Tristochastic operations and convolutions of quantum states
- URL: http://arxiv.org/abs/2305.17978v1
- Date: Mon, 29 May 2023 09:37:36 GMT
- Title: Tristochastic operations and convolutions of quantum states
- Authors: Rafa{\l} Bistro\'n, Wojciech \'Smia{\l}ek and Karol \.Zyczkowski
- Abstract summary: We study the problem of associativity, commutativity and the existence of neutral elements and inverses in binary operations determined by (tri)stochastic tensors.
We propose a quantum analogue of the convolution of probability vectors defined for two arbitrary density matrices of the same size.
- Score: 0.0
- License: http://creativecommons.org/licenses/by-sa/4.0/
- Abstract: The notion of convolution of two probability vectors, corresponding to a
coincidence experiment can be extended for a family of binary operations
determined by (tri)stochastic tensors, to describe Markov chains of a higher
order. The problem of associativity, commutativity and the existence of neutral
elements and inverses is analyzed for such operations. For a more general setup
of multi-stochastic tensors, we present the characterization of their
probability eigenvectors. Similar results are obtained for the quantum case: we
analyze tristochastic channels, which induce binary operations defined in the
space of quantum states. Studying coherifications of tristochastic tensors we
propose a quantum analogue of the convolution of probability vectors defined
for two arbitrary density matrices of the same size. Possible applications of
this notion to construct schemes of error mitigation or building blocks in
quantum convolutional neural networks are discussed.
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