743 research outputs found
Structure and Properties of Hughston's Stochastic Extension of the Schr\"odinger Equation
Hughston has recently proposed a stochastic extension of the Schr\"odinger
equation, expressed as a stochastic differential equation on projective Hilbert
space. We derive new projective Hilbert space identities, which we use to give
a general proof that Hughston's equation leads to state vector collapse to
energy eigenstates, with collapse probabilities given by the quantum mechanical
probabilities computed from the initial state. We discuss the relation of
Hughston's equation to earlier work on norm-preserving stochastic equations,
and show that Hughston's equation can be written as a manifestly unitary
stochastic evolution equation for the pure state density matrix. We discuss the
behavior of systems constructed as direct products of independent subsystems,
and briefly address the question of whether an energy-based approach, such as
Hughston's, suffices to give an objective interpretation of the measurement
process in quantum mechanics.Comment: Plain Tex, no figure
The no-signaling condition and quantum dynamics
We show that the basic dynamical rules of quantum physics can be derived from
its static properties and the condition that superluminal communication is
forbidden. More precisely, the fact that the dynamics has to be described by
linear completely positive maps on density matrices is derived from the
following assumptions: (1) physical states are described by rays in a Hilbert
space, (2) probabilities for measurement outcomes at any given time are
calculated according to the usual trace rule, (3) superluminal communication is
excluded. This result also constrains possible non-linear modifications of
quantum physics.Comment: 4 page
Complete parameterization, and invariance, of diffusive quantum trajectories for Markovian open systems
The state matrix for an open quantum system with Markovian evolution
obeys a master equation. The master equation evolution can be unraveled into
stochastic nonlinear trajectories for a pure state , such that on average
reproduces . Here we give for the first time a complete
parameterization of all diffusive unravelings (in which evolves
continuously but non-differentiably in time). We give an explicit measurement
theory interpretation for these quantum trajectories, in terms of monitoring
the system's environment. We also introduce new classes of diffusive
unravelings that are invariant under the linear operator transformations under
which the master equation is invariant. We illustrate these invariant
unravelings by numerical simulations. Finally, we discuss generalized gauge
transformations as a method of connecting apparently disparate descriptions of
the same trajectories by stochastic Schr\"odinger equations, and their
invariance properties.Comment: 10 pages, including 5 figures, submitted to J. Chem Phys special
issue on open quantum system
Robustness and diffusion of pointer states
Classical properties of an open quantum system emerge through its interaction
with other degrees of freedom (decoherence). We treat the case where this
interaction produces a Markovian master equation for the system. We derive the
corresponding distinguished local basis (pointer basis) by three methods. The
first demands that the pointer states mimic as close as possible the local
non-unitary evolution. The second demands that the local entropy production be
minimal. The third imposes robustness on the inherent quantum and emerging
classical uncertainties. All three methods lead to localized Gaussian pointer
states, their formation and diffusion being governed by well-defined quantum
Langevin equations.Comment: 5 pages, final versio
Classical Teleportation of a Quantum Bit
Classical teleportation is defined as a scenario where the sender is given
the classical description of an arbitrary quantum state while the receiver
simulates any measurement on it. This scenario is shown to be achievable by
transmitting only a few classical bits if the sender and receiver initially
share local hidden variables. Specifically, a communication of 2.19 bits is
sufficient on average for the classical teleportation of a qubit, when
restricted to von Neumann measurements. The generalization to
positive-operator-valued measurements is also discussed.Comment: 4 pages, RevTe
Non-realism : deep thought or a soft option ?
The claim that the observation of a violation of a Bell inequality leads to
an alleged alternative between nonlocality and non-realism is annoying because
of the vagueness of the second term.Comment: 5 page
Physical interpretation of stochastic Schroedinger equations in cavity QED
We propose physical interpretations for stochastic methods which have been
developed recently to describe the evolution of a quantum system interacting
with a reservoir. As opposed to the usual reduced density operator approach,
which refers to ensemble averages, these methods deal with the dynamics of
single realizations, and involve the solution of stochastic Schr\"odinger
equations. These procedures have been shown to be completely equivalent to the
master equation approach when ensemble averages are taken over many
realizations. We show that these techniques are not only convenient
mathematical tools for dissipative systems, but may actually correspond to
concrete physical processes, for any temperature of the reservoir. We consider
a mode of the electromagnetic field in a cavity interacting with a beam of two-
or three-level atoms, the field mode playing the role of a small system and the
atomic beam standing for a reservoir at finite temperature, the interaction
between them being given by the Jaynes-Cummings model. We show that the
evolution of the field states, under continuous monitoring of the state of the
atoms which leave the cavity, can be described in terms of either the Monte
Carlo Wave-Function (quantum jump) method or a stochastic Schr\"odinger
equation, depending on the system configuration. We also show that the Monte
Carlo Wave-Function approach leads, for finite temperatures, to localization
into jumping Fock states, while the diffusion equation method leads to
localization into states with a diffusing average photon number, which for
sufficiently small temperatures are close approximations to mildly squeezed
states.Comment: 12 pages RevTeX 3.0 + 6 figures (GIF format; for higher-resolution
postscript images or hardcopies contact the authors.) Submitted to Phys. Rev.
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
- …