Efficient computation of the Zassenhaus formula

How can relevant information be extracted from a quantum process? In many situations, only some part of the total information content produced by an information source is useful. Can one then find an efficient encoding, in the sense of retaining the largest fraction of relevant information? This paper offers one possible solution by giving a generalization of a classical method designed to retain as much relevant information as possible in a lossy data compression. A key feature of the method is to introduce a second information source to define relevance. We quantify the advantage a quantum encoding has over the best classical encoding in general, and we demonstrate using examples that a substantial quantum advantage is possible. We show analytically, however, that if the relevant information is purely classical, then a classical encoding is optimal.

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“…To see that this is possible, consider the Zassenhaus formula for the expansion of an exponential [42],…”

Section: Optimally Predictive Quantum Memoriesmentioning

confidence: 99%

Quantum predictive filtering

Grimsmo

Still

2016

Phys. Rev. A

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“…For the isotropic case J = ∆, the eigenvalues and eigenvectors are given by Using the Zassenhaus formula [43] with N operators, we can apply up to second order term, which reads as follows…”

Section: Appendix a Explicit Representation Of The Hamiltoniansmentioning

confidence: 99%

“…Now we want to apply the decoration transformation for whole lattice system, then we can use the Zassenhaus formula [43] Now let us define the following system operator W = e −βH . Using the Zassenhaus formula [43] with N operators to obtain the correction of decoration transformation, as described in Appendix C, up to second order term.…”

Section: Quantum Decoration Transformation Correction Using Zassenhaumentioning

confidence: 99%

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Quantum decoration transformation for spin models

et al. 2016

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It is quite relevant the extension of decoration transformation for quantum spin models since most of the real materials could be well described by Heisenberg type models. Here we propose an exact quantum decoration transformation and also showing interesting properties such as the persistence of symmetry and the symmetry breaking during this transformation. Although the proposed transformation, in principle, cannot be used to map exactly a quantum spin lattice model into another quantum spin lattice model, since the operators are non-commutative. However, it is possible the mapping in the "classical" limit, establishing an equivalence between both quantum spin lattice models. To study the validity of this approach for quantum spin lattice model, we use the Zassenhaus formula, and we verify how the correction could influence the decoration transformation. But this correction could be useless to improve the quantum decoration transformation because it involves the second-nearest-neighbor and further nearest neighbor couplings, which leads into a cumbersome task to establish the equivalence between both lattice models. This correction also gives us valuable information about its contribution, for most of the Heisenberg type models, this correction could be irrelevant at least up to the third order term of Zassenhaus formula. This transformation is applied to a finite size Heisenberg chain, comparing with the exact numerical results, our result is consistent for weak xy-anisotropy coupling. We also apply to bond-alternating Ising-Heisenberg chain model, obtaining an accurate result in the limit of the quasi-Ising chain.

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“…Like in ordinary space-time, a gauge theory can be defined on a NC space-time [34] see also [35][36][37][38][39] and references therein. In the sequel, the NC variables are denoted with a "hat" notation.…”

Section: Nc Gauge Theory and Seiberg-witten Mapsmentioning

confidence: 99%

Pair production of Dirac particles in a $$d+1$$ d + 1 -dimensional noncommutative space–time

2014

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This work addresses the computation of the probability of fermionic particle pair production in (d + 1)-dimensional noncommutative Moyal space. Using SeibergWitten maps, which establish relations between noncommutative and commutative field variables, up to the first order in the noncommutative parameter θ , we derive the probability density of vacuum-vacuum pair production of Dirac particles. The cases of constant electromagnetic, alternating time-dependent, and space-dependent electric fields are considered and discussed.

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Efficient computation of the Zassenhaus formula

Cited by 116 publications

References 16 publications

Quantum predictive filtering

Quantum predictive filtering

Quantum decoration transformation for spin models

Pair production of Dirac particles in a $$d+1$$ d + 1 -dimensional noncommutative space–time

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