Model Of Quantum Measurement Research Articles

Experimental Demonstration of Quantum State Expansion in a Cluster of Dipolar-Coupled Nuclear Spins

It is experimentally demonstrated that an arbitrary quantum state of a single spin 1/2, a| upward arrow+b| downward arrow, can be converted into a superposition of the two ferromagnetic states of a spin cluster: a| upward arrow upward arrow... upward arrow upward arrow+b| downward arrow downward arrow... downward arrow downward arrow. The physical system is a cluster of seven dipolar-coupled nuclear spins of single-labeled 13C-benzene molecules in a liquid-crystalline matrix. In this complex system, the pseudopure ground state and the required controlled unitary transformations have been implemented. The experimental scheme can be considered as an explicit model of quantum measurement.

Sequential product of quantum effects

Unsharp quantum measurements can be modelled by means of the class E ( H ) \mathcal {E}(\mathcal {H}) of positive contractions on a Hilbert space H \mathcal {H} , in brief, quantum effects. For A , B ∈ E ( H ) A,B\in \mathcal {E}(\mathcal {H}) the operation of sequential product A ∘ B = A 1 / 2 B A 1 / 2 A\circ B=A^{1/2}BA^{1/2} was proposed as a model for sequential quantum measurements. We continue these investigations on sequential product and answer positively the following question: the assumption A ∘ B ≥ B A\circ B\geq B implies A B = B A = B AB=BA=B . Then we propose a geometric approach of quantum effects and their sequential product by means of contractively contained Hilbert spaces and operator ranges. This framework leads us naturally to consider lattice properties of quantum effects, sums and intersections, and to prove that the sequential product is left distributive with respect to the intersection.

Degree of entanglement in a quantum-measurement process

We suggest a quantum measurement model in an ion trap which specifies the probability distribution of two, distinct internal ground states of a trapped four-level ion. The external degrees of motion of the four-level ion constitute the meter which, in turn, is coupled to the environment by engineered reservoirs. In a previous publication, a similar measurement model was employed to test decoherence effects on quantum nonlocality in phase space on the basis of coincidence measurements of the entangled system-meter scheme. Here, we study the effects of decoherence on the entanglement of formation characterized by the concurrence. The concurrence of the system enables to find the maximum possible violation of the Bell inequality. Surprisingly, this model gives illustrative insights into the question to what extend the Bell inequality can be considered as a measure of entanglement.

Quantum measurement apparatus with a squeezed reservoir: Control of decoherence and nonlocality in phase space

We propose a quantum measurement model where the environment is taken to be a squeezed reservoir. This kind of meter-environment coupling has a dramatic influence on the decoherence rate. Depending on the phase and the squeezing parameter the decoherence time can be enhanced or reduced arbitrarily. We derive the Wigner function for the system-meter state, and discuss its nonclassical features. Further, we test quantum nonlocality in phase space on the basis of coincidence measurements of the entangled system-meter scheme, and investigate the effect of a highly reduced decoherence rate. Surprisingly, in sharp contrast to popular notion, violations of the Bell inequality can be observed even when the meter has reached a macroscopic state.

Quantum measurement as a driven phase transition: An exactly solvable model

A model of quantum measurement is proposed, which aims to describe statistical mechanical aspects of this phenomenon, starting from a purely Hamiltonian formulation. The macroscopic measurement apparatus is modeled as an ideal Bose gas, the order parameter of which, that is, the amplitude of the condensate, is the pointer variable. It is shown that properties of irreversibility and ergodicity breaking, which are inherent in the model apparatus, ensure the appearance of definite results of the measurement, and provide a dynamical realization of wave-function reduction or collapse. The measurement process takes place in two steps: First, the reduction of the state of the tested system occurs over a time of order $\hbar/(TN^{1/4})$, where $T$ is the temperature of the apparatus, and $N$ is the number of its degrees of freedom. This decoherence process is governed by the apparatus-system interaction. During the second step classical correlations are established between the apparatus and the tested system over the much longer time-scale of equilibration of the apparatus. The influence of the parameters of the model on non-ideality of the measurement is discussed. Schr\"{o}dinger kittens, EPR setups and information transfer are analyzed.

