Showing papers on "Quantum error correction published in 1993"

Quantum circuit complexity

Abstract: We propose a complexity model of quantum circuits analogous to the standard (acyclic) Boolean circuit model. It is shown that any function computable in polynomial time by a quantum Turing machine has a polynomial-size quantum circuit. This result also enables us to construct a universal quantum computer which can simulate, with a polynomial factor slowdown, a broader class of quantum machines than that considered by E. Bernstein and U. Vazirani (1993), thus answering an open question raised by them. We also develop a theory of quantum communication complexity, and use it as a tool to prove that the majority function does not have a linear-size quantum formula. >

A Potentially Realizable Quantum Computer

Abstract: Arrays of weakly coupled quantum systems might compute if subjected to a sequence of electromagnetic pulses of well-defined frequency and length. Such pulsed arrays are true quantum computers: Bits can be placed in superpositionsof 0 and 1, logical operations take place coherently, and dissipation is required only for error correction. Operated with frequent error correction, such a system functions as a parallel digital computer. Operated in a quantum-mechanically coherent manner, such a device functions as a generalpurpose quantum-mechanical micromanipulator, capable of both creating any desired quantum state of the array and transforming that state in any desired way.

Comment on "Computational approach to the quantum Zeno effect: Position measurements"

Abstract: We examine results presented by Fearn and Lamb [Phys. Rev. A 46, 1199 (1992)], who search for, but fail to find, the quantum Zeno effect in measurements of the position of a particle in a double potential well, and criticize the basic statement of the effect given by Misra and Sudarshan [J. Math. Phys. 18, 756 (1977)]. We suggest that position measurements are an inappropriate area to look for the effect; nevertheless, we show that some of the results of Fearn and Lamb should, and do, exhibit a form of weak effect. Though the collapse postulate, as used by Misra and Sudarshan, is not required to discuss quantum measurement and the quantum Zeno effect, its application describes adequately the results of measurement, and we reject the idea that the basic statement of the quantum Zeno effect is flawed.

Many-body theory of quantum noise.

Abstract: A self-consistent many-body approach to quantum noise is presented. Many-photon polarization effects produce system-size scaling in quantum dissipative systems. The role of system-size quantum noise on the dynamics near the bifurcation point in an optical parametric oscillator is investigated, and nonlinear spectra are presented in the nonadiabatic limit.

Problem of signal transmission via quantum correlations and Einstein incompleteness in quantum mechanics

Abstract: The question of (superluminal) signaling by means of quantum correlations is reconsidered and previous arguments are generalized and completed to yielding conclusive answers to the negative. Statistical analysis of the amplified input on the receiver's side shows that the state discrimination needed for defining a signal is in conflict with the linearity of quantum dynamics. Connections with fundamental issues of quantum mechanics are pointed out.

Inconsistency between alternative approaches to Quantum Decoherence in special systems

Abstract: We study the decoherence properties of a certain class of Markovian quantum open systems from both the Decohering Histories and Environment Induced Superselection paradigms. The class studied includes many familiar quantum optical cases. For this class, we show that there always exists a basis which leads to {\em exactly} consistent histories for any coarse graining {\em irrespective} of the initial conditions. The magnitude of the off--diagonal elements of the reduced density matrix $\rho$ in this basis however, depends on the initial conditions. Necessary requirements for classicality as advanced by the two paradigms are thus in direct conflict in these systems.

A nonlocal approach to vertex models and quantum spin systems

Abstract: We discuss the loop-algorithm, a new type of cluster algorithm that reduces critical slowing down in vertex models and in quantum spin systems. We cover the example of the 6-vertex model in detail. For the F-model, we present numerical results that demonstrate the effectiveness of the loop algorithm. We show how to modify the original algorithm for some more complicated situations, especially for quantum spin systems in one and two dimensions, and we discuss parallelization.

Quantum non-demolition measurements in optics and quantum optical repeaters

Abstract: The efficiency of an optical quantum non-demolition (QND) measurement can be characterized using three criteria, which describe respectively the quality of the quantum measurement, the non-destruction of the signal, and the conditional variance of the output signal beam, given the output meter beam (quantum-state-preparation criterion). Quantitative limits can be defined with respect to these criteria, delimiting “classical” and “quantum” domains of operation. We describe the implementation of two experiments which fulfill these criteria, using either three-level atoms inside a doubly-resonant optical cavity, or semiconductors emitters and receivers.

A theorem on light‐front quantum models

Abstract: A sufficient condition for a relativistic front‐form quantum mechanical model to be scattering equivalent to a relativistic front‐form quantum model with an interaction‐independent front‐form spin is given.

