Witnessing Multipartite Entanglement by Detecting Asymmetry

While the scaling of entanglement in a quantum system can be used to distinguish many-body quantum phases, it is usually hard to quantify the amount of entanglement in mixed states of open quantum systems, while measuring entanglement experimentally, even for the closed systems, requires in general quantum state tomography. In this work we show how to remedy this situation in system with a fixed or conserved charge, e.g., density or magnetization, due to an emerging relation between quantum correlations and coherence. First, we show how, in these cases, the presence of multipartite entanglement or quantumness can be faithfully witnessed simply by detecting coherence in the quantum system, while bipartite entanglement or bipartite quantum discord are implied by asymmetry (block coherence) in the system. Second, we prove that the relation between quantum correlations and coherence is also quantitative. Namely, we establish upper and lower bounds on the amount of multipartite and bipartite entanglement in a many-body system with a fixed local charge, in terms of the amount of coherence and asymmetry present in the system. Importantly, both for pure and mixed quantum states, these bounds are expressed as closed formulas, and furthermore, for bipartite entanglement, are experimentally accessible by means of the multiple quantum coherence spectra. In particular, in one-dimensional systems, our bounds may detect breaking of the area law of entanglement entropy. We illustrate our results on the example of a many-body localized system, also in the presence of dephasing.

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“…In contrast, for separable states, the QFI is not larger than the separability threshold [15,16,[47][48][49][50][51][52][53][54]57],…”

Section: B Witnessing Coherence As a Proxy For Witnessing Entanglementmentioning

confidence: 99%

Section: Curvaturementioning

confidence: 99%

Coherence, entanglement, and quantumness in closed and open systems with conserved charge, with an application to many-body localization

et al. 2019

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“…When one considers recent work on quantifying coherence from the perspective of the speakable/unspeakable distinction, it is clear that it concerns itself only with the speakable notion (see, e.g., [20,22,[61][62][63][64][65][66][67]). Most of this work builds on a proposal by Baumgratz, Cramer, and Plenio (BCP) [20].…”

Section: B Resource-theoretic Approaches To Speakable Coherencementioning

confidence: 99%

How to quantify coherence: Distinguishing speakable and unspeakable notions

2016

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Quantum coherence is a critical resource for many operational tasks. Understanding how to quantify and manipulate it also promises to have applications for a diverse set of problems in theoretical physics. For certain applications, however, one requires coherence between the eigenspaces of specific physical observables, such as energy, angular momentum, or photon number, and it makes a difference which eigenspaces appear in the superposition. For others, there is a preferred set of subspaces relative to which coherence is deemed a resource, but it is irrelevant which of the subspaces appear in the superposition. We term these two types of coherence unspeakable and speakable, respectively. We argue that a useful approach to quantifying and characterizing unspeakable coherence is provided by the resource theory of asymmetry when the symmetry group is a group of translations, and we translate a number of prior results on asymmetry into the language of coherence. We also highlight some of the applications of this approach, for instance, in the context of quantum metrology, quantum speed limits, quantum thermodynamics, and nuclear magnetic resonance (NMR). The question of how best to treat speakable coherence as a resource is also considered. We review a popular approach in terms of operations that preserve the set of incoherent states, propose an alternative approach in terms of operations that are covariant under dephasing, and we outline the challenge of providing a physical justification for either approach. Finally, we note some mathematical connections that hold among the different approaches to quantifying coherence.

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“…Also, note that for closed-system dynamics under Hamiltonian H , any measure of asymmetry (relative to time translation) remains constant, i.e., [20,21,26,29,30,[36][37][38][39][40][41]). In particular, Refs.…”

Section: A Coherence As Asymmetry Relative To Translationsmentioning

confidence: 99%

Quantum speed limits, coherence, and asymmetry

2016

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The resource theory of asymmetry is a framework for classifying and quantifying the symmetry-breaking properties of both states and operations relative to a given symmetry. In the special case where the symmetry is the set of translations generated by a fixed observable, asymmetry can be interpreted as coherence relative to the observable eigenbasis, and the resource theory of asymmetry provides a framework to study this notion of coherence. We here show that this notion of coherence naturally arises in the context of quantum speed limits. Indeed, the very concept of speed of evolution, i.e., the inverse of the minimum time it takes the system to evolve to another (partially) distinguishable state, is a measure of asymmetry relative to the time translations generated by the system Hamiltonian. Furthermore, the celebrated Mandelstam-Tamm and Margolus-Levitin speed limits can be interpreted as upper bounds on this measure of asymmetry by functions which are themselves measures of asymmetry in the special case of pure states. Using measures of asymmetry that are not restricted to pure states, such as the Wigner-Yanase skew information, we obtain extensions of the Mandelstam-Tamm bound which are significantly tighter in the case of mixed states. We also clarify some confusions in the literature about coherence and asymmetry, and show that measures of coherence are a proper subset of measures of asymmetry.

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Witnessing Multipartite Entanglement by Detecting Asymmetry

Cited by 47 publications

References 71 publications

Coherence, entanglement, and quantumness in closed and open systems with conserved charge, with an application to many-body localization

Coherence, entanglement, and quantumness in closed and open systems with conserved charge, with an application to many-body localization

How to quantify coherence: Distinguishing speakable and unspeakable notions

Quantum speed limits, coherence, and asymmetry

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