The quantum stochastic processes as the reduced dynamics of EEQT

A quantum measurement model is built in terms of the event enhanced quantum theory (EEQT). The model includes detailed description of interacting quantum and classical systems. It is shown that reduced dynamics of the coupled systems reconstructs the quantum stochastic processes proposed by Davies.

Reducing decoherence in quantum-computer memory with all quantum bits coupling to the same environment

Decoherence in quantum-computer memory due to the inevitable coupling to the external environment is examined. We make the assumption that all quantum bits (qubits) interact with the same environment rather than the assumption of separate environments for different qubits. It is found that the qubits decohere collectively. For some kinds of entangled input states, no decoherence occurs at all in the memory, even if the qubits are interacting with the environment. Based on this phenomenon, a scheme is proposed for reducing the collective decoherence. We also discuss possible implications of this decoherence model for quantum measurements.

Extension of the GRWP model to translation symmetry breaking processes

This work is concerned with the quantum measurement model proposed by Ghirardi-Rimini-Weber [1] (GRW) in its version presented by Pearle [2], as a stochastic modification of the Schrodinger evolution. These authors conjectured a spontaneous random hitting process which is described by a localization operator, a guassian function acting on microscopic particles which carries two free parameters; the frequency λ and the localization width α−1/2. These two parameters can be understood as new constants of nature if the spontaneous localization is considered as a fundamental physical process. We can extend the model by making new conjectures about the possible values of these parameters. In particular, assuming the localization width of order of the atomic distance, the breakdown of the translational symmetry demands that the hitting process must be applied to a non-isolated quantum system. In this way we show that in the present approach the suppression of the coherence of quantum states is mainly due to the dissipation/fluctuation process and not to the random hitting process introduced by the GRW model.

A stochastic wave function approach to quantum measurement

A stochastic formulation of open quantum systems is applied to a microscopic system-meter-reservoir model of quantum measurement. The quantum statistical variance is decomposed into two variances which allow a quantitative description of the transformation from quantum to classical probabilities during the process of measurement.

Quantum measurement and the transformation from quantum to classical probabilities.

A specific model of quantum measurement [D. F. Walls, M. J. Collet, and G. J. Milburn, Phys. Rev. D 32, 3208 (1985)] based on a generic system-meter-environment measurement scheme is investigated in terms of probability distributions on projective Hilbert space. Starting from the unitary evolution of the total system a stochastic process for the wave function of the reduced system-meter system is derived by elimination of the degrees of freedom of the environment. The stochastic process is interpreted in terms of the direct detection of the photoelectrons created by the meter quanta in the environment. Two general variances are introduced which represent, respectively, the average intrinsic quantum fluctuations and the statistical fluctuations of the quantum expectation of the measured observable. Involving fourth moments of the wave function, these variances allow to monitor the transformation from quantum to classical probabilities during the process of measurement. \textcopyright{} 1996 The American Physical Society.

Preselection with certainty of photons in a singlet state from a set of independent photons

It is shown that one canpreselect with certainty photons in the singlet state from a set of completely unpolarized and independent photons which did not in any way directly interact with each other-without in any way affecting them. The result is based on an experiment which puts together two unpolarized photons from two independent singlet pairs, making them interfere in the fourth order at a beam splitter so as to preselect the singlet state of the other two photons from the pairs, although no polarization measurement has been carried out on the photons coming out from the beam splitter. One can obtain the expectation value for the correlated state of the former two unpolarized photons in the Hilbert space and therefore write down the singlet state for them, but one apparently cannotinfer the state within the Hilbert space. This might suggest that the Hilbert space is not amaximal model for quantum measurements.

