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arXiv:1306.2145 · Scientific Reports

Zeno dynamics in quantum open systems

Yu-Ran Zhang, Heng Fan

Published Jun 23, 2015• 29 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1038/srep11509

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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.
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.
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.
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.
In this thesis we explore aspects of dynamics of open quantum systems related to coherence and quantum correlations - necessary resources for enhanced quantum metrology and quantum computation. We first discuss limits to the precision of parameter estimation when using a quantum system in the presence of noise. To this end we introduce a variational principle for the quantum Fisher information (QFI) bounding the estimation errors of any measurement, which motivates an efficient iterative algorithm for finding optimal system preparations for noisy estimation experiments. Furthermore, we investigate influence of noise correlations on the precision in phase and frequency estimation, by delivering bounds for both spatially and temporarily correlated (non-Markovian) dephasing noise. This allows us to prove the Zeno limit in frequency estimation, conjectured in Phys. Rev. A 84, 012103 (2011) and Phys. Rev. Lett. 109, 233601 (2012). The enhanced estimation precision in quantum metrology can be, however, achieved only using highly entangled states. We propose a scheme of generating such highly correlated states as outputs of Markovian open quantum systems near first-order dynamical phase transitions. We show that the quadratic scaling of the QFI with time is present for experiments within the correlation time of the dynamics and describe a theoretical scheme for quantum enhanced estimation of an optical phase-shift using the photons being emitted from an intermittent quantum system. Finally, we establish the basis for a theory of metastability in Markovian open quantum systems, by extending methods from classical stochastic dynamics. We argue that the partial relaxation into long-lived metastable states - distinct from the asymptotic stationary state - may preserve initial coherences within decoherence-free subspaces or noiseless subsystems, thus allowing for quantum computation during the metastable regime.
In this paper, we show that the quantum Zeno effect can occur for generalized quantum measurements or operations. As a consequence of frequently performing nonselective measurements (or trace-preserving completely positive maps), the evolution of a certain measurement-invariant state is governed by an effective Hamiltonian defined by the measurement (or map) and the free-evolution Hamiltonian. For selective measurements, the state may change randomly with time according to measurement outcomes, but some physical quantities (operators) still evolve according to the effective Hamiltonian.
The Quantum Zeno effect is often interpreted as demonstrating that frequent measurements physically inhibit the dynamical evolution of a quantum system. This paper develops an Observer-First Interpretation (OFI) in which quantum states are treated as observer-relative informational constructs constrained by evidence accessibility and record stability. Within this framework, Zeno-like stabilization does not arise from a physical freezing of dynamics, but from repeated informational conditioning that continuously redefines the effective state of the system relative to the observer. The proposed interpretation preserves unitary evolution, respects causal structure, and reproduces all experimentally observed Quantum Zeno and anti-Zeno phenomena without modifying the formalism of quantum mechanics.