The quantum Zeno effect (QZE) is the striking prediction that the decay of any unstable quantum state can be inhibited by sufficiently frequent observations (measurements). The consensus opinion has upheld the QZE as a general feature of quantum mechanics, which should lead to the inhibition of any decay. The claim of QZE generality hinges on the assumption that successive observations can in principle be made at time intervals too short for the system to change appreciably. However, this assumption and the generality of the QZE have scarcely been investigated thus far. We have addressed these issues by showing that (i) the QZE is principally unattainable in radiative or radioactive decay, because the required measurement rates would cause the system to disintegrate; (ii) decay acceleration by frequent measurements (the anti-Zeno effect -- AZE) is much more ubiquitous than its inhibition. The AZE is shown to be observable as the enhancement of tunneling rates (e.g., for atoms trapped in ramped-up potentials or in current-swept Josephson junctions), fluorescence rates (e.g., for Rydberg atoms perturbed by noisy optical fields) and photon depolarization rates (in randomly modulated Pockels cells).
A quantum Zeno dynamics can be obtained by means of frequent measurements, frequent unitary kicks or a strong continuous coupling and yields a partition of the total Hilbert space into quantum Zeno subspaces, among which any transition is hindered. We focus on the "continuous" version of the quantum Zeno effect and look at several interesting examples. We first analyze these examples in practical terms, towards applications, then propose a novel experiment.
Three different manifestations of the quantum Zeno effect are discussed, compared and shown to be physically equivalent. We look at frequent projective measurements, frequent unitary "kicks" and strong continuous coupling. In all these cases, the Hilbert space of the system splits into invariant "Zeno" subspaces, among which any transition is hindered.
Frequent observation of a quantum system leads to quantum Zeno physics, where the system evolution is constrained to states commensurate with the measurement outcome. We show that, more generally, the system can evolve between such states through higher-order virtual processes that pass through states outside the measurement subspace. We derive effective Hamiltonians to describe this evolution, and the dependence on the time between measurements. We demonstrate application of this phenomena to prototypical quantum many-body system examples, spin chains and atoms in optical lattices, where it f…
Using numerical calculations, we compare the collective transition probabilities of many spins in random magnetic fields, subject to either frequent projective measurements, frequent phase modulations, or a mix of modulations and measurements. For three different distribution functions (Gaussian, Lorentzian, and exponential) we consider here, the transition probability under frequent modulations is suppressed most if the pulse delay is short and the evolution time is larger than a critical value. Furthermore, decoherence freezing (with a transition rate equals to zero) occurs when there are fr…
The quantum Zeno effect freezes the evolution of a quantum system subject to frequent measure- ments. We apply a Fisher information analysis to show that because of this effect, a closed quantum system should be probed as rarely as possible while a dissipative quantum systems should be probed at specifically determined intervals to yield the optimal estimation of parameters governing the sys- tem dynamics. With a Bayesian analysis we show that a few frequent measurements are needed to identify the parameter region within which the Fisher information analysis applies
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…
We point out that the quantum Zeno effect, i.e., inhibition of spontaneous decay by frequent measurements, is observable only in spectrally finite reservoirs, i.e., in cavities and waveguides, using a sequence of evolution-interrupting pulses or randomly-modulated CW fields. By contrast, such measurements can only accelerate decay in free space.
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.
The effect of entangling evolution induced by frequently repeated quantum measurement is presented. The interesting possibility of conditional freezing the system in maximally entangled state out of Zeno effect regime is also revealed. The illustration of the phenomena in terms of dynamical version of ``interaction free'' measurement is presented. Some general conclusions are provided.
