Classical analogs of the covariance matrix, purity, linear entropy, and von Neumann entropy

Díaz, Bogar; González, Diego López; Gutiérrez‐Ruiz, Daniel; Vergara, J. David

doi:10.1103/physreva.105.062412

Cited by 8 publications

(14 citation statements)

References 51 publications

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“…A related criterion for entanglement of a two-part quantum system has been established [ 99 ]. Remarkably, Diaz et al [ 100 ] described a classical analog of the quantum covariance matrix and, in the case of Gaussian states, derived expressions for classical analogs of the purity, linear quantum entropy, and von Neumann entropy for classical integrable systems.…”

Section: Resultsmentioning

confidence: 99%

“…As an example, Diaz et al [ 100 ] considered classical coupled harmonic oscillators, described by the Hamiltonian

…”

Section: Resultsmentioning

confidence: 99%

“…While active research continues in this area, approaches to detect entanglement or compute the degree to which a system is entangled (typically, for bipartite systems) have been developed for a long time (see, e.g., refs. [ 48 , 98 , 99 , 100 , 101 ]). It is thus interesting to consider the possibility of applying similar metrics for the non-separability question, whether in quantum or classical case.…”

Section: Resultsmentioning

confidence: 99%

“…Computations of entanglement entropy starting from Wigner function have been achieved [ 103 , 104 , 105 ], and may be used to describe the degree of non-separability in a classical system, taking the transition from the Wigner function to the classical Liouville density function in the phase space. As discussed above, we would expect in this case that quantum non-locality will vanish, but some degree of non-separability may remain [ 100 ]. The entropy-based measures characterizing non-separability, such as entanglement entropy, will then have non-zero values, although one would expect those values to be lower than for a similar quantum system in an entangled state containing non-locality.…”

Section: Resultsmentioning

confidence: 99%

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Non-Separability of Physical Systems as a Foundation of Consciousness

Arkhipov

2022

Entropy

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A hypothesis is presented that non-separability of degrees of freedom is the fundamental property underlying consciousness in physical systems. The amount of consciousness in a system is determined by the extent of non-separability and the number of degrees of freedom involved. Non-interacting and feedforward systems have zero consciousness, whereas most systems of interacting particles appear to have low non-separability and consciousness. By contrast, brain circuits exhibit high complexity and weak but tightly coordinated interactions, which appear to support high non-separability and therefore high amount of consciousness. The hypothesis applies to both classical and quantum cases, and we highlight the formalism employing the Wigner function (which in the classical limit becomes the Liouville density function) as a potentially fruitful framework for characterizing non-separability and, thus, the amount of consciousness in a system. The hypothesis appears to be consistent with both the Integrated Information Theory and the Orchestrated Objective Reduction Theory and may help reconcile the two. It offers a natural explanation for the physical properties underlying the amount of consciousness and points to methods of estimating the amount of non-separability as promising ways of characterizing the amount of consciousness.

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Section: Resultsmentioning

confidence: 99%

“…As an example, Diaz et al [ 100 ] considered classical coupled harmonic oscillators, described by the Hamiltonian

…”

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

See 2 more Smart Citations

Non-Separability of Physical Systems as a Foundation of Consciousness

Arkhipov

2022

Entropy

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“…In this case, introducing a metric tensor using a symmetric Jordan product could be the indicated procedure [ 17 , 18 ]. In the case of pure states, it is easy to check that the approach of Provost and Vallee is equivalent to the introduction of a Jordan product using the covariance matrix [ 19 ]. Because, for the moment, we are interested only in pure states, we will consider an extension of the work of Provost and Vallee [ 1 ].…”

Section: Introductionmentioning

confidence: 99%

The Quantum Geometric Tensor in a Parameter-Dependent Curved Space

Austrich-Olivares

Vergara

2022

Entropy

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We introduce a quantum geometric tensor in a curved space with a parameter-dependent metric, which contains the quantum metric tensor as the symmetric part and the Berry curvature corresponding to the antisymmetric part. This parameter-dependent metric modifies the usual inner product, which induces modifications in the quantum metric tensor and Berry curvature by adding terms proportional to the derivatives with respect to the parameters of the determinant of the metric. The quantum metric tensor is obtained in two ways: By using the definition of the infinitesimal distance between two states in the parameter-dependent curved space and via the fidelity susceptibility approach. The usual Berry connection acquires an additional term with which the curved inner product converts the Berry connection into an object that transforms as a connection and density of weight one. Finally, we provide three examples in one dimension with a nontrivial metric: an anharmonic oscillator, a Morse-like potential, and a generalized anharmonic oscillator; and one in two dimensions: the coupled anharmonic oscillator in a curved space.

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Molecule–plasmon–photon hybridization and applications

Lü¹,

Badshah²,

Li³

et al. 2023

J. Phys. D: Appl. Phys.

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We study a potential hybrid quantum system with a plasmonic nanocavity coupled to a vibrating mode of single molecule and another optical cavity mode. To explore some important and valuable applications in quantum physics, we discuss and estimate several different applications with respect to the plasmon-mediated quantum interface, the plasmon-assisted engineering of two-mode continuous-variable entanglement, and pursuing an indirect and ultrastrong molecule-photon cooperativity. In addition, governed by the relation of symmetry breaking and quantum phase transitions (QPTs), the single-molecule induced QPTs is also studied in this tripartite hybrid quantum system. This theoretical study can strongly support the potential applications of this hybrid system in the field of quantum information processing (QIP). It is believed that our investigation on molecule-plasmon-photon hybridization can not only open a new avenue towards quantum manipulations, but also provide a fresh and reliable platform to carry out many applications with high efficiencies.

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Classical analogs of the covariance matrix, purity, linear entropy, and von Neumann entropy

Cited by 8 publications

References 51 publications

Non-Separability of Physical Systems as a Foundation of Consciousness

Non-Separability of Physical Systems as a Foundation of Consciousness

The Quantum Geometric Tensor in a Parameter-Dependent Curved Space

Molecule–plasmon–photon hybridization and applications

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