On Mutually Unbiased Unitary Bases in prime dimensional Hilbert spaces
| Autor: | Jesni Shamsul Shaari, Rinie N. M. Nasir, Stefano Mancini |
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| Rok vydání: | 2018 |
| Předmět: |
Monoid
Quantum Physics Hilbert space Structure (category theory) FOS: Physical sciences Statistical and Nonlinear Physics 01 natural sciences Unitary state Prime (order theory) 010305 fluids & plasmas Theoretical Computer Science Electronic Optical and Magnetic Materials Combinatorics symbols.namesake Modeling and Simulation 0103 physical sciences Signal Processing symbols Isomorphism Electrical and Electronic Engineering 010306 general physics Quantum Physics (quant-ph) Mutually unbiased bases Mathematics Vector space |
| DOI: | 10.48550/arxiv.1811.07314 |
| Popis: | Akin to the idea of complete sets of Mutually Unbiased Bases for prime dimensional Hilbert spaces, $\mathcal{H}_d$, we study its analogue for a $d$ dimensional subspace of $M (d,\mathbb{C})$, i.e. Mutually Unbiased Unitary Bases (MUUBs) comprising of unitary operators. We note an obvious isomorphism between the vector spaces and beyond that, we define a relevant monoid structure for $\mathcal{H}_d$ isomorphic to one for the subspace of $M (d,\mathbb{C})$. This provides us not only with the maximal number of such MUUBs, but also a recipe for its construction. Comment: Lemma 5 corrected, new appendixes B, D included, typos corrected |
| Databáze: | OpenAIRE |
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