The driven evolution of the spin of an individual atomic ion on the ground-state hyperfine resonance is impeded by the observation of the ion in one of the pertaining eigenstates. Detection of resonantly scattered light identifies the ion in its upper ``bright'' state. The lower ``dark'' ion state is free of relaxation and correlated with the detector by a null signal. Null events represent the straightforward demonstration of the quantum Zeno paradox. Also, high probability of survival was demonstrated when the ion, driven by a fractionated $π$ pulse, was probed {\em and monitored} during the intermissions of the drive, such that the ion's evolution is completely documented.
One can reduce the involved derivation of Balachandran and Roy of their `anti-Zeno' effect [Phys.Rev.Lett. 84, 4019 (2000)] to the derivation of standard Zeno effect. The mechanism of what the authors call `anti-Zeno' effect is a dynamic version of Zeno effect.
As of October 2006, there were approximately 535 citations to the seminal 1977 paper of Misra and Sudarshan that pointed out the quantum Zeno paradox (more often called the quantum Zeno effect). In simple terms, the quantum Zeno effect refers to a slowing down of the evolution of a quantum state in the limit that the state is observed continuously. There has been much disagreement as to how the quantum Zeno effect should be defined and as to whether it is really a paradox, requiring new physics, or merely a consequence of "ordinary" quantum mechanics. The experiment of Itano, Heinzen, Bollinge…
The quantum Zeno paradox is fully resolved for purely indirect and incomplete measurements performed by the detectors outside the system. If the outside detectors are prepared to observe propagating signals of a decay event of an excited state in the core region, the survival probability of the state is not changed at all by the outside measurements, as long as the wavefunction of the signals does not have reflectional-wave contributions going back to the core by the outside detectors. The proof is independendent of the decay law of the survival probabilities. Just watching frequently from out…
Quantum Zeno effect is a significant tool in quantum manipulating and computing. We propose its observation in superconducting phase qubit with two experimentally feasible measurement schemes. The conventional measurement method is used to achieve the proposed pulse and continuous readout of the qubit state, which are analyzed by projection assumption and Monte Carlo wave-function simulation, respectively. Our scheme gives a direct implementation of quantum Zeno effect in a superconducting phase qubit.
The Zeno effect occurs in quantum systems when a very strong measurement is applied, which can alter the dynamics in non-trivial ways. Despite being dissipative, the dynamics stay coherent within any degenerate subspaces of the measurement. Here we show that such a measurement can turn a single-qubit operation into a two- or multi-qubit entangling gate, even in a non-interacting system. We demonstrate this gate between two effectively non-interacting transmon qubits. Our Zeno gate works by imparting a geometric phase on the system, conditioned on it lying within a particular non-local subspace…
The possibility to observe quantum Zeno and anti-Zeno scenarios for atom-diatom reactive collisions is investigated for two diferent processes (F+HD and H+O_2) by means of time-dependent wave packet propagations. A novel approach is proposed in which the survival probabilities investigated are those obtained when the initial state is redefined after time intervals tau at which measurements are performed on the system. The comparison with the actual probability for the unperturbed system reveals the existence of a regime in which the decay from the initial state appears to be inhibited (the qua…
A discussion of the quantum Zeno effect and paradox is given. The quantum Zeno paradox claims that a continuously observed system, prepared in a state which is not an eigenstate of the Hamiltonian operator, never decays. To recover the classical behavior of unstable systems we consider a two-level system interacting with a Bose field, respectively prepared in the excited state and in the Poincare invariant vacuum state. Using time-dependent perturbation theory, we evaluate for a finite time interval the probability of spontaneous decay of the two-level system. Using the standard argument to ob…
We establish an exact differential equation for the operator describing time-dependent measurements continuous in time and obtain a series solution. Suppose the projection operator $E(t) = U(t) E U^\dagger(t)$ is measured continuously from t = 0 to T, where E is a projector leaving the initial state unchanged and U(t) a unitary operator obeying U(0) = 1 and some smoothness conditions in t. We prove that the probability of always finding E(t) = 1 from t = 0 to T is unity. If $U(t) \neq 1$, the watched kettle is sure to `boil'.
