Quantum Zeno Effect in Open Quantum Systems

Becker, Simon; Datta, Nilanjana; Salzmann, Robert

doi:10.1007/s00023-021-01075-8

Cited by 10 publications

(22 citation statements)

References 52 publications

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“…1 Main contributions In this paper, we achieve the optimal convergence rate O(n −1 ) of the Zeno sequence consistent with the finite-dimensional case [5] by providing an explicit bound which recently attracted interest in finite closed quantum systems [19,Theorem 1]. Moreover, we generalize the results of [2] in two complementary directions: In Theorem 5.1, we assume a special case of the uniform power convergence assumption on M , that is M n −P ≤ δ n for some δ ∈ (0, 1), and weaken the assumption on the semigroup to the uniform asymptotic Zeno condition inherited from the unitary setting of [35]: for t → 0 (1 − P )e tL P ∞ = O(t) and P e tL (1 − P ) ∞ = O(t).…”

Section: Introductionmentioning

confidence: 92%

“…More recently, Becker, Datta, and Salzmann generalized the Zeno effect further and interpreted the Zeno sequence as a product formula consisting of a contraction M (quantum operation) and a C 0 -contraction semigroup (quantum time evolution) on an abstract Banach space. Under a condition of uniform power convergence of the power sequence {M k } k∈N toward a projection P and boundedness of M L and LM , they proved a quantitative bound on the convergence rate [2]:…”

Section: Introductionmentioning

confidence: 99%

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Optimal Convergence Rate in the Quantum Zeno Effect for Open Quantum Systems in Infinite Dimensions

Tim

Rouzé

2022

Ann. Henri Poincaré

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In open quantum systems, the quantum Zeno effect consists in frequent applications of a given quantum operation, e.g., a measurement, used to restrict the time evolution (due, for example, to decoherence) to states that are invariant under the quantum operation. In an abstract setting, the Zeno sequence is an alternating concatenation of a contraction operator (quantum operation) and a $$C_0$$ C 0 -contraction semigroup (time evolution) on a Banach space. In this paper, we prove the optimal convergence rate $$\mathcal {O}(\tfrac{1}{n})$$ O ( 1 n ) of the Zeno sequence by proving explicit error bounds. For that, we derive a new Chernoff-type $$\sqrt{n}$$ n -Lemma, which we believe to be of independent interest. Moreover, we generalize the convergence result for the Zeno effect in two directions: We weaken the assumptions on the generator, inducing the Zeno dynamics generated by an unbounded generator, and we improve the convergence to the uniform topology. Finally, we provide a large class of examples arising from our assumptions.

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Section: Introductionmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Optimal Convergence Rate in the Quantum Zeno Effect for Open Quantum Systems in Infinite Dimensions

Tim

Rouzé

2022

Ann. Henri Poincaré

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“…The bound in Ref. [43,Theorem 1] only shows an O(n −2/3 ) scaling. Reference [44,Lemma 4] studies an error bound in a more general setting, which still depends on an undetermined constant.…”

Section: Convergence Of the Average Evolution Of Systemmentioning

confidence: 99%

Unification of Random Dynamical Decoupling and the Quantum Zeno Effect

Hahn,

Burgarth,

Yuasa

2021

Preprint

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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 over random decoupling evolutions. This protocol is a manifestation of the quantum Zeno dynamics and leads to a unitary bath evolution. By providing a framework that we call equitability of system and bath, we show that the system dynamics under random dynamical decoupling converges to a unitary with a decoupling error that characteristically depends on the convergence speed of the Zeno limit. This reveals a unification of the random dynamical decoupling and the quantum Zeno effect.

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“…Since the purpose of this paper is however to understand the relationship between the Zeno effect and mostly finite-dimensional semigroups, we will not be too concerned with technical barriers in non-tracial settings. For infinite-dimensional versions of the Zeno effect, see [BDS21,MR21].…”

Section: Appendix B Reanalysis Of the Generalized Zeno Effectmentioning

confidence: 99%

Self-restricting Noise and Quantum Relative Entropy Decay

LaRacuente¹

2022

Preprint

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Open quantum systems as modeled by quantum channels and quantum Markov semigroups usually decay to subspaces that are invariant under environmental interactions. It is known that finite-dimensional semigroups with detailed balance decay exponentially under modified logarithmic-Sobolev inequalities (MLSIs). Here we analyze discrete and continuous processes that include unitary components, breaking the detailed balance assumption. We find counter-examples to analogs of MLSIs for these systems. The generalized quantum Zeno effect appears for many Lindbladians that combine a decay process with unitary drift. As incompatible long-time and Zeno limits compete, strong noise often protects subsystems and subspaces from its own spread. We observe this interplay between decay and Zeno-like effects experimentally on superconducting qubits using IBM Q devices. Nonetheless, by combining MLSIs for effective self-adjoint decay processes across different times, we obtain eventual exponential decay. We similarly obtain decay rate lower bounds for discrete compositions of quantum channels.

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Quantum Zeno Effect in Open Quantum Systems

Cited by 10 publications

References 52 publications

Optimal Convergence Rate in the Quantum Zeno Effect for Open Quantum Systems in Infinite Dimensions

Optimal Convergence Rate in the Quantum Zeno Effect for Open Quantum Systems in Infinite Dimensions

Unification of Random Dynamical Decoupling and the Quantum Zeno Effect

Self-restricting Noise and Quantum Relative Entropy Decay

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