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Infinite-Dimensional Quantum Entropy: The Unified Entropy Case
Roman Gielerak1, Joanna Wiśniewska2, Marek Sawerwain1
1Institute of Control & Computation Engineering, University of Zielona Góra, Licealna 9, 65-417 Zielona Góra, Poland.
Abstract:
Infinite-dimensional systems play an important role in the continuous-variable quantum computation model, which can compete with a more standard approach based on qubit and quantum circuit computation models. But, in many cases, the value of entropy unfortunately cannot be easily computed for states originating from an infinite-dimensional Hilbert space. Therefore, in this article, the unified quantum entropy (which extends the standard von Neumann entropy) notion is extended to the case of infinite-dimensional systems by using the Fredholm determinant theory. Some of the known (in the finite-dimensional case) basic properties of the introduced unified entropies were extended to this case study. Certain numerical examples for computing the proposed finite- and infinite-dimensional entropies are outlined as well, which allowed us to calculate the entropy values for infinite Hilbert spaces.
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