Quantum learning algorithms for quantum measurements

We study quantum learning algorithms for quantum measurements. The optimal learning algorithm is derived for arbitrary von Neumann measurements in the case of training with one or two examples. The analysis of the case of three examples reveals that, differently from the learning of unitary gates, the optimal algorithm for learning of quantum measurements cannot be parallelized, and requires quantum memories for the storage of information.     

Quantum correlations in dual quantum measurements

 We analyze the quantum measurement properties of dual non-degenerate parametric amplifers in the twin-beam configuration, in the cascaded back-action-evasion configuration, and in Kerr-type photon-number quantum non-demolition measurements. It is found that Einstein-Podolsky-Rosen correlations can be obtained between the quadrature components of an idler mode and the sum of the readout of two signal modes. Furthermore, we discuss dual-mode quantum non-demolition measurements on the combination of two light modes, and the generation of number-state entanglement. Received: 12 April 1996/Revised version: 2 July 1996     

Quantum theory of continuous measurements and its applications in quantum optics

We present an overview of the quantum theory of continuous measurements and discuss some of its important applications in quantum optics. Quantum theory of continuous measurements is the appropriate generalization of the conventional formulation of quantum theory, which is adequate to deal with counting experiments where a detector monitors a system continuously over an interval of time and records the times of occurrence of a given type of event, such as the emission or arrival of a particle. We first discuss the classical theory of counting processes and indicate how one arrives at the celebrated photon counting formula of Mandel for classical optical fields. We then discuss the inadequacies of the so called quantum Mandel formula. We explain how the unphysical results that arise from the quantum Mandel formula are due to the fact that the formula is obtained on the basis of an erroneous identification of the coincidence probability densities associated with a continuous measurement situation. We then summarize the basic framework of the quantum theory of continuous measurements as developed by Davies. We explain how a complete characterization of the counting process can be achieved by specifying merely the measurement transformation associated with the change in the state of the system when a single event is observed in an infinitesimal interval of time. In order to illustrate the applications of the quantum theory of continuoius measurements in quantum optics, we first derive the photon counting probabilities of a single-mode free field and also of a single-mode field in interaction with an external source. We then discuss the general quantum counting formula of Chmara for a multi-mode electromagnetic field coupled to an external source. We explain how the Chmara counting formula is indeed the appropriate quantum generalization of the classical Mandel formula. To illustrate the fact that the quantum theory of continuous measurements has other diverse applications in quantum optics, besides the theory of photodetection, we summarize the theory of ‘quantum jumps’ developed by Zoller, Marte and Walls and Barchielli, where the continuous measurements framework is employed to evaluate the statistics of photon emission events in the resonance fluorescence of an atomic system.     

Quantum nondemolition measurements in systems with nonstationary squeezing of quantum noise

Summary A Weber detector with optical readout system is considered. The measuring device consists of circulators, homodyne detector and two degenerate parametric amplifiers (or four wave mixers), modifying vacuum fluctuations of the load. In this scheme the greater the squeezing of backaction noise, the smaller the measurable force acting on the mechanical resonator. Postulation of gedanken state reduction is not necessary in our model.

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Riassunto Si considera il rivelatore Weber con sistema di lettura ottico. Lo strumento di misura consiste di circolatori, di un rivelatore omodino e due amplificatori parametrici degenerati (o quattro miscelatori d'onda), che modificano le fluttuazioni nel vuoto del carico. In questo schema, maggiore è la compressione del rumore di retroazione e minore risulta la forza misurabile che agisce sul risonatore meccanico. Nel modello in questione non è necessario postulare la riduzione dello stato concettuale.

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Резюме Рассматривается детектор Вебера с оптической системой считывания. Измерительная аппаратура состоит из циркуляционных насосов, детектора и двух вырожденных параметрических усилителей (или преобразователей четырех волн), преобразуюших вакуумные флуктуации нагрузки. В этой схеме, чем меньше измеряемая сила, действующая на механический резонатор, тем больше подавление шума. В нашей модели не требуется постулирование преобразования состояния.

