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Zeno dynamics in quantum open systems.

Zhang YR, Fan H - Sci Rep (2015)

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China.

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.

No MeSH data available.


QFI of separable state and entangled state.Solid lines are for QFI of entangled state (en) and dashed lines are for separable state (se). (a)  against ω0τ with different interaction strength: Γ/ω0 = 1 (blue lines), 2 (red lines) and 4 (black lines). The qubit number is set as N = 24. (b)  against Γ/ω0 with different qubit numbers: N = 8 (blue lines), 16 (red lines) and 24 (black lines). The time interval is set as ω0τ = 0.2.
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f2: QFI of separable state and entangled state.Solid lines are for QFI of entangled state (en) and dashed lines are for separable state (se). (a) against ω0τ with different interaction strength: Γ/ω0 = 1 (blue lines), 2 (red lines) and 4 (black lines). The qubit number is set as N = 24. (b) against Γ/ω0 with different qubit numbers: N = 8 (blue lines), 16 (red lines) and 24 (black lines). The time interval is set as ω0τ = 0.2.

Mentions: Specifically, we can obviously see from Fig. 2(a) that for some time interval. In Fig. 2(b) we find that when the strength of environment Γ is weak, is larger than , i.e., quantum Zeno dynamics of entangled states may be harder to realize. As the increase of Γ, quantum Zeno dynamics of both cases are equally accessible. However, given “strong environment” Γ/ω0 ≪ 1, both and tend to be infinity and the ZT is confined to be so small that it makes the quantum Zeno dynamics nearly accessible as predicted in Ref. 18. It is thus significant that the appropriate environmental interaction can be favourable for realizing QZE of entangled states compared with the case of unitary time evolution in closed system. This effect may be explained by the fact that some decoherence acts like an effective further continuous measurement on the system, therefore making the QZE more accessible. Besides, we can also figure out the optimal model of environment given the definite form of states and the definite noisy channel, which is shown in Methods. Our theory is also able to settle the case for states which are not maximally entangled but may bring new interesting results of QZE in open system.


Zeno dynamics in quantum open systems.

Zhang YR, Fan H - Sci Rep (2015)

QFI of separable state and entangled state.Solid lines are for QFI of entangled state (en) and dashed lines are for separable state (se). (a)  against ω0τ with different interaction strength: Γ/ω0 = 1 (blue lines), 2 (red lines) and 4 (black lines). The qubit number is set as N = 24. (b)  against Γ/ω0 with different qubit numbers: N = 8 (blue lines), 16 (red lines) and 24 (black lines). The time interval is set as ω0τ = 0.2.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4477237&req=5

f2: QFI of separable state and entangled state.Solid lines are for QFI of entangled state (en) and dashed lines are for separable state (se). (a) against ω0τ with different interaction strength: Γ/ω0 = 1 (blue lines), 2 (red lines) and 4 (black lines). The qubit number is set as N = 24. (b) against Γ/ω0 with different qubit numbers: N = 8 (blue lines), 16 (red lines) and 24 (black lines). The time interval is set as ω0τ = 0.2.
Mentions: Specifically, we can obviously see from Fig. 2(a) that for some time interval. In Fig. 2(b) we find that when the strength of environment Γ is weak, is larger than , i.e., quantum Zeno dynamics of entangled states may be harder to realize. As the increase of Γ, quantum Zeno dynamics of both cases are equally accessible. However, given “strong environment” Γ/ω0 ≪ 1, both and tend to be infinity and the ZT is confined to be so small that it makes the quantum Zeno dynamics nearly accessible as predicted in Ref. 18. It is thus significant that the appropriate environmental interaction can be favourable for realizing QZE of entangled states compared with the case of unitary time evolution in closed system. This effect may be explained by the fact that some decoherence acts like an effective further continuous measurement on the system, therefore making the QZE more accessible. Besides, we can also figure out the optimal model of environment given the definite form of states and the definite noisy channel, which is shown in Methods. Our theory is also able to settle the case for states which are not maximally entangled but may bring new interesting results of QZE in open system.

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China.

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.

No MeSH data available.