تقرير
Towards exact algorithmic proofs of maximal mutually unbiased bases sets in arbitrary integer dimension
| العنوان: | Towards exact algorithmic proofs of maximal mutually unbiased bases sets in arbitrary integer dimension |
|---|---|
| المؤلفون: | Cifuentes, Santiago, Ciancaglini, Nicolás, Bellomo, Guido, Figueira, Santiago, Bendersky, Ariel |
| سنة النشر: | 2023 |
| المجموعة: | Quantum Physics |
| مصطلحات موضوعية: | Quantum Physics, 81P55 (Primary), 03C10 (Secondary), F.4.1 |
| الوصف: | In this paper, we explore the concept of Mutually Unbiased Bases (MUBs) in discrete quantum systems. It is known that for dimensions $d$ that are powers of prime numbers, there exists a set of up to $d+1$ bases that form an MUB set. However, the maximum number of MUBs in dimensions that are not powers of prime numbers is not known. To address this issue, we introduce three algorithms based on First-Order Logic that can determine the maximum number of bases in an MUB set without numerical approximation. Our algorithms can prove this result in finite time, although the required time is impractical. Additionally, we present a heuristic approach to solve the semi-decision problem of determining if there are $k$ MUBs in a given dimension $d$. As a byproduct of our research, we demonstrate that the maximum number of MUBs in any dimension can be achieved with definable complex parameters, computable complex parameters, and other similar fields. Comment: 11 pages, 0 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2309.12399 |
| رقم الأكسشن: | edsarx.2309.12399 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |