16,153 research outputs found
Quantum trajectories for a class of continuous matrix product input states
We introduce a new class of continuous matrix product (CMP) states and
establish the stochastic master equations (quantum filters) for an arbitrary
quantum system probed by a bosonic input field in this class of states. We show
that this class of CMP states arise naturally as outputs of a Markovian model,
and that input fields in these states lead to master and filtering (quantum
trajectory) equations which are matrix-valued. Furthermore, it is shown that
this class of continuous matrix product states include the (continuous-mode)
single photon and time-ordered multi-photon states.Comment: 17 pages, 2 figure
Quantum trajectories for propagating Fock states
We derive quantum trajectories (also known as stochastic master equations)
that describe an arbitrary quantum system probed by a propagating wave packet
of light prepared in a continuous-mode Fock state. We consider three detection
schemes of the output light: photon counting, homodyne detection, and
heterodyne detection. We generalize to input field states that are
superpositions and or mixtures of Fock states and illustrate the formalism with
several examples.Comment: 20 pages, 4 figure
Efficient simulation scheme for a class of quantum optics experiments with non-negative Wigner representation
We provide a scheme for efficient simulation of a broad class of quantum
optics experiments. Our efficient simulation extends the continuous variable
Gottesman-Knill theorem to a large class of non-Gaussian mixed states, thereby
identifying that these non-Gaussian states are not an enabling resource for
exponential quantum speed-up. Our results also provide an operationally
motivated interpretation of negativity as non-classicality. We apply our scheme
to the case of noisy single-photon-added-thermal-states to show that this class
admits states with positive Wigner function but negative P -function that are
not useful resource states for quantum computation.Comment: 14 pages, 1 figur
Quantum Trajectories, State Diffusion and Time Asymmetric Eventum Mechanics
We show that the quantum stochastic unitary dynamics Langevin model for
continuous in time measurements provides an exact formulation of the Heisenberg
uncertainty error-disturbance principle. Moreover, as it was shown in the 80's,
this Markov model induces all stochastic linear and non-linear equations of the
phenomenological "quantum trajectories" such as quantum state diffusion and
spontaneous localization by a simple quantum filtering method. Here we prove
that the quantum Langevin equation is equivalent to a Dirac type boundary-value
problem for the second-quantized input "offer waves from future" in one extra
dimension, and to a reduction of the algebra of the consistent histories of
past events to an Abelian subalgebra for the "trajectories of the output
particles". This result supports the wave-particle duality in the form of the
thesis of Eventum Mechanics that everything in the future is constituted by
quantized waves, everything in the past by trajectories of the recorded
particles. We demonstrate how this time arrow can be derived from the principle
of quantum causality for nondemolition continuous in time measurements.Comment: 21 pages. See also relevant publications at
http://www.maths.nott.ac.uk/personal/vpb/publications.htm
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