Hiromichi Nakazato

From the quantum zeno to the inverse quantum zeno effect.

The temporal evolution of an unstable quantum mechanical system undergoing repeated measurements is investigated. In general, by changing the time interval between successive measurements, the decay can be accelerated (inverse quantum Zeno effect) or slowed down (quantum Zeno effect), depending on the features of the interaction Hamiltonian. A geometric criterion is proposed for a transition to occur between these two regimes.

TEMPORAL BEHAVIOR OF QUANTUM MECHANICAL SYSTEMS

The temporal behavior of quantum mechanical systems is reviewed. We mainly focus our attention on the time development of the so-called “survival” probability of those systems that are initially prepared in eigenstates of the unperturbed Hamiltonian, by assuming that the latter has a continuous spectrum. The exponential decay of the survival probability, familiar, for example, in radioactive decay phenomena, is representative of a purely probabilistic character of the system under consideration and is naturally expected to lead to a master equation. This behavior, however, can be found only at intermediate times, for deviations from it exist both at short and long times and can have significant consequences. After a short introduction to the long history of the research on the temporal behavior of such quantum mechanical systems, the short-time behavior and its controversial consequences when it is combined with von Neumann’s projection postulate in quantum measurement theory are critically overviewed fro...

Control of decoherence: Analysis and comparison of three different strategies

We analyze and compare three different strategies, all aimed at controlling and eventually halting decoherence. The first strategy hinges upon the quantum Zeno effect, the second makes use of frequent unitary interruptions s“bang-bang” pulses and their generalization, quantum dynamical decoupling d, and the third uses a strong, continuous coupling. Decoherence is shown to be suppressed only if the frequency N of the measurements or pulses is large enough or if the coupling K is sufficiently strong. Otherwise, if N or K is large, but not extremely large, all these control procedures accelerate decoherence. We investigate the problem in a general setting and then consider some practical examples, relevant for quantum computation.

Understanding the quantum zeno effect

Abstract The quantum Zeno effect consists in the hindrance of the evolution of a quantum system that is very frequently monitored and found to be in its initial state at every single measurement. On the basis of the correct formula for the survival probability, i.e. the probability of finding the system in its initial state at every single measurement, we critically analyze a recent proposal and experimental test that make use of an oscillating system.

ON THE QUANTUM ZENO EFFECT

Abstract The limit of infinitely frequent measurements (continuous observation), yielding the quantum Zeno paradox, is critically analyzed and shown to be unphysical. A specific example involving neutron spin is considered and some practical estimates are given.

Resonant scattering can enhance the degree of entanglement

Generation of entanglement between two qubits by scattering an entanglement mediator is discussed. The mediator bounces between the two qubits and exhibits a resonant scattering. It is clarified how the degree of the entanglement is enhanced by the constructive interference of such bouncing processes. Maximally entangled states are available via adjusting the incident momentum of the mediator or the distance between the two qubits, but their fine tunings are not necessarily required to gain highly entangled states and a robust generation of entanglement is possible.

Preparation and entanglement purification of qubits through Zeno-like measurements

A method of purification, purification through Zeno-like measurements [H. Nakazato, T. Takazawa, and K. Yuasa, Phys. Rev. Lett. 90, 060401 (2003)], is discussed extensively and applied to a few simple qubit systems. It is explicitly demonstrated how it works and how it is optimized. As possible applications, schemes for initialization of multiple qubits and entanglement purification are presented, and their efficiency is investigated in detail. Simplicity and flexibility of the idea allow us to apply it to various kinds of settings in quantum information and computation, and would provide us with useful and practical methods of state preparation.

Infinitely frequent measurements and quantum Zeno effect

Abstract The limit of infinitely many measurements is critically analyzed within the quantum mechanical framework, in connection with the quantum Zeno effect. It is shown that such a limit is unphysical and that quantum losses are unavoidable. A specific example involving neutron spin is considered.

Exponential rise of dynamical complexity in quantum computing through projections

Daniel Burgarth,1 Paolo Facchi,2, 3 Vittorio Giovannetti,4 Hiromichi Nakazato,5 Saverio Pascazio,2, 3 and Kazuya Yuasa5 Department of Mathematics and Physics, Aberystwyth University, SY23 3BZ Aberystwyth, United Kingdom Dipartimento di Fisica and MECENAS, Università di Bari, I-70126 Bari, Italy INFN, Sezione di Bari, I-70126 Bari, Italy NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa, Italy Department of Physics, Waseda University, Tokyo 169-8555, JapanThe ability of quantum systems to host exponentially complex dynamics has the potential to revolutionize science and technology. Therefore, much effort has been devoted to developing of protocols for computation, communication and metrology, which exploit this scaling, despite formidable technical difficulties. Here we show that the mere frequent observation of a small part of a quantum system can turn its dynamics from a very simple one into an exponentially complex one, capable of universal quantum computation. After discussing examples, we go on to show that this effect is generally to be expected: almost any quantum dynamics becomes universal once ‘observed’ as outlined above. Conversely, we show that any complex quantum dynamics can be ‘purified’ into a simpler one in larger dimensions. We conclude by demonstrating that even local noise can lead to an exponentially complex dynamics.

Solution of the Lindblad equation in the Kraus representation

The so-called Lindblad equation, a typical master equation describing the dissipative quantum dynamics, is shown to be solvable for finite-level systems in a compact form without resort to writing it down as a set of equations among matrix elements. The solution is then naturally given in an operator form, known as the Kraus representation. Following a few simple examples, the general applicability of the method is clarified.