Directly Coupled Observers for Quantum Harmonic Oscillators with Discounted Mean Square Cost Functionals and Penalized Back-action

This paper is concerned with quantum harmonic oscillators consisting of a quantum plant and a directly coupled coherent quantum observer. We employ discounted quadratic performance criteria in the form of exponentially weighted time averages of second-order moments of the system variables. A coherent quantum filtering (CQF) problem is formulated as the minimization of the discounted mean square of an estimation error, with which the dynamic variables of the observer approximate those of the plant. The cost functional also involves a quadratic penalty on the plant-observer coupling matrix in order to mitigate the back-action of the observer on the covariance dynamics of the plant. For the discounted mean square optimal CQF problem with penalized back-action, we establish first-order necessary conditions of optimality in the form of algebraic matrix equations. By using the Hamiltonian structure of the Heisenberg dynamics and related Lie-algebraic techniques, we represent this set of equations in a more explicit form in the case of equally dimensioned plant and observer.Comment: 11 pages, a brief version to be submitted to the IEEE 2016 Conference on Norbert Wiener in the 21st Century, 13-15 July, Melbourne, Australi

Relativistic quantum clocks

The conflict between quantum theory and the theory of relativity is exemplified in their treatment of time. We examine the ways in which their conceptions differ, and describe a semiclassical clock model combining elements of both theories. The results obtained with this clock model in flat spacetime are reviewed, and the problem of generalizing the model to curved spacetime is discussed, before briefly describing an experimental setup which could be used to test of the model. Taking an operationalist view, where time is that which is measured by a clock, we discuss the conclusions that can be drawn from these results, and what clues they contain for a full quantum relativistic theory of time.Comment: 12 pages, 4 figures. Invited contribution for the proceedings for "Workshop on Time in Physics" Zurich 201

Decoherence, einselection, and the quantum origins of the classical

Decoherence is caused by the interaction with the environment. Environment monitors certain observables of the system, destroying interference between the pointer states corresponding to their eigenvalues. This leads to environment-induced superselection or einselection, a quantum process associated with selective loss of information. Einselected pointer states are stable. They can retain correlations with the rest of the Universe in spite of the environment. Einselection enforces classicality by imposing an effective ban on the vast majority of the Hilbert space, eliminating especially the flagrantly non-local "Schr\"odinger cat" states. Classical structure of phase space emerges from the quantum Hilbert space in the appropriate macroscopic limit: Combination of einselection with dynamics leads to the idealizations of a point and of a classical trajectory. In measurements, einselection replaces quantum entanglement between the apparatus and the measured system with the classical correlation.Comment: Final version of the review, with brutally compressed figures. Apart from the changes introduced in the editorial process the text is identical with that in the Rev. Mod. Phys. July issue. Also available from http://www.vjquantuminfo.or

Decoherence and definite outcomes

This thesis has three aims: (1) to clarify in detail the relation between the decoherence mechanism and the problem of definite outcomes, (2) to dispel common misconceptions about the measurement problem in quantum mechanics, and (3) to present some recent alternative approaches in the quest for a satisfactory solution of the definite outcomes problem.Comment: 102 pages, in English. Thesis work for the "Laura Magistrale Interfacolt\`a in Logica, Filosofia e Storia della Scienza" at Universit\`a degli studi di Firenze. Supervisors: Prof. Roberto Casalbuoni and Prof. Elena Castellan

A Direct Coupling Coherent Quantum Observer for an Oscillatory Quantum Plant

A direct coupling coherent observer is constructed for a linear quantum plant which has oscillatory solutions. It is shown that a finite time moving average of the quantum observer output can provide an estimate of the quantum plant output without disturbing this plant signal. By choosing a sufficiently small averaging time and a sufficiently large observer gain, the observer tracking error can be made arbitrarily small.This work was supported by the Air Force Office of Scientific Research (AFOSR), under agreement number FA2386-16-1-4065. Some of the research presented in this paper was also supported by the Australian Research Council under grant FL110100020

Stochastic Master Equation Analysis of Optimized Three-Qubit Nondemolition Parity Measurement

We analyze a direct parity measurement of the state of three superconducting qubits in circuit quantum electrodynamics. The parity is inferred from a homodyne measurement of the reflected/transmitted microwave radiation and the measurement is direct in the sense that the parity is measured without the need for any quantum circuit operations or for ancilla qubits. Qubits are coupled to two resonant cavity modes, allowing the steady state of the emitted radiation to satisfy the necessary conditions to act as a pointer state for the parity. However, the transient dynamics violates these conditions and we analyze this detrimental effect and show that it can be overcome in the limit of weak measurement signal. Our analysis shows that, with a moderate degree of post-selection, it is possible to achieve post-measurement states with fidelity of order 95%. We believe that this type of measurement could serve as a benchmark for future error-correction protocols in a scalable architecture