23 research outputs found
Functional Wigner representation of BEC quantum dynamics
We develop a method of simulating the full quantum field dynamics of
multi-mode multi-component Bose-Einstein condensates in a trap. We use the
truncated Wigner representation to obtain a probabilistic theory that can be
sampled. This method produces c-number stochastic equations which may be solved
using conventional stochastic methods. The technique is valid for large mode
occupation numbers. We give a detailed derivation of methods of functional
Wigner representation appropriate for quantum fields. Our approach describes
spatial evolution of spinor components and properly accounts for nonlinear
losses. Such techniques are applicable to calculating the leading quantum
corrections, including effects like quantum squeezing, entanglement, EPR
correlations and interactions with engineered nonlinear reservoirs. By using a
consistent expansion in the inverse density, we are able to explain an
inconsistency in the nonlinear loss equations found by earlier authors
Quantum probabilistic sampling of multipartite 60-qubit Bell inequality violations
We show that violation of genuine multipartite Bell inequalities can be
obtained with sampled, probabilistic phase space methods. These genuine Bell
violations cannot be replicated if any part of the system is described by a
local hidden variable theory. The Bell violations are simulated
probabilistically using quantum phase-space representations. We treat
mesoscopically large Greenberger-Horne-Zeilinger (GHZ) states having up to 60
qubits, using both a multipartite SU(2) Q-representation and the positive
P-representation. Surprisingly, we find that sampling with phase-space
distributions can be exponentially faster than experiment. This is due to the
classical parallelism inherent in the simulation of quantum measurements using
phase-space methods. Our probabilistic sampling method predicts a contradiction
with local realism of "Schr\"odinger-cat" states that can be realized as a GHZ
spin state, either in ion traps or with photonic qubits. We also present a
quantum simulation of the observed super-decoherence of the ion-trap "cat"
state, using a phenomenological noise model
Probabilistic simulation of mesoscopic "Schr\"odinger cat" states
We carry out probabilistic phase-space sampling of mesoscopic Schr\"odinger
cat quantum states, demonstrating multipartite Bell violations for up to 60
qubits. We use states similar to those generated in photonic and ion-trap
experiments. These results show that mesoscopic quantum superpositions are
directly accessible to probabilistic sampling, and we analyze the properties of
sampling errors. We also demonstrate dynamical simulation of super-decoherence
in ion traps. Our computer simulations can be either exponentially faster or
slower than experiment, depending on the correlations measured
Probabilistic quantum phase-space simulation of Bell violations and their dynamical evolution
Quantum simulations of Bell inequality violations are numerically obtained
using probabilistic phase space methods, namely the positive P-representation.
In this approach the moments of quantum observables are evaluated as moments of
variables that have values outside the normal eigenvalue range. There is thus a
parallel with quantum weak measurements and weak values. Nevertheless, the
representation is exactly equivalent to quantum mechanics. A number of states
violating Bell inequalities are sampled, demonstrating that these quantum
paradoxes can be treated with probabilistic methods. We treat quantum dynamics
by simulating the time evolution of the Bell state formed via parametric
down-conversion, and discuss multi-mode generalizations