We use a non-Markovian approach to study the decoherence dynamics of a qubit in either a low- or high-frequency bath modeling the qubit environment. This approach is based on a unitary transformation and does not require the rotating-wave approximation. We show that for low-frequency noise, the bath shifts the qubit energy towards higher energies (blue shift), while the ordinary high-frequency cutoff Ohmic bath shifts the qubit energy towards lower energies (red shift). In order to preserve the coherence of the qubit, we also investigate the quantum Zeno effect in two cases: low- and high-freq…
Quantum repeaters pave the way for long-distance quantum communications and quantum Internet, and the idea of quantum repeaters is based on entanglement swapping which requires the implementation of controlled quantum gates. Frequently measuring a quantum system affects its dynamics which is known as the quantum Zeno effect (QZE). Beyond slowing down its evolution, QZE can be used to control the dynamics of a quantum system by introducing a carefully designed set of operations between measurements. Here, we propose an entanglement swapping protocol based on QZE, which achieves almost unit fide…
We demonstrate that near threshold decay processes may be accelerated by repeated measurements. Examples include near threshold photodetachment of an electron from a negative ion, and spontaneous emission in a cavity close to the cutoff frequency, or in a photon band gap material.
The Zeno time has been calculated for a metastable two level atom tunneling through a interacting thermal magnetic field. The process of weak measurement has been utilized for the the estimation of the timescale. The temperature dependence of the Zeno time has been shown. From the calculation it is evident that the Zeno time decreases with the increase of temperature. Moreover, the result restricts the Zeno time to a maximum limiting value, irrespective of how frequent is the measurement process.
We analyze the experimental observations reported by Fischer et. al. [in Phys. Rev. Lett. 87, 040402 (2001)] by considering a system of coupled unstable bound quantum states A and B. The state B is coupled to a set of continuum states C. We investigate the time evolution of A when it decays into C via B, and find that frequent measurements on A leads to both the quantum Zeno effect and the anti-Zeno effects depending on the frequency of measurements. We show that it is the presence of B which allows for the anti-Zeno effect.
The time evolution of an unstable quantum mechanical system coupled with an external measuring agent is investigated. According to the features of the interaction Hamiltonian, a quantum Zeno effect (hindered decay) or an inverse quantum Zeno effect (accelerated decay) can take place, depending on the response time of the apparatus. The transition between the two regimes is analyzed for both pulsed and continuous measurements.
In this work we show that is possible to obtain Total Quantum Zeno Effect in an unstable systems for times larger than the correlation time of the bath. The effect is observed for some particular systems in which one can chose appropriate observables which frequent measurements freeze the system into the initial state. For a two level system in a squeezed bath one can show that there are two bath dependent observables displaying Total Zeno Effect when the system is initialized in some particular states. We show also that these states are intelligent states of two conjugate observables associat…
A series of frequent measurements on a quantum system (Zeno-like measurements) is shown to result in the ``purification'' of another quantum system in interaction with the former. Even though the measurements are performed on the former system, their effect drives the latter into a pure state, irrespectively of its initial (mixed) state, provided certain conditions are satisfied.
The evolution of a quantum system undergoing very frequent measurements takes place in a proper subspace of the total Hilbert space (quantum Zeno effect). When the measuring apparatus is included in the quantum description, the Zeno effect becomes a pure consequence of the dynamics. We show that for continuous measurement processes the quantum Zeno evolution derives from an adiabatic theorem. The system is forced to evolve in a set of orthogonal subspaces of the total Hilbert space and a dynamical superselection rule arises. The dynamical properties of this evolution are investigated and sever…
We consider a point particle in one dimension initially confined to a finite spatial region whose state is frequently monitored by projection operators onto that region. In the limit of infinitely frequent monitoring, the state never escapes from the region -- this is the Zeno effect. The aim of this paper is to show how the Zeno effect disappears in the classical limit in this and similar examples. We give a general argument showing that the Zeno effect is suppressed in the presence of a decoherence mechanism which kills interference between histories. We show how this works explicitly by cou…
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.
The dynamics of a quantum system undergoing measurements is investigated. Depending on the features of the interaction Hamiltonian, the decay can be slowed (quantum Zeno effect) or accelerated (inverse quantum Zeno effect), by changing the time interval between successive (pulsed) measurements or, alternatively, by varying the "strength" of the (continuous) measurement.