Hardy's paradox was originally presented as a demonstration, without inequalities, of the incompatibility between quantum mechanics and the hypothesis of local causality. Equipped with newly developed tools that allow for a quantitative assessment of realism, here we revisit Hardy's paradox and argue that non-local causality is not mandatory for its solution; quantum irrealism suffices.
We present an overview of the mathematics underlying the quantum Zeno effect. Classical, functional analytic results are put into perspective and compared with more recent ones. This yields some new insights into mathematical preconditions entailing the Zeno paradox, in particular a simplified proof of Misra's and Sudarshan's theorem. We empahsise the complex-analytic structures associated to the issue of existence of the Zeno dynamics. On grounds of the assembled material, we reason about possible future mathematical developments pertaining to the Zeno paradox and its counterpart, the anti-Ze…
We derive differential equations for the modified Feynman propagator and for the density operator describing time-dependent measurements or histories continuous in time. We obtain an exact series solution and discuss its applications. Suppose the system is initially in a state with density operator $ρ(0)$ and the projection operator $E(t) = U(t) E U^\dagger(t)$ is measured continuously from $t = 0$ to $T$, where $E$ is a projector obeying $Eρ(0) E = ρ(0)$ and $U(t)$ a unitary operator obeying $U(0) = 1$ and some smoothness conditions in $t$. Then the probability of always finding $E(t) = 1$ fr…
We analyse the track of an α-particle passing through a cloud chamber using the Bohm theory and show that the resulting classical track has its origins in the quantum Zeno effect. By assuming the ionised gas molecules reveal the positions of the α-particle on its trajectory and using these positions in a short time propagator technique developed by de Gosson, we show it is the failure of the quantum potential to develop quickly enough that leads to the appearance of the classical trajectory. Bohm and Hiley have already argued that it is this failure of the quantum potential to develop appropri…
We experimentally demonstrate all-optical interaction-free switching using the quantum Zeno effect, achieving a high contrast of 35:1. The experimental data matches a zero-parameter theoretical model for several different regimes of operation, indicating a good understanding of the switch's characteristics. We also discuss extensions of this work that will allow for significantly improved performance, and the integration of this technology onto chip-scale devices.
We experimentally demonstrate, for the first time, noise diagnostics by repeated quantum measurements. Specifically, we establish the ability of a single photon, subjected to random polarisation noise, to diagnose non-Markovian temporal correlations of such a noise process. In the frequency domain, these noise correlations correspond to colored noise spectra, as opposed to the ones related to Markovian, white noise. Both the noise spectrum and its corresponding temporal correlations are diagnosed by probing the photon by means of frequent, (partially-)selective polarisation measurements. Our m…
In 1977, Mishra and Sudarshan showed that an unstable particle would never be found decayed while it was continuously observed. They called this effect the quantum Zeno effect (or paradox). Later it was realized that the frequent measurements could also accelerate the decay (quantum anti-Zeno effect). In this paper we investigate the quantum Zeno effect using the definite model of the measurement. We take into account the finite duration and the finite accuracy of the measurement. A general equation for the jump probability during the measurement is derived. We find that the measurements can c…
The EPR (Einstein, Podolsky, Rosen) argument and the Schrodinger cat paradox are revisited in relation with modern quantum optics and atomic physics and with the concept of decoherence. It is shown that the questions raised fifty years ago are still at the heart of our understanding of quantum physics today.
We describe Nuclear Magnetic Resonance (NMR) demonstrations of the quantum Zeno effect, and discuss briefly how these are related to similar phenomena in more conventional NMR experiments.
We experimentally demonstrate that when three single photons transmit through two polarization channels, in a well-defined pre- and postselected ensemble, there are no two photons in the same polarization channel by weak-strength measurement, a counter-intuitive quantum counting effect called quantum pigeonhole paradox. We further show that this effect breaks down in second-order measurement. These results indicate the existence of quantum pigeonhole paradox and its operating regime.