Quantum measurement theory and the quantum Zeno effect

Abstract: This is a theoretical thesis in the area of quantum measurement theory. Due to the extensive breadth of this field we choose to narrow our focus to examine a particular problem - the quantum Zeno effect (defined below). Quantum measurement theory is introduced in Chap. 1, using the terminology of effects and operations. This approach allows an operational definition of such terms as a state vector, an ensemble, and a measurement device (for instance), and a consideration of interactions between quantum systems and inaccurate measurement devices. We further introduce the quantum trajectories approach to consider the evolution of an individual quantum system subject to measurement. The quantum Zeno effect is introduced in Chap. 2. Any quantum treatment of a measurement interaction must consider the measurement backaction onto the measured system and this backaction will disrupt the free evolution of the system. The quantum Zeno effect occurs in the strong measurement limit where the measurement backaction totally freezes the evolution of the system, thus rendering the measurement useless. The effect is introduced via projective measurements of two level systems subject to measurement of level populations. At this stage we are able to discuss the main questions addressed by this thesis, and present its structure in Chap. 2. We then develop a new measurement model for the interaction between a system and a measurement device in Chap. 3. Our motivation in doing this is to better model the usual laboratory meter, and in our approach the meter dynamics are such that it relaxes towards an appropriate readout of the system parameter of interest. The irreducible quantum noise of the meter introduces fluctuations that drive the stochastic dynamical collapse of the system wavefunction. In our model, the measured system dynamics (if treated selectively) are described by a stochastic, nonlinear Schroedinger equation. A double well system subject to position measurement provides a natural first application for this model. This is done in Chap. 4 where we monitor the coherent tunnelling of a particle from one well to the other. The advantage afforded by considering this system is that it displays differing regimes where the measurement observable (position) is approximated as possessing either, respectively, a continuous or a discrete eigenvalue structure. Thus, we use this one model to explore the quantum Zeno effect in both measurement regimes. The above treatment is of a theoretical measurement model. In Chap. 5 we turn to consider a recent experimental test of the quantum Zeno effect which examined the dynamics of a two level atom subject to pulsed measurements of atomic level populations. We treat a slightly modified experiment in a fully continuous measurement regime. By first unravelling the optical Bloch equations, and second, using the quantum trajectories approach we demonstrate the existence of certain measurement regimes where there is a quantum Zeno effect, and other regimes where no measurement of the atomic populations is being effected at all. Through these results we demonstrate the importance of making a full analysis of the system-detector interaction before any conclusions can be made. In the remainder of the thesis we propose further possible tests of the quantum Zeno effect. In Chap. 6 the evolution of a Rydberg atom exchanging one photon with a single cavity mode subject to measurement is examined. The measurement is made by monitoring the photon number occupancy of the cavity mode using a beam of Rydberg atoms configured so as to perform phase sensitive detection. In the limit of frequent monitoring we show that the free oscillation of the atomic inversion is disrupted, and the atom is trapped close to its initial state. This is the quantum Zeno effect. In Chap. 7 we realize the Zeno effect on two possible systems. We consider first, a two level Jaynes-Cumming atom interacting with a cavity mode, and second, two electromagnetic modes configured as a multi-level parametric frequency converter. These systems interact with another cavity mode via a quadratic coupling system based on four wave mixing, and constructed to be a quantum nondemolition measurement of the photon number. This mode is damped to the environment thus effecting a measurement of the system populations. Again we show that this interaction, can manifest the quantum Zeno effect. Our explicit modelling of the system-detector interaction enables us to show how the effect depends on the resolution time of the detector. Finally, we consider a proposed measurement of the square of the quadrature phase of an electromagnetic mode in Chap. 8. Here, a three mode interaction mediated by a second order nonlinear susceptibility is considered. One mode, the pump, is prepared in a feedback generated photon number state to give insight into the role of pump noise. The other two modes are treated as an angular momentum system, and we show that photon counting on the two mode rotation system effects the above mentioned measurement. In addition, this measurement provides a direct measure of the second order squeezing of the signal. With that we finish our investigation of the quantum Zeno effect using the techniques of quantum measurement theory. However, in the epilogue [Chap. 9] we note that no thesis in quantum measurement theory would be complete without some consideration of the ``meaning" attributed to the theory. In the epilogue we take a novel historical approach and examine the method by which metaphysical theories are formed to draw conclusions regarding quantum metaphysics.

Compact quantum systems and the Pauli data problem

Abstract: Compact quantum systems have underlying compact kinematical Lie algebras, in contrast to familiar noncompact quantum systems built on the Weyl-Heisenberg algebra. Pauli asked in the latter case: to what extent does knowledge of the probability distributions in coordinate and momentum space determine the state vector? The analogous question for compact quantum systems is raised, and some preliminary results are obtained.

Disturbance, the uncertainty principle and quantum optics

Abstract: It is shown how a disturbance-type uncertainty principle can be derived from an uncertainty principle for joint measurements. To achieve this, we first clarify the meaning of 'inaccuracy' and 'disturbance' in quantum mechanical measurements. The case of photon number and phase is treated as an example, and it is applied to a quantum non-demolition measurement using the optical Kerr effect.