In this paper, we show that the quantum Zeno effect occurs for any frequent quantum measurements or operations. As a result of the Zeno effect, for non-selective measurements (or trace preserving completely positive maps), the evolution of a measurement invariant state is governed by an effective Hamiltonian defined by the measurements and the free-evolution Hamiltonian. For selective measurements, the state may change randomly with time according to measurement outcomes, while some physical quantities (operators) still evolve as the effective dynamics.
The time evolution of some quantum states can be slowed down or even stopped under frequent measurements. This is the usual quantum Zeno effect. Here, we report an operator quantum Zeno effect, in which the evolution of some physical observables is slowed down through measurements even though the quantum state changes randomly with time. Based on the operator quantum Zeno effect, we show how we can protect quantum information from decoherence with two-qubit measurements, realizable with noisy two-qubit interactions.
The usual semiclassical approximation for atom-field dynamics consists in substituting the field operators by complex numbers related to the (supposedly large enough) intensity of the field. We show that a semiclassical evolution for coupled systems can always be obtained by frequent Zeno-like measurements on the state of one subsystems, independently of the field intensity in the example given. We study the Jaynes Cummings model from this perspective.
We study transitions of a particle between two wells, separated by a reservoir, under the condition that the particle is not detected in the reservoir. Conventional quantum trajectory theory predicts that such no-result continuous measurement would not affect these transitions. We demonstrate that it holds only for Markovian reservoirs (infinite bandwidth $Λ$). In the case of finite $Λ$, the probability of the particle's interwell transition is a function of the ratio $Λ/ν$, where $ν$ is the frequency of measurements. This scaling tells us that in the limit $ν\to\infty$, the measurement freeze…
The control of thermal decoherence via dynamical decoupling and via the quantum Zeno effect (Zeno control) is investigated for a model of trapped ion, where the dynamics of two low lying hyperfine states undergoes decoherence due to the thermal interaction with an excited state. Dynamical decoupling is a procedure that consists in periodically driving the excited state, while the Zeno control consists in frequently measuring it. When the control frequency is high enough, decoherence is shown to be suppressed. Otherwise, both controls may accelerate decoherence.
We critically study the possibility of quantum Zeno effect for indirect measurements. If the detector is prepared to detect the emitted signal from the core system, and the detector does not reflect the signal back to the core system, then we can prove the decay probability of the system is not changed by the continuous measurement of the signal and the quantum Zeno effect never takes place. This argument also applies to the quantum Zeno effect for accelerated two-level systems, unstable particle decay, etc.
In this work we show that by frequent measurements of adequately chosen observables, a complete suppression of the decay in an exponentially decaying two level system interacting with a squeezed bath is obtained. The observables for which the effect is observed depend on the the squeezing parameters of the bath. The initial states which display Total Zeno Effect are intelligent states of two conjugate observables associated to the electromagnetic fluctuations of the bath.
We report the first observation of the Quantum Zeno and Anti-Zeno effects in an unstable system. Cold sodium atoms are trapped in a far-detuned standing wave of light that is accelerated for a controlled duration. For a large acceleration the atoms can escape the trapping potential via tunneling. Initially the number of trapped atoms shows strong non-exponential decay features, evolving into the characteristic exponential decay behavior. We repeatedly measure the number of atoms remaining trapped during the initial period of non-exponential decay. Depending on the frequency of measurements we …
The quantum Zeno effect -- suppression of decay by frequent measurements -- was believed to occur only when the response of the detector is so quick that the initial tiny deviation from the exponential decay law is detectable. However, we show that it can occur even for exactly exponentially decaying systems, for which this condition is never satisfied, by considering a realistic case where the detector has a finite energy band of detection. The conventional theories correspond to the limit of an infinite bandwidth. This implies that the Zeno effect occurs more widely than expected so far.
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.