Low-contrast all-optical Zeno switching has been demonstrated in a silicon nitride microdisk resonator coupled to a hot atomic vapor. The device is based on the suppression of the field build-up within a microcavity due to non-degenerate two-photon absorption. This experiment used one beam in a resonator and one in free-space due to limitations related to device physics. These results suggest that a similar scheme with both beams resonant in the cavity would correspond to input power levels near 20 nW.
The dynamics of a quantum system undergoing frequent "measurements", leading to the so-called quantum Zeno effect, is examined on the basis of a neutron-spin experiment recently proposed for its demonstration. When the spatial degrees of freedom are duely taken into account, neutron-reflection effects become very important and may lead to an evolution which is totally different from the ideal case.
We experimentally demonstrate a new dynamic fashion of quantum Zeno effect in nuclear magnetic resonance systems. The frequent measurements are implemented through quantum entanglement between the target qubit(s) and the measuring qubit, which dynamically results from the unitary evolution of duration $τ_{m}$ due to dispersive-coupling. Experimental results testify the presence of "the critical measurement time effect", that is, the quantum Zeno effect does not occur when $τ_{m}$ takes the some critical values, even if the measurements are frequent enough. Moreover, we provide a first experime…
Quantum Zeno Dynamics is the phenomenon that the observation or strong driving of a quantum system can freeze its dynamics to a subspace, effectively truncating the Hilbert space of the system. It represents the quantum version of the famous flying arrow Zeno paradox. Here, we study how temporal stochasticity in the system observation (or driving) affects the survival probability of the system in the subspace. In particular, we introduce a strong and a weak Zeno regime for which we quantify the confinement by providing an analytical expression for this survival probability. We investigate seve…
A quantum system being observed evolves more slowly. This `'quantum Zeno effect'' is reviewed with respect to a previous attempt of demonstration, and to subsequent criticism of the significance of the findings. A recent experiment on an {\it individual} cold trapped ion has been capable of revealing the micro-state of this quantum system, such that the effect of measurement is indeed discriminated from dephasing of the quantum state by either the meter or the environment.
The protection of the coherence of open quantum systems against the influence of their environment is a very topical issue. A scheme is proposed here which protects a general quantum system from the action of a set of arbitrary uncontrolled unitary evolutions. This method draws its inspiration from ideas of standard error-correction (ancilla adding, coding and decoding) and the Quantum Zeno Effect. A pedagogical demonstration of our method on a simple atomic system, namely a Rubidium isotope, is proposed.
A generalization of the 1935 Einstein-Podolsky-Rosen (EPR) argument for measurements with continuous variable outcomes is presented to establish criteria for the demonstration of the EPR paradox, for situations where the correlation between spatially separated subsystems is not perfect. Two types of criteria for EPR correlations are determined. The first type are based on measurements of the variances of conditional probability distributions and are necessary to reflect directly the situation of the original EPR paradox. The second weaker set of EPR criteria are based on the proven failure of …
In the 5th century B.C.,the philosopher and logician Zeno of Elea posed several paradoxes which remained unresolved for over two thousand five hundred years. The $20^{th}$ century saw some resolutions to Zeno's mind boggling problems. This long journey saw many significant milestones in the form of discoveries like the tools of converging series and theories on infinite sets in mathematics. In recent times, the Zeno effect made an intriguing appearance in a rather unlikely place - a situation involving the time evolution of a quantum system, which is subject to "observations" over a period of …
The quantum Zeno effect (QZE) is the phenomenon where the unitary evolution of a quantum state is suppressed e.g. due to frequent measurements. Here, we investigate the use of the QZE in a class of communication complexity problems (CCPs). Quantum entanglement is known to solve certain CCPs beyond classical constraints. However, recent developments have yielded CCPs where super-classical results can be obtained using only communication of a single d-level quantum state (qudit) as a resource. In the class of CCPs considered here, we show quantum reduction of complexity in three ways: using i) e…
