Related papers: Quantum Wasserstein isometries on the qubit state space

Quantum Wasserstein isometries on the qubit state space

URL: http://arxiv.org/abs/2204.14134v3
Date: Fri, 28 Oct 2022 14:05:53 GMT
Title: Quantum Wasserstein isometries on the qubit state space
Authors: Gy\"orgy P\'al Geh\'er, J\'ozsef Pitrik, Tam\'as Titkos, D\'aniel Virosztek
Abstract summary: We describe Wasserstein isometries of the quantum bit state space with respect to distinguished cost operators. For the cost generated by the qubit "clock" and "shift" operators, we discovered non-surjective and non-injective isometries as well, beyond the regular ones.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We describe Wasserstein isometries of the quantum bit state space with respect to distinguished cost operators. We derive a Wigner-type result for the cost operator involving all the Pauli matrices: in this case, the isometry group consists of unitary or anti-unitary conjugations. In the Bloch sphere model, this means that the isometry group coincides with the classical symmetry group $\mathbf{O}(3).$ On the other hand, for the cost generated by the qubit "clock" and "shift" operators, we discovered non-surjective and non-injective isometries as well, beyond the regular ones. This phenomenon mirrors certain surprising properties of the quantum Wasserstein distance.

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