We analyze the Zeno phenomenon in quantum field theory. The decay of an unstable system can be modified by changing the time interval between successive measurements (or by varying the coupling to an external system that plays the role of measuring apparatus). We speak of quantum Zeno effect if the decay is slowed and of inverse quantum Zeno (or Heraclitus) effect if it is accelerated. The analysis of the transition between these two regimes requires close scrutiny of the features of the interaction Hamiltonian. We look in detail at quantum field theoretical models of the Lee type.
Frequent measurements can modify the decay of an unstable quantum state with respect to the free dynamics given by Fermi's golden rule. In a landmark article, Nature 405, 546 (2000), Kofman and Kurizki concluded that in quantum decay processes, acceleration of the decay by frequent measurements, called the quantum anti-Zeno effect (AZE), appears to be ubiquitous, while its counterpart, the quantum Zeno effect, is unattainable. However, up to now there have been no experimental observations of the AZE for atomic radiative decay (spontaneous emission) in free space. In this work, making use of a…
In this paper it is proposed the dynamical quantum Zeno Effect in quantum decision theory. The measurement postulate is not an essential ingredient for the explanation of the quantum Zeno effect, a dynamical account is given in quantum physics. In this account, the entanglement between the system of interest and the apparatus inhibit the quantum transition. The collapse postulate is not considered. It is show in this paper that the belief-action entanglement model provides a mathematical framework for the dynamical quantum Zeno effect in quantum decision theory. It is also shown that, in this …
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…
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…
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…
We devise a new technique to enhance transmission of quantum information through linear optical quantum information processors. The idea is based on applying the Quantum Zeno effect to the process of photon absorption. By frequently monitoring the presence of the photon through a QND (quantum non-demolition) measurement the absorption is suppressed. Quantum information is encoded in the polarization degrees of freedom and is therefore not affected by the measurement. Some implementations of the QND measurement are proposed.
We study the quantum Zeno effect (QZE) and quantum anti-Zeno effect (QAZE) of a two-level system interacting with an environment of harmonic oscillators, the spin-boson model. By applying a numerically exact method based on matrix product states, the previously obtained picture on the influence of counter-rotating terms has to be modified: For physical bath initial states, the transition from QZE to QAZE with increasing measurement interval is only absent at weak coupling, while present at strong coupling. Furthermore, we find that the transition occurs always for the widely used bare bath ini…
We propose a scheme for entangling two photons via the quantum Zeno effect, which describes the inhibition of quantum evolution by frequent measurements and is based on the difference between summing amplitudes and probabilities. For a given error probability $P_{\rm error}$, our scheme requires that the one-photon loss rate $ξ_{1γ}$ and the two-photon absorption rate $ξ_{2γ}$ in some medium satisfy $ξ_{1γ}/ξ_{2γ}=2P_{\rm error}^2/π^2$, which is significantly improved in comparison to previous approaches. Again based on the quantum Zeno effect, as well as coherent excitations, we present a pos…
Quantum Zeno effect shows that frequent observations can slow down or even stop the unitary time evolution of an unstable quantum system. This effect can also be regarded as a physical consequence of the the statistical indistinguishability of neighboring quantum states. The accessibility of quantum Zeno dynamics under unitary time evolution can be quantitatively estimated by quantum Zeno time in terms of Fisher information. In this work, we investigate the accessibility of quantum Zeno dynamics in quantum open systems by calculating noisy Fisher information, in which a trace preserving and co…
We examine the quantum Zeno effect on the dynamics of quantum discord in two initially entangled qubits which are subjected to frequent measurements via decoherent coupling with independent reservoirs. The links between characteristic parameters such as system bias, measurement time duration, strength of initial entanglement between the two qubit systems and the dynamics of quantum discord are examined in the case of two initial state configurations. For weak or unsharp measurements, the quantum discord, which is an intrinsically distinct entity from concurrence, serves as a reliable indicator…