A model of quantum measurement in Josephson junctions

A model for the quantum measurement of the electronic current in a Josephson junction is presented and analyzed. The model is similar to a Stern-Gerlach apparatus, relying on the deflection of a spin-polarized particle beam by the magnetic field created by the Josephson current. The aim is (1) to explore, with the help of a simple model, some general ideas about the nature of the information which can be obtained by measurements upon a quantum system and (2) to find new approaches for obtaining information about the nature of the states of a macroscopic quantum system. In the case of sufficiently strong coupling between the system and the apparatus, we find that the model provides in principle a standard ideal measurement of the value of the instantaneous Josephson current. In the case of weak coupling, where the measurement is not ideal, we show that the scattering of neutrons from a junction can in principle be used to measure the average value of the Josephson current, thereby allowing an experimental distinction to be made between an eigenstate of relative phase and one of relative Cooper pair number. The possibility of the latter type of measurement suggests an experimental approach to answer a question of fundamental interest, namely whether two isolated superconductors (or superfluids) possess a definite relative phase or a definite relative number of superconducting (or super/lowing) particles.

Generalization of Cini's model for quantum measurement and dynamical realization of wavefunction collapse

A quantum dynamical model for the measurement of an N-level system is proposed based on the correlation between the states of the detector and the states of the measured system in the measurement process. It is shown that the postulate of wavefunction collapse for the measured system can be realized in a dynamical evolution of the total system formed by the measured system plus the detector, which is governed by the Schrödinger equation.

MEASUREMENT, IRREVERSIBILITY AND DECOHERENCE IN QUANTUM MECHANICS

We review Prigogine's model of quantum measurement. The measuring apparatus is considered to be an unstable quantum system with its state vector belonging to a rigged Hilbert space. Time irreversibility arises due to the dissipative nature of the measuring apparatus (an unstable quantum system) which induces decoherence in the system being measured. Friedrichs' model is used to concretely illustrate these ideas.

Recurrence and decoherence times of quantum states in a measurement process

We revisit a time-reversible quantum measurement model proposed by Zurek [Phys. Rev. D 24 (1981) 1516; 26 (1982) 1862], which, besides the system and measurement apparatus, also involves the environment. Here, we introduce two additional assumptions: (1) The environment is considered thermalized, with all its two-level atoms having the same energy spacing. (2) The eigenvalues of the apparatus-environment interaction are not assumed all the same for the atoms of the environment, instead, the eigenvalues follow an inverse distance power law according to the “proximity” of these to the apparatus. We verify that the recurrence time is only sensible to the number of environment atoms ( N), while the decoherence time is much more sensible to the temperature than to N. The ratio of these two characteristic times exhibits a behavior (decreasing with inverse power of N) compatible with what is supposed to happen in a measurement process, when the collapse or reduction of the system-apparatus quantum state takes place.

Comment on a recent model of imprecise measurement

A quantum-measurement model introduced recently to describe measurements leading to statistical mixtures of nonorthogonal states is questioned.

Transition between incompatible properties: Dynamical model for quantum measurement.

Transition between incompatible properties: Dynamical model for quantum measurement.

Discrete stochastic variational principles and quantum mechanics

We consider stochastic variational principles for random processes taking values on a discrete configuration space. For a suitable time-reversal-invariant choice of the stochastic action, the resulting programming equations can be related to the Schr\odinger equation for a discrete system. If the discrete system is considered as an approximation of a continuous system, then the limit reproduces Nelson's stochastic mechanics and allows one to derive the assumptions on the random noise acting on the system. In fact, the variational principle also gives information about the osmotic behavior of the process. Finally, we show that there are also critical processes whose behavior can be interpreted as a model for quantum measurement, because they relax in time to mixtures of processes. Therefore, stochastic variational principles can provide a very simple conceptual model simulating quantum behavior, both from the point of view of unperturbed time evolution and of the measurement phenomena leading to wave-function collapse.