Quantum speed limits, coherence, and asymmetry

Marvian, Iman; Spekkens, Robert W.; Zanardi, Paolo

doi:10.1103/physreva.93.052331

Cited by 257 publications

(275 citation statements)

References 57 publications

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“…Measures of quantum coherence have been studied quite extensively in the last few years, see e.g. [42,69,43,48,49,71,44,45,46,82,83,70,47] and the very recent review [84]. While several connections between coherence, entanglement, and QCs have been pointed out quite recently, including quantitative interconversion schemes [85,49,86,46,47] somehow analogous to the entanglement activation framework [36,35], a consistent definition of QCs quantifiers in terms of coherence has not been reported in full generality (to our knowledge), and will be introduced here.…”

Section: Examples Of Measures Q U δmentioning

confidence: 99%

“…In entanglement theory, for example, LOCC are singled out by the physical paradigm of distant laboratories, and form a strict subset of the maximal set of operations preserving separable states [68] (as the latter also contain certain nonlocal operations such as the swap gate), while in the resource theories of quantum coherence there are currently several alternative proposals for free operations, with different characterisations, and a still ongoing debate on their physical consistency [69,43,70,44,71,45,72,73].…”

Section: Requirements For a Bona Fide Measure Of Quantum Correlationsmentioning

confidence: 99%

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Measures and applications of quantum correlations

Adesso¹,

Bromley²,

Cianciaruso³

2016

J. Phys. A: Math. Theor.

397

416

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Abstract. Quantum information theory is built upon the realisation that quantum resources like coherence and entanglement can be exploited for novel or enhanced ways of transmitting and manipulating information, such as quantum cryptography, teleportation, and quantum computing. We now know that there is potentially much more than entanglement behind the power of quantum information processing. There exist more general forms of non-classical correlations, stemming from fundamental principles such as the necessary disturbance induced by a local measurement, or the persistence of quantum coherence in all possible local bases. These signatures can be identified and are resilient in almost all quantum states, and have been linked to the enhanced performance of certain quantum protocols over classical ones in noisy conditions. Their presence represents, among other things, one of the most essential manifestations of quantumness in cooperative systems, from the subatomic to the macroscopic domain. In this work we give an overview of the current quest for a proper understanding and characterisation of the frontier between classical and quantum correlations in composite states. We focus on various approaches to define and quantify general quantum correlations, based on different yet interlinked physical perspectives, and comment on the operational significance of the ensuing measures for quantum technology tasks such as information encoding, distribution, discrimination and metrology. We then provide a broader outlook of a few applications in which quantumness beyond entanglement looks fit to play a key role.

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Section: Examples Of Measures Q U δmentioning

confidence: 99%

Section: Requirements For a Bona Fide Measure Of Quantum Correlationsmentioning

confidence: 99%

Measures and applications of quantum correlations

Adesso¹,

Bromley²,

Cianciaruso³

2016

J. Phys. A: Math. Theor.

397

416

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show abstract

“…(1) constitutes a loose bound for the speed of unitary evolution of mixed states is well known, and there are several proposals to tackle this problem [45][46][47]. In particular Ref.…”

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confidence: 99%

Tightening Quantum Speed Limits for Almost All States

et al. 2018

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Conventional quantum speed limits perform poorly for mixed quantum states: They are generally not tight and often significantly underestimate the fastest possible evolution speed. To remedy this, for unitary driving, we derive two quantum speed limits that outperform the traditional bounds for almost all quantum states. Moreover, our bounds are significantly simpler to compute as well as experimentally more accessible. Our bounds have a clear geometric interpretation; they arise from the evaluation of the angle between generalized Bloch vectors.Quantum speed limits (QSLs) set fundamental bounds on the shortest time required to evolve between two quantum states [1][2][3]. The earliest derivation of minimal time of evolution was in 1945 by Mandelstam and Tamm [4] with the aim of operationalising the famous (but oft misunderstood) timeenergy uncertainty relations [5-9] ∆t ≥ /∆E, relating the standard deviation of energy with the time it takes to go from one state to another. QSLs were originally derived for the unitary evolution of pure states [10][11][12]; since then they have been generalized to the case of mixed states [13][14][15][16], nonunitary evolution [17][18][19], and multi-partite systems [20][21][22][23][24].Extending their original scope, their significance has evolved from fundamental physics to practical relevance, defining the limits of the rate of information transfer [25] and processing [26], entropy production [27], precision in quantum metrology [28] and time-scale of quantum optimal control [29]. For example, in [30], the authors use QSLs to calculate the maximal rate of information transfer along a spin chain; similarly, Reich et al. show that optimization algorithms and QSLs can be used together to achieve quantum control over a large class of physical systems [31]. In Refs. [32][33][34] QSLs are used to bound the charging power of non-degenerate multi-partite systems, which are treated as batteries. The latter results imply a significant speed advantage for entangling over local unitary driving of quantum systems, given the same external constraints.Combining the Mandelstam-Tamm result with the results by Margolus and Levitin, along with elements of quantum state space geometry [35], leads to a unified QSL [36]. It bounds the shortest time required to evolve a (mixed) state ρ to another state σ by means of a unitary operator U t generated by some time-dependent Hamiltonian H twhere L(ρ, σ) = arccos(F(ρ, σ)) is the Bures angle, a measure of the distance between states ρ and σ, F(ρ, σ) = tr[ √ ρσ √ ρ] is the Uhlmann root fidelity [37,38]; For pure states ρ = |ψ ψ| and σ = |φ φ|, the Bures angle reduces to the Fubini-Study distance d(|ψ , |φ ) = arccos | ψ|φ | [35,39,40]. Under this condition Eq. (1) is provably tight [36]. An insightful geometric interpretation of QSLs for pure states (in a Hilbert space of any dimension) is that the geodesic connecting initial and final states lives on a complex projective line CP 1 (isomorphic to a 2-sphere S 2 ), defined by the linear combinations of |ψ an...

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“…Recently, resource theory of asymmetry or reference frame has emerged which treats individual formulations of coherence measures as special cases [18][19][20][21][22][23][24]. It has been noted that both operational and geometric perspectives are in general significant for resource theory [15]- [17], [28], [45].…”

Section: Discussionmentioning

confidence: 99%

“…Defined in a quantitative manner based on the framework of resource theory [16], [17], [18][19][20][21][22][23][24] quantum coherence may be exploited to perform quantum tasks. Several operational measures of quantum coherence have been proposed [25], [26], enabling it to be used for detection of genuine non-classicality in physical states.…”

Section: Introductionmentioning

confidence: 99%

Preservation of quantum coherence under Lorentz boost for narrow uncertainty wave packets

Chatterjee

Majumdar

2017

Phys. Rev. A

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We consider the effect of relativistic boosts on single particle Gaussian wave packets. The coherence of the wave function as measured by the boosted observer is studied as a function of the momentum and the boost parameter. Using various formulations of coherence it is shown that in general the coherence decays with the increase of the momentum of the state, as well as the boost applied to it. Employing a basis-independent formulation, we show however, that coherence may be preserved even for large boosts applied on narrow uncertainty wave packets. Our result is exemplified quantitatively for practically realizable neutron wave functions.

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Quantum speed limits, coherence, and asymmetry

Cited by 257 publications

References 57 publications

Measures and applications of quantum correlations

Measures and applications of quantum correlations

Tightening Quantum Speed Limits for Almost All States

Preservation of quantum coherence under Lorentz boost for narrow uncertainty wave packets

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