while the
honest parties (Alice and Bob) use present day technology, in particular an
attenuated laser as an approximation of a single-photon source. They exploit
the nonorthogonality of quantum states for decreasing the information
accessible to Eve in the multi-photon pulses accidentally produced by the
imperfect source. An implementation of some of these protocols using present
day technology allow for a secure key distribution up to distances of
150 km. We also show that strong-pulse implementations, where a strong pulse is
included as a reference, allow for key distribution robust against photon
number splitting attacks.Comment: 16 pages, 11 figure
Quantum trajectories for Brownian motion
We present the stochastic Schroedinger equation for the dynamics of a quantum
particle coupled to a high temperature environment and apply it the dynamics of
a driven, damped, nonlinear quantum oscillator. Apart from an initial slip on
the environmental memory time scale, in the mean, our result recovers the
solution of the known non-Lindblad quantum Brownian motion master equation. A
remarkable feature of our approach is its localization property: individual
quantum trajectories remain localized wave packets for all times, even for the
classically chaotic system considered here, the localization being stronger the
smaller .Comment: 4 pages, 3 eps figure
Quantum correlations in Newtonian space and time: arbitrarily fast communication or nonlocality
We investigate possible explanations of quantum correlations that satisfy the
principle of continuity, which states that everything propagates gradually and
continuously through space and time. In particular, following [J.D. Bancal et
al, Nature Physics 2012], we show that any combination of local common causes
and direct causes satisfying this principle, i.e. propagating at any finite
speed, leads to signalling. This is true even if the common and direct causes
are allowed to propagate at a supraluminal-but-finite speed defined in a
Newtonian-like privileged universal reference frame. Consequently, either there
is supraluminal communication or the conclusion that Nature is nonlocal (i.e.
discontinuous) is unavoidable.Comment: It is an honor to dedicate this article to Yakir Aharonov, the master
of quantum paradoxes. Version 2 contains some more references and a clarified
conclusio
Optimal minimal measurements of mixed states
The optimal and minimal measuring strategy is obtained for a two-state system
prepared in a mixed state with a probability given by any isotropic a priori
distribution. We explicitly construct the specific optimal and minimal
generalized measurements, which turn out to be independent of the a priori
probability distribution, obtaining the best guesses for the unknown state as
well as a closed expression for the maximal mean averaged fidelity. We do this
for up to three copies of the unknown state in a way which leads to the
generalization to any number of copies, which we then present and prove.Comment: 20 pages, no figure
Quantum Trajectories and Quantum Measurement Theory
Beyond their use as numerical tools, quantum trajectories can be ascribed a
degree of reality in terms of quantum measurement theory. In fact, they arise
naturally from considering continuous observation of a damped quantum system. A
particularly useful form of quantum trajectories is as linear (but non-unitary)
stochastic Schrodinger equations. In the limit where a strong local oscillator
is used in the detection, and where the system is not driven, these quantum
trajectories can be solved. This gives an alternate derivation of the
probability distributions for completed homodyne and heterodyne detection
schemes. It also allows the previously intractable problem of real-time
adaptive measurements to be treated. The results for an analytically soluble
example of adaptive phase measurements are presented, and future developments
discussed.Comment: 17 pages. A review article publihsed in 1996 which has been picking
up some citations, so I thought I would post it her
Multipartite bound entangled states that violate Bell's inequality
We study the relation between distillability of multipartite states and
violation of Bell's inequality. We prove that there exist multipartite bound
entangled states (i.e. non-separable, non-distillable states) that violate a
multipartite Bell inequality. This implies that (i) violation of Bell's
inequality is not a sufficient condition for distillability and (ii) some bound
entangled states cannot be described by a local hidden variable model.Comment: 4 pages, no figure
- …