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Physical Review Letters

Zeno Dynamics, Indistinguishability of State, and Entanglement

Augusto Smerzi

Published Oct 10, 2012• 70 citations
Publisher

Abstract

According to the quantum Zeno effect (QZ), frequent observations of a system can dramatically slow down its dynamical evolution. We show that the QZ is a physical consequence of the statistical indistinguishability of neighboring quantum states. The time scale of the problem is expressed in terms of the Fisher information and we demonstrate that the Zeno dynamics of particle entangled states might require quite smaller measurement intervals than classically correlated states. We propose an interferometric experiment to test the prediction.

DOI
10.1103/physrevlett.109.150410

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According to the quantum Zeno effect (QZ), frequent observations of a system can dramatically slow down its dynamical evolution. We show that the QZ is a physical consequence of the statistical indistinguishability of neighboring quantum states. The time scale of the problem is expressed in terms of the Fisher information and we demonstrate that the Zeno dynamics of particle entangled states might require quite smaller measurement intervals than classically correlated states. We propose an interferometric experiment to test the prediction.
According to the quantum Zeno effect, the frequent observations of a system can dramatically slow down its dynamical evolution. We show that the Zeno dynamics is the result of projective measurements among quantum states which are indistinguishable. The physical time scale of the problem is provided by the Cramer-Rao lower bound, which measure the distinguishability of states along a path in the Hilbert space. We finally show that the Zeno dynamics with particle entangled states might require quite smaller measurement intervals than classically correlated states, and propose a realistic interferometric experiment to test the prediction.
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 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 when a trace preserving and completely positive map is assumed. We firstly study the consequences of non-Markovian noise on quantum Zeno effect and give the exact forms of the dissipative Fisher information and the quantum Zeno time. Then, for the operator-sum representation, an achievable upper bound of the quantum Zeno time is given with the help of the results in noisy quantum metrology. It is of significance that the noise reducing the accuracy in the entanglement-enhanced parameter estimation can conversely be favorable for the accessibility of quantum Zeno dynamics of entangled states.
The term 'quantum Zeno paradox' or 'quantum Zeno effect' refers to the slowing down of the evolution of a quantum system as it is observed more and more frequently.In 1977, Misra and Sudarshan gave a theoretical demonstration of its existence.There has been disagreement regarding the definition of the effect and whether it is really a paradox, requiring new physics, or a consequence of ordinary quantum mechanics.The experiment of Itano, Heinzen, Bollinger and Wineland, published in 1990, is the one most often called a demonstration of the quantum Zeno effect.Some different interpretations are discussed.
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, Bollinger, and Wineland, published in 1990, has been cited around 347 times and seems to be the one most often called a demonstration of the quantum Zeno effect. Given that there is disagreement as to what the quantum Zeno effect is , there naturally is disagreement as to whether that experiment demonstrated the quantum Zeno effect. Some differing perspectives regarding the quantum Zeno effect and what would constitute an experimental demonstration are discussed.
The evolution of a quantum system undergoing very frequent measurements takes place in a subspace of the total Hilbert space (quantum Zeno effect). The dynamical properties A quantum system, prepared in a state that does not belong to an eigenvalue of its total Hamiltonian, starts to evolve quadratically in time [1, 2]. This behavior leads to the so-called quantum Zeno phenomenon: by performing frequent measurements on the system, in order to check whether it is still in its initial state, one can “slow
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.