Quantum Speed Limit for States with a Bounded Energy Spectrum

Ness, Gal; Alberti, Andrea; Sagi, Yoav

doi:10.1103/physrevlett.129.140403

Cited by 29 publications

(19 citation statements)

References 22 publications

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“…This estimate generalizes the main result in [14] to an arbitrary fidelity between initial and final states. We adhere to the terminology used in [14] and call τ * ml (δ) the dual extended Margolus-Levitin QSL. Note that for some states, τ * ml (δ) is greater than τ ml (δ) and τ mt (δ).…”

Section: B the Dual Extended Margolus-levitin Qslsupporting

confidence: 84%

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The Margolus-Levitin quantum speed limit for an arbitrary fidelity

Hörnedal¹,

Sönnerborn²

2023

Preprint

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The Mandelstam-Tamm and Margolus-Levitin quantum speed limits are two well-known evolution time estimates for isolated quantum systems. These bounds are usually formulated for fully distinguishable initial and final states, but both have tight extensions to systems that evolve between states with arbitrary fidelity. However, the foundations for these extensions differ in some essential respects. The extended Mandelstam-Tamm quantum speed limit has been proven analytically and has a clear geometric interpretation. Furthermore, the systems that saturate the limit have been completely classified. The derivation of the extended Margolus-Levitin quantum speed limit, on the other hand, is based on numerical estimates. Moreover, the limit lacks a geometric interpretation, and there is no complete characterization of the systems reaching it. In this paper, we derive the extended Margolus-Levitin quantum speed limit analytically and describe in detail the systems that saturate the limit. We also provide the limit with a symplectic-geometric interpretation, indicating that it is of a different character than most existing quantum speed limits. At the end of the paper, we analyze the maximum of the extended Mandelstam-Tamm and Margolus-Levitin quantum speed limits, and we derive a dual version of the extended Margolus-Levitin quantum speed limit. The maximum limit is tight regardless of the fidelity of the initial and final states. However, the conditions under which the maximum limit is saturated differ depending on whether or not the initial and final states are fully distinguishable. The dual limit is also tight and follows from a time reversal argument. We describe all systems that saturate the dual quantum speed limit.

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Section: B the Dual Extended Margolus-levitin Qslsupporting

confidence: 84%

“…We describe this difference in Section IV A. In Section IV B, we derive a QSL that extends the dual Margolus-Levitin QSL studied in [14], and in Section IV C we provide three QSLs that are less sharp but easier to calculate than the extended Margolus-Levitin QSL. These three QSLs are not new but can be found in the cited papers.…”

Section: Related Qslsmentioning

confidence: 99%

The Margolus-Levitin quantum speed limit for an arbitrary fidelity

Hörnedal¹,

Sönnerborn²

2023

Preprint

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“…( 7) and (6), and noting that (|O ij |/ O ) 2 ≤ 1 defines a proper probability distribution over the energy states pairs, it is clear that the operators O max flowing at the maximal speed are the ones whose non-zero elements are only between energy eigenstates with the maximum gap |∆ max | = E max − E 0 , where E max and E 0 are the highest and the lowest energy eigenvalues, respectively. This maximal speed for operators is the analog of the one identified by the dual ML bound, recently introduced for state evolution [67]. If these levels are non-degenerate, the fastest operator will be of the form…”

Section: Quantum Speed Limits For Operatorsmentioning

confidence: 86%

“…1), we observe that the divergence of the bound does not keep increasing when considering an increasing Hilbert space dimension. ML-type bounds were recently found to lose tightness for higher dimensions than a qubit also in [67].…”

Section: Random Matrix Examplementioning

confidence: 99%

Quantum speed limits on operator flows and correlation functions

Nicoletta

Hörnedal

Campo

2022

Quantum

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Quantum speed limits (QSLs) identify fundamental time scales of physical processes by providing lower bounds on the rate of change of a quantum state or the expectation value of an observable. We introduce a generalization of QSL for unitary operator flows, which are ubiquitous in physics and relevant for applications in both the quantum and classical domains. We derive two types of QSLs and assess the existence of a crossover between them, that we illustrate with a qubit and a random matrix Hamiltonian, as canonical examples. We further apply our results to the time evolution of autocorrelation functions, obtaining computable constraints on the linear dynamical response of quantum systems out of equilibrium and the quantum Fisher information governing the precision in quantum parameter estimation.

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“…Thus, it can be seen as an energy bandwidth normalisation. A similar approach was recently pursued by Ness et al [29]. Normalisation endows us with operators H with eigenvalues E i ∈ [0, 1] in the natural units, which will be used throughout the rest of this paper.…”

Section: Time-energy Trade Off-speed Of Evolutionmentioning

confidence: 99%

The fastest generation of multipartite entanglement with natural interactions

Cieśliński,

Kłobus,

Kurzyński

et al. 2023

New J. Phys.

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Natural interactions among multiple quantum objects are fundamentally composed of two-body terms only. In contradistinction, single global unitaries that generate highly entangled states typically arise from Hamiltonians that couple multiple individual subsystems simultaneously. Here, we study the time to produce strongly nonclassical multipartite correlations with a single unitary generated by the natural interactions. We restrict the symmetry of two-body interactions to match the symmetry of the target states and focus on the fastest generation of multipartite entangled Greenberger–Horne–Zeilinger, W, Dicke and absolutely maximally entangled states for up to seven qubits. These results are obtained by constraining the energy in the system and accordingly can be seen as state-dependent quantum speed limits for symmetry-adjusted natural interactions. They give rise to a counter-intuitive effect where the creation of particular entangled states with an increasing number of particles does not require more time. The methods used rely on extensive numerical simulations and analytical estimations.

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Quantum Speed Limit for States with a Bounded Energy Spectrum

Cited by 29 publications

References 22 publications

The Margolus-Levitin quantum speed limit for an arbitrary fidelity

The Margolus-Levitin quantum speed limit for an arbitrary fidelity

Quantum speed limits on operator flows and correlation functions

The fastest generation of multipartite entanglement with natural interactions

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