Negative Entropy in Quantum Information Theory

Cerf, Nicolas J.; Adami, Christoph

doi:10.1007/978-94-011-5886-2_11

Cited by 45 publications

(17 citation statements)

References 11 publications

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“…The formal proof of this statement is outsourced to Appendix B.3. Here we sketch it: The key insight is to quantify the entanglement between G and S using the conditional von-Neumann entropy [22][23][24]. As the function f from the HSP is constant on cosets g + H ∈ G/H, the only entanglement that is generated by the function oracle O f comes from a sum over the the different cosets in G/H.…”

Section: Resultsmentioning

confidence: 99%

Thermodynamic optimization of quantum algorithms: on-the-go erasure of qubit registers

Meier¹,

Rio²

2021

Preprint

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We consider two bottlenecks in quantum computing: limited memory size and noise caused by heat dissipation. Trying to optimize both, we investigate "on-the-go erasure" of quantum registers that are no longer needed for a given algorithm: freeing up auxiliary qubits as they stop being useful would facilitate the parallelization of computations. We study the minimal thermodynamic cost of erasure in these scenarios, applying results on the Landauer erasure of entangled quantum registers. For the class of algorithms solving the Abelian hidden subgroup problem, we find optimal online erasure protocols. We conclude that there is a trade-off: if we have enough partial information about a problem to build efficient on-the-go erasure, we can use it to instead simplify the algorithm, so that fewer qubits are needed to run the computation in the first place. We provide explicit protocols for these two approaches."I've a grand memory for forgetting."

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Section: Resultsmentioning

confidence: 99%

Thermodynamic optimization of quantum algorithms: on-the-go erasure of qubit registers

Meier¹,

Rio²

2021

Preprint

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“…Information is the possibility that negative (virtual) information can be carried by entangled particles suggests a consistent interpretation of quantum informational processes (Cerf & Adami, 1995). Unlike in Shannon theory, conditional entropies can be negative when considering quantum entangled systems (Cerf & Adami, 1996). The information dynamics methodology occurs also in the analysis of stochastic dynamical systems.…”

Section: The Discussion About Information Entropymentioning

confidence: 99%

Limit and Dynamics of Information Entropy in Transmission

Yan

2012

NCT

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This paper presents a theoretical explanation and test results that an amount of information would not increase infinitely in transmission via the mathematical model of the matter for deciphering original works of information entropy and the principle of thermodynamic entropy. The rate formula with energy is derived via retrieval speed testing the vast amount of data in DBMS and variables in rate formula proved via other testing methods. We found that the actual value in the rate formula was quite different from the theoretical value that calculating the entropy per bit of information needed energy and the speed need energy. We used of testing data to illustrate these relations between bit and energy, 1 bit =3.92×10-4 J/K. We assumed that the energy of Brillouin's information entropy was the surface entropy changes between information source and information channel rather than the information source itself.

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“…Many also tried to analyze biological organization in terms of (Shannon's) information: since entropy increase may characterize loss of information, its negation should provide (an increase of) information. Besides its relevance in transmission theory, this approach has inspired new analyses also as for negative entropy in quantum systems (see, among others, [Cerf, Adami, 1997]). Yet, both classical and quantum information basically refer to classical or quantum bits, as the discrete mathematical frames are at the core of information and computation theories.…”

Section: More On Negative Entropy In Physics and Anti-entropy In Biology Concluding Remarkmentioning

confidence: 99%

Biological Organization and Anti-Entropy

Bailly

Longo

2009

J. Biol. Syst.

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This paper proposes a systemic perspective for some aspects of both phylogenesis and ontogenesis by expressing biological organization in terms of "anti-entropy", a notion to be defined below and which conceptually differs from the common use of "negative entropy". To this purpose, we introduce two principles, in addition to the thermodynamic ones, which are (mathematically) compatible with traditional principles but which have no meaning with regard to inert matter. A traditional balance equation for the metabolism will then be extended to the new notion as specified by these principles. We examine far from equilibrium systems and we focus in particular on the production of global entropy associated to the irreversible character of the processes. A close analysis of anti-entropy will be performed from the perspective of a diffusion equation of biomass over "complexity" and, as a complementary approach and as a tool for specifying a source term, in connection to Schrödinger's method regarding his equation in the field of Quantum Mechanics. We borrow only the operatorial approach from this equation and do so using a classical framework, since we use real coefficients instead of complex ones, thus falling outside of the mathematical framework of quantum theories. The first application of our proposal is a simple mathematical reconstruction of Gould's complexity curve of biomass over complexity as it applies to evolution. We then present, based on the existence of different time scales, a partition of ontogenetic time, in reference to entropy and anti-entropy variation. On the grounds of this approach, we analyze the metabolism and scaling laws. This allows to compare various relevant coefficients appearing in these scaling laws, which fit empirical data. Finally, a tentative and quantitative evaluation of complexity is proposed, also in relation to some empirical data (Caenorhabditis elegans).

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Negative Entropy in Quantum Information Theory

Cited by 45 publications

References 11 publications

Thermodynamic optimization of quantum algorithms: on-the-go erasure of qubit registers

Thermodynamic optimization of quantum algorithms: on-the-go erasure of qubit registers

Limit and Dynamics of Information Entropy in Transmission

Biological Organization and Anti-Entropy

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