A model for quantum Zeno effect based upon an effective Schrödinger equation originated by the path-integral approach is developed and applied to a two-level system simultaneously stimulated by a resonant perturbation. It is shown that inhibition of stimulated transitions between the two levels appears as a consequence of the influence of the meter whenever measurements of energy, either continuous or pulsed, are performed at quantum level of sensitivity. The generality of this approach allows to qualitatively understand the inhibition of spontaneous transitions as the decay of unstable partic…
The quantum measurement problem, namely how the deterministic quantum evolution leads to probabilistic measurement outcomes, remains a profound question to be answered. In the present work, we propose a spectacular demonstration and test of the subtle and peculiar character of the quantum measurement process. We show that a bright soliton supported by a Bose-Einstein condensate can be reflected as a whole by an electron beam, with neither attraction nor repulsion between the condensate's neutral atoms and the beam's electrons. This macroscopic reflection is purely due to the quantum Zeno dynam…
We present a unified approach, based on the use of quantum uncertainty relations, for arriving at criteria for the demonstration of the EPR paradox and macroscopic superpositions. We suggest to view each criterion as a means to demonstrate an EPR-type paradox, where there is an inconsistency between the assumptions of a form of realism, either macroscopic realism (MR) or local realism (LR), and the completeness of quantum mechanics.
Prevention of a quantum system's time evolution by repetitive, frequent measurements of the system's state has been called the quantum Zeno effect (or paradox). Here we investigate theoretically and numerically the effect of repeated measurements on the quantum dynamics of the multilevel systems that exhibit the quantum localization of the classical chaos. The analysis is based on the wave function and Schroedinger equation, without introduction of the density matrix. We show how the quantum Zeno effect in simple few-level systems can be recovered and understood by formal modeling the measurem…
Maximizing Nonclassicality of Massive Objects via Quantum Zeno Effect
Shiv Nadar Institution of Eminence（希夫纳达尔卓越学院）；S. N. Bose National Centre for Basic Sciences（S.N. 玻色基础科学国家中心）；Faculty of Mathematics and Physics, University of Ljubljana（卢布尔雅那大学数学与物理学院）；School of Physics and Astronomy, University of Southampton（南安普顿大学物理与天文学院）；Raman Research Institute (RRI)（拉曼研究所）；Bose Institute（玻色研究所）；Department of Physics and Astronomy, University College London（伦敦大学学院物理与天文学系）
Demonstrations of quantum entanglement which confirm the violation of Bell's inequality indicate that under certain conditions action at a distance is possible. This consequence seems to contradict the relativistic principle of causality, which asserts that an effect never precedes its cause, in any reference frame. By analyzing a numerical example of Bell's experiment with entangled pairs of photons, we show how observers in two inertial reference frames can disagree about the causality relation between two events. One observer claims that event 1 is the cause of event 2, while the other clai…
Since the pillars of quantum theory were established, it was already noted that quantum physics may allow certain correlations defying any local realistic picture of nature, as first recognized by Einstein, Podolsky and Rosen. These quantum correlations, now termed quantum nonlocality and tested by violation of Bell's inequality that consists of statistical correlations fulfilling local realism, have found loophole-free experimental confirmation. A more striking way to demonstrate the conflict exists, and can be extended to the multipartite scenario. Here we report experimental confirmation of…
We demonstrate the control of quantum tunneling in an ultracold lattice gas by the measurement backaction imposed by an imaging process. A {\em in situ} imaging technique is used to acquire repeated images of an ultracold gas confined in a shallow optical lattice. The backaction induced by these position measurements modifies the coherent quantum tunneling of atoms within the lattice. By smoothly varying the rate at which spatial information is extracted from the atomic ensemble, we observe the continuous crossover from the 'weak measurement regime' where position measurements have little infl…
The Greenberger-Horne-Zeilinger (GHZ) effect provides an example of quantum correlations that cannot be explained by classical local hidden variables. This paper reports on the experimental realization of GHZ correlations using nuclear magnetic resonance (NMR). The NMR experiment differs from the originally proposed GHZ experiment in several ways: it is performed on mixed states rather than pure states; and instead of being widely separated, the spins on which it is performed are all located in the same molecule. As a result, the NMR version of the GHZ experiment cannot entirely rule out class…
