Fuzzy measurements and coarse graining in quantum many-body systems

Pineda, Carlos; Davalos, David; Viviescas, Carlos; Rosado, A. S.

doi:10.1103/physreva.104.042218

Cited by 7 publications

(4 citation statements)

References 37 publications

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“…Instead, it is an exploration of the SOI and their volumes in the context of "thermalization" as it relates to information exchange/entanglement. Our choice to use CG to study our volume is also justified since using reduced density operators as coarse representations of composite systems is common within the literature [7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

A Differential-Geometric Approach to Quantum Ignorance Consistent with Entropic Properties of Statistical Mechanics

Ray

Alsing

Cafaro

et al. 2023

Entropy

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In this paper, we construct the metric tensor and volume for the manifold of purifications associated with an arbitrary reduced density operator ρS. We also define a quantum coarse-graining (CG) to study the volume where macrostates are the manifolds of purifications, which we call surfaces of ignorance (SOI), and microstates are the purifications of ρS. In this context, the volume functions as a multiplicity of the macrostates that quantifies the amount of information missing from ρS. Using examples where the SOI are generated using representations of SU(2), SO(3), and SO(N), we show two features of the CG: (1) A system beginning in an atypical macrostate of smaller volume evolves to macrostates of greater volume until it reaches the equilibrium macrostate in a process in which the system and environment become strictly more entangled, and (2) the equilibrium macrostate takes up the vast majority of the coarse-grained space especially as the dimension of the total system becomes large. Here, the equilibrium macrostate corresponds to a maximum entanglement between the system and the environment. To demonstrate feature (1) for the examples considered, we show that the volume behaves like the von Neumann entropy in that it is zero for pure states, maximal for maximally mixed states, and is a concave function with respect to the purity of ρS. These two features are essential to typicality arguments regarding thermalization and Boltzmann’s original CG.

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Section: Introductionmentioning

confidence: 99%

A Differential-Geometric Approach to Quantum Ignorance Consistent with Entropic Properties of Statistical Mechanics

Ray

Alsing

Cafaro

et al. 2023

Entropy

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“…The coarsening measurement was proposed by Kofle and Brukner 18 , which is mainly used to understand the mechanism of quantum-to-classical transition. Then, a lot of research on the coarsening measurement has been done 15 , 18 – 25 . Sumit et al 24 investigated the effect of the coarsening measurement time on quantum violations of macrorealism for multilevel spin systems, and found that classicality in large spin system does not emerge out of quantum mechanics under the coarsening measurement time.…”

Section: Introductionmentioning

confidence: 99%

Quantum violation of LGI under an energy constraint for different scenarios systems

Zhang

Tan

Qiu

2023

Sci Rep

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In this paper, we consider a qubit in four scenarios: with drive, without drive, and in the presence of dissipation and dephasing, to investigate the quantum violation of the Leggett–Garg inequality (LGI) in an energy constraint. In the case of the energy constraint, we find that under the coarsening measurement in reference and final resolution, the quantum violation of the LGI for the pure qubit is the most robust; on the other hand, the quantum violation of the LGI for the dephasing qubit is the most vulnerable, and the quantum violation of the LGI for driven qubit lies between that of pure qubit and dissipation qubit. Under the coarsening of measurement temporal reference, the quantum violation of the LGI for the pure qubit is more robust than that of the qubit with driven. Moreover, in the case of a qubit that is subjected to driving and is in the presence of dissipation and dephasing, the robustness of quantum violations of the LGI for these scenario systems will become vulnerable, with the driven intensity and the rate of spontaneous emission increasing, respectively, for coarsening measurement both in reference and in final resolution. In addition, in the energy constraint and the projective measurement, the LGI can attain its maximum violation value, 1.5, for the coherent dynamics; while for drive, dissipative and dephasing qubits, the LGI cannot attain the value of 1.5. For systems in the presence of dissipation and dephasing, we find that in the energy constraint, the robustness of the coarsening measurement in final resolution exhibits more vulnerable than that of the coarsening measurement in reference. And for systems with drive and without drive, the robustness of the coarsening measurement in temporal reference is the most robust, and the robustness of the coarsening of measurement final measurement resolution is the most vulnerable.

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“…One of the main tools to study the effects of decoherence are quantum channels. Quantum channels can describe quantum noise [15,16], open quantum systems dynamics [6,17], and recently even coarse graining [18,19]. One of the main difficulties in characterizing quantum channels is that, like for quatum states, the number of parameters required for their description increases quite rapidly with Hilbert space dimension.…”

Section: Introductionmentioning

confidence: 99%

Pauli component erasing quantum channels

de Leon,

Fonseca,

Leyvraz

et al. 2022

Preprint

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Decoherence of quantum systems is described by quantum channels. However, a complete understanding of such channels, specially in the multi-particle setting, is still an ongoing difficult task. We propose the family of quantum maps that preserve or completely erase the components of a multiqubit system in the basis of Pauli strings, which we call Pauli component erasing (PCE) maps. For the corresponding channels, it is shown that the preserved components can be interpreted as a finite vector subspace, from which we derive several properties and complete the characterization. Moreover, we show that the obtained family of channels form a semigroup and derive its generators. We use this simple structure to determine physical implementations and connect the obtained family of channels with Markovian processes.

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Fuzzy measurements and coarse graining in quantum many-body systems

Cited by 7 publications

References 37 publications

A Differential-Geometric Approach to Quantum Ignorance Consistent with Entropic Properties of Statistical Mechanics

A Differential-Geometric Approach to Quantum Ignorance Consistent with Entropic Properties of Statistical Mechanics

Quantum violation of LGI under an energy constraint for different scenarios systems

Pauli component erasing quantum channels

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