Barycentric decomposition for quantum instruments




Pellonpää Juha-Pekka, Haapasalo Erkka, Uola Roope

PublisherIOP Publishing Ltd

BRISTOL

2024

Journal of Physics A: Mathematical and Theoretical

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL

J PHYS A-MATH THEOR

095302

57

9

20

1751-8113

1751-8121

DOIhttps://doi.org/10.1088/1751-8121/ad233c(external)

https://10.1088/1751-8121/ad233c(external)

https://research.utu.fi/converis/portal/detail/Publication/387392222(external)

https://arxiv.org/abs/