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Abstract <p>The problem of determining the linear independence for a vector system arises in quantum mechanics in the context of the unambiguous state discrimination and other postselective transformations. For several copies of the same set of quantum states, the conditions of linear independence are known, whereas in this paper we consider tensor product for two general sets of vectors. We obtain a necessary and sufficient condition for the linear independence of the tensor product of two vector systems.</p>

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Linear Independence of Tensor Products and Its Application in Quantum Transformations

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • T. R. Klevtsov,
  • D. A. Kronberg

摘要

Abstract

The problem of determining the linear independence for a vector system arises in quantum mechanics in the context of the unambiguous state discrimination and other postselective transformations. For several copies of the same set of quantum states, the conditions of linear independence are known, whereas in this paper we consider tensor product for two general sets of vectors. We obtain a necessary and sufficient condition for the linear independence of the tensor product of two vector systems.