We formally link the concept of steering (a concept created by Schrodinger but only recently formalised by Wiseman, Jones and Doherty [Phys. Rev. Lett. 98, 140402 (2007)] and the criteria for demonstrations of Einstein-Podolsky-Rosen (EPR) paradox introduced by Reid [Phys. Rev. A, 40, 913 (1989)]. We develop a general theory of experimental EPR-steering criteria, derive a number of criteria applicable to discrete as well as continuous-variables observables, and study their efficacy in detecting that form of nonlocality in some classes of quantum states. We show that previous versions of EPR-ty…
Pseudo-density matrices are a generalisation of quantum states and do not obey monogamy of quantum correlations. Could this be the solution to the paradox of information loss during the evaporation of a black hole? In this paper we discuss this possibility, providing a theoretical proposal to extend quantum theory with these pseudo-states to describe the statistics arising in black-hole evaporation. We also provide an experimental demonstration of this theoretical proposal, using a simulation in optical regime, that tomographically reproduces the correlations of the pseudo-density matrix descr…
Closed timelike curves (CTCs) are trajectories in spacetime that effectively travel backwards in time: a test particle following a CTC can in principle interact with its former self in the past. CTCs appear in many solutions of Einstein's field equations and any future quantum version of general relativity will have to reconcile them with the requirements of quantum mechanics and of quantum field theory. A widely accepted quantum theory of CTCs was proposed by Deutsch. Here we explore an alternative quantum formulation of CTCs and show that it is physically inequivalent to Deutsch's. Because i…
The well known interpretational difficulties with nonlinear Schrödinger and von Neumann equations can be reduced to the problem of computing multiple-time correlation functions in the absence of Heisenberg picture. Having no Heisenberg picture one often resorts to Zeno-type reasoning which explicitly involves the projection postulate as a means of computing conditional and joint probabilities. Although the method works well in linear quantum mechanics, it completely fails for nonlinear evolutions. We propose an alternative way of performing the same task in linear quantum mechanics and show th…
In a previous paper certain measurable criteria have been derived, that are sufficient to demonstrate the existence of Einstein-Podolsky-Rosen (EPR) correlations for measurements with continuous variable outcomes. Here it is shown how such EPR criteria, which do not demand perfect EPR correlations, can be used to prove the extent of security for continuous variable quantum cryptographic schemes (in analogy to that proposed by Ekert) where Alice and Bob hope to construct a secure sequence of values from measurements performed on continuous-variable EPR-correlated fields sent from a distant sour…
In this article we argue that thermal reservoirs (baths) are potentially useful resources in processes involving atoms interacting with quantized electromagnetic fields and their applications to quantum technologies. One may try to suppress the bath effects by means of dynamical control, but such control does not always yield the desired results. We wish instead to take advantage of bath effects, that do not obliterate "quantumness" in the system-bath compound. To this end, three possible approaches have been pursued by us: (i) Control of a quantum system faster than the correlation time of th…
This paper surveys our recent research on quantum information processing by nuclear magnetic resonance (NMR) spectroscopy. We begin with a geometric introduction to the NMR of an ensemble of indistinguishable spins, and then show how this geometric interpretation is contained within an algebra of multispin product operators. This algebra is used throughout the rest of the paper to demonstrate that it provides a facile framework within which to study quantum information processing more generally. The implementation of quantum algorithms by NMR depends upon the availability of special kinds of m…
The violation of a Bell inequality is a striking demonstration of how quantum mechanics contradicts local realism. Although the original argument was presented with a pair of spin 1/2 particles, so far Bell inequalities have been shown to be violated using entangled pairs of photons, with recent measurements closing all possible loopholes in such a scheme. Equivalent demonstrations using massive particles have proven to be much more challenging, generally relying on post-selection of data or measuring an entanglement witness that relies on quantum mechanics. Here, we use a collision between tw…