Near term quantum hardware promises to achieve quantum supremacy. From a quantum dynamical point of view, however, it is not unambiguously clear whether fundamental peculiarities of quantum physics permit any arbitrary speed-ups in real time. We show that an only recently unveiled property of the quantum Fisher information has profound implications for the rate of possible quantum information processing. To this end, we analyze an exemplary and pedagogical example for a quantum computer consisting of a computational qubit and a quantum memory. We find that frequent interaction between memory a…
The Zeno and anti-Zeno effects are features of measurement-driven quantum evolution where frequent measurement inhibits or accelerates the decay of a quantum state. Either type of evolution can emerge depending on the system-environment interaction and measurement method. In this experiment, we use a superconducting qubit to map out both types of Zeno effect in the presence of structured noise baths and variable measurement rates. We observe both the suppression and acceleration of qubit decay as repeated measurements are used to modulate the qubit spectrum causing the qubit to sample differen…
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…
Repeated observations inhibit the coherent evolution of quantum states through the quantum Zeno effect. In multi-qubit systems this effect provides new opportunities to control complex quantum states. Here, we experimentally demonstrate that repeatedly projecting joint observables of multiple spins creates coherent quantum Zeno subspaces and simultaneously suppresses dephasing caused by the environment. We encode up to two logical qubits in these subspaces and show that the enhancement of the dephasing time with increasing number of projections follows a scaling law that is independent of the …
Periodic deterministic bang-bang dynamical decoupling and the quantum Zeno effect are known to emerge from the same physical mechanism. Both concepts are based on cycles of strong and frequent kicks provoking a subdivision of the Hilbert space into independent subspaces. However, previous unification results do not capture the case of random bang-bang dynamical decoupling, which can be advantageous to the deterministic case but has an inherently acyclic structure. Here, we establish a correspondence between random dynamical decoupling and the quantum Zeno effect by investigating the average ov…
Quantum tunneling is a fundamental quantum mechanical effect involved in plenty of physical phenomena. Its control would impact these phenomena and the technologies based on them. We show that the quantum tunneling probability through a potential barrier can be increased to approach unity in a quantum Zeno dynamics undergone by the tunneling particle in which the direction of the momentum is frequently monitored. We first model the measurements of the momentum direction as selective von Neumann projections, and then as nonselective, direction-sensitive interactions of the particle with probe p…
We discuss a simple, experimentally feasible scheme, which elucidates the principles of controlling ("engineering") the reservoir spectrum and the spectral broadening incurred by repeated measurements. This control can yield either the inhibition (Zeno effect) or the acceleration (anti-Zeno effect) of the quasi-exponential decay of the observed state by means of frequent measurements. In the discussed scheme, a photon is bouncing back and forth between two perfect mirrors, each time passing a polarization rotator. The horizontal and vertical polarizations can be viewed as analogs of an excited…
We provide a general dynamical approach for the quantum Zeno and anti-Zeno effects in an open quantum system under repeated non-demolition measurements. In our approach the repeated measurements are described by a general dynamical model without the wave function collapse postulation. Based on that model, we further study both the short-time and long-time evolutions of the open quantum system under repeated non-demolition measurements, and derive the measurement-modified decay rates of the excited state. In the cases with frequent ideal measurements at zero-temperature, we re-obtain the same d…
The quantum Zeno effect arises due to frequent observation. That implies the existence of some experimenter and its interaction with the system. In this contribution, we examine what happens for a closed system if one considers a quantum Zeno type of question, namely: "what is the probability of a system, remaining always in a particular subspace". This has implications to the arrival time problem that is also discussed. We employ the decoherent histories approach to quantum theory, as this is the better developed formulation of closed system quantum mechanics, and in particular, dealing with …
If frequent measurements ascertain whether a quantum system is still in its initial state, transitions to other states are hindered and the quantum Zeno effect takes place. However, in its broader formulation, the quantum Zeno effect does not necessarily freeze everything. On the contrary, for frequent projections onto a multidimensional subspace, the system can evolve away from its initial state, although it remains in the subspace defined by the measurement. The continuing time evolution within the projected "quantum Zeno subspace" is called "quantum Zeno dynamics:" for instance, if the meas…
