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Entanglement Theory Quantum Correlations Quantum Simulation

Maximum Dimension of Subspaces with No Product Basis

arXiv
Authors: Yuuya Yoshida

Year

2020

Paper ID

7069

Status

Preprint

Abstract Read

~2 min

Abstract Words

149

Citations

N/A

Abstract

Let nge2 and d1,ldots,dnge2 be integers, and mathcal{F} be a field. A vector uinmathcal{F}d1otimescdotsotimesmathcal{F}dn is called a product vector if u=u[1]otimescdotsotimes u[n] for some u[1]inmathcal{F}d1,ldots,u[n]inmathcal{F}dn. A basis composed of product vectors is called a product basis. In this paper, we show that the maximum dimension of subspaces of mathcal{F}d1otimescdotsotimesmathcal{F}dn with no product basis is equal to d1d2cdots dn-2 if either (i) n=2 or (ii) nge3 and \#mathcal{F}>max\{di : inot=n1,n2\} for some n1 and n2. When mathcal{F}=mathbb{C}, this result is related to the maximum number of simultaneously distinguishable states in general probabilistic theories (GPTs).

Why This Paper Matters

  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
  • It adds a 2020 reference point for readers tracking recent quantum research.
  • Let nge2 and d1,ldots,dnge2 be integers, and mathcalF be a field.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2010.16293 [2] arXiv https://arxiv.org/abs/2010.16293 [3] Publisher https://arxiv.org/abs/2010.16293

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