1,468 research outputs found
Covariance Dynamics and Entanglement in Translation Invariant Linear Quantum Stochastic Networks
This paper is concerned with a translation invariant network of identical
quantum stochastic systems subjected to external quantum noise. Each node of
the network is directly coupled to a finite number of its neighbours. This
network is modelled as an open quantum harmonic oscillator and is governed by a
set of linear quantum stochastic differential equations. The dynamic variables
of the network satisfy the canonical commutation relations. Similar large-scale
networks can be found, for example, in quantum metamaterials and optical
lattices. Using spatial Fourier transform techniques, we obtain a sufficient
condition for stability of the network in the case of finite interaction range,
and consider a mean square performance index for the stable network in the
thermodynamic limit. The Peres-Horodecki-Simon separability criterion is
employed in order to obtain sufficient and necessary conditions for quantum
entanglement of bipartite systems of nodes of the network in the Gaussian
invariant state. The results on stability and entanglement are extended to the
infinite chain of the linear quantum systems by letting the number of nodes go
to infinity. A numerical example is provided to illustrate the results.Comment: 11 pages, 3 figures, submitted to the 54th IEEE Conference on
Decision and Control, December 15-18, 2015, Osaka, Japa
Robust adaptive quantum phase estimation
Quantum parameter estimation is central to many fields such as quantum computation, communications and metrology. Optimal estimation theory has been instrumental in achieving the best accuracy in quantum parameter estimation, which is possible when we have very precise knowledge of and control over the model. However, uncertainties in key parameters underlying the system are unavoidable and may impact the quality of the estimate. We show here how quantum optical phase estimation of a squeezed state of light exhibits improvement when using a robust fixed-interval smoother designed with uncertainties explicitly introduced in parameters underlying the phase noise
Heisenberg Picture Approach to the Stability of Quantum Markov Systems
Quantum Markovian systems, modeled as unitary dilations in the quantum
stochastic calculus of Hudson and Parthasarathy, have become standard in
current quantum technological applications. This paper investigates the
stability theory of such systems. Lyapunov-type conditions in the Heisenberg
picture are derived in order to stabilize the evolution of system operators as
well as the underlying dynamics of the quantum states. In particular, using the
quantum Markov semigroup associated with this quantum stochastic differential
equation, we derive sufficient conditions for the existence and stability of a
unique and faithful invariant quantum state. Furthermore, this paper proves the
quantum invariance principle, which extends the LaSalle invariance principle to
quantum systems in the Heisenberg picture. These results are formulated in
terms of algebraic constraints suitable for engineering quantum systems that
are used in coherent feedback networks
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