Error trade-off relations for two-parameter unitary model with commuting generators

• URL: http://arxiv.org/abs/2010.00789v1
• Date: Fri, 2 Oct 2020 05:22:24 GMT
• Title: Error trade-off relations for two-parameter unitary model with commuting generators
• Authors: Shin Funada, Jun Suzuki
• Abstract summary: We show that the error trade-off relation which exists in our models of a finite dimension system is a generic phenomenon. We analyze a qutrit system to show that there can be an error trade-off relation given by the SLD and RLD Cramer-Rao bounds.
• Score: 21.22196305592545
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate whether a trade-off relation between the diagonal elements of the mean square error matrix exists for the two-parameter unitary models with mutually commuting generators. We show that the error trade-off relation which exists in our models of a finite dimension system is a generic phenomenon in the sense that it occurs with a finite volume in the spate space. We analyze a qutrit system to show that there can be an error trade-off relation given by the SLD and RLD Cramer-Rao bounds that intersect each other. First, we analyze an example of the reference state showing the non-trivial trade-off relation numerically, and find that its eigenvalues must be in a certain range to exhibit the trade-off relation. For another example, one-parameter family of reference states, we analytically show that the non-trivial relation always exists and that the range where the trade-off relation exists is up to about a half of the possible range.

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