     

Quantum phase expectation values of a mesoscopic Josephson junction from quantum current measurements

A simple way to acquire information on the mean values of the phase operators sinϕ and cosϕ of an ultrasmall Josephson junction prepared in an arbitrary pure or not state is reported. Our proposal exploits the recently predicted occurrence of current spikes in the I-V characteristic of a mesojunction irradiated by a quantum single-mode low-intensity coherent electromagnetic field. A necessary condition for the validity of our treatment is presented and discussed. Received 11 April 2001     

Quantum parameter estimation in a spin-boson dephasing quantum system by periodical projective measurements

In this paper,we explore how to estimate the phase damping parameter γ and the tunneling amplitude parameter ?from a spin-boson dephasing quantum model by periodical projective measurements.The preparation of initial states is accomplished by performing the period measurements in our scheme.The parameter γ can be always estimated when projective measurement bases are chosen as θ = π/2 and φ = 0.Based on the estimated value of γ and the interval information of ?,we can select another measurement bases(θ = π/4 and φ = π/2) to obtain the estimated value of ?.A coherent control is indispensable to estimate ? if γ is in the interval of ?;whereas the control is not necessary if γ is out of the known interval of ?.We establish the relation between the optimal period time and the parameter γ or ? in terms of Fisher information.Although the optimal measurement period cannot be selected beforehand,the aforementioned relation can be utilized to adjust the measurement period to approach the optimal one.     

量子非破坏性测量

介绍了量子光学中的量子非破坏性（QND）测量,并列举了两个实例,指出QND测量是很重要的。     

On quantum measurements

Is the reduction of the wavefunction a real physical process? A mental experiment providing an answer to this question is considered.     

Nonideal quantum measurements

A partial ordering in the class of observables ( positive operator-valued measures, introduced by Davies and by Ludwig) is explored. The ordering is interpreted as a form of nonideality, and it allows one to compare ideal and nonideal versions of the same observable. Optimality is defined as maximality in the sense of the ordering. The framework gives a generalization of the usual (implicit) definition of self-adjoint operators as optimal observables (von Neumann), but it can, in contrast to this latter definition, be justified operationally. The nonideality notion is compared to other quantum estimation theoretic methods. Measures for the amount of nonideality are derived from information theory.     

Quantum mechanical interaction-free measurements

A novel manifestation of nonlocality of quantum mechanics is presented. It is shown that it is possible to ascertain the existence of an object in a given region of space without interacting with it. The method might have practical applications for delicate quantum experiments.     

Repeated quantum non-demolition measurements

 We describe, in detail, theoretical and experimental aspects related to our recently reported repeated back-action evading measurements performed using two travelling-wave optical parametric amplifiers in series. The state of the observable being measured is almost perfectly preserved after two successive measurements. The final signal, and the intermediate measurement of the two successive setups are quantum correlated with conditional variances that lie in the quantum regime. Moreover, we show that the two independent measurements are quantum correlated up to 30%. Received: 11 April 1996/Revised version: 18 July 1996     

Mesoscopic quadratic quantum measurements

We develop a theory of quadratic quantum measurements by a mesoscopic detector. It is shown that the quadratic measurements should have nontrivial quantum information properties, providing, for instance, a simple way of entangling two noninteracting qubits. We also calculate the output spectrum of a detector with both linear and quadratic response, continuously monitoring two qubits.     

Maximum confidence quantum measurements

We consider the problem of discriminating between states of a specified set with maximum confidence. For a set of linearly independent states unambiguous discrimination is possible if we allow for the possibility of an inconclusive result. For linearly dependent sets an analogous measurement is one which allows us to be as confident as possible that when a given state is identified on the basis of the measurement result, it is indeed the correct state.     

Quantum instantons and quantum chaos

We suggest a closed form expression for the path integral of quantum transition amplitudes to construct a quantum action. Based on this we propose rigorous definitions of both, quantum instantons and quantum chaos. As an example we compute the quantum instanton of the double well potential.     

Quantum oscillations without quantum coherence

We study numerically the damping of quantum oscillations and the dynamics of the density matrix in model many-spin systems decohered by a spin bath. We show that oscillations of some density matrix elements can persist with considerable amplitude long after other elements, along with the entropy, have come close to saturation, i.e., when the system has been decohered almost completely. The oscillations exhibit very slow decay, and may be observable in experiments.     

Quantum optics with quantum gases

Quantum optics with quantum gases represents a new field, where the quantum nature of both light and ultracold matter plays equally important role. Only very recently this ultimate quantum limit of light-matter interaction became feasible experimentally. In traditional quantum optics, the cold atoms are considered classically, whereas, in quantum atom optics, the light is used as an essentially classical auxilary tool. On the one hand, the quantization of optical trapping potentials can significantly modify many-body dynamics of atoms, which is well-known only for classical potentials. On the other hand, atomic fluctuations can modify the properties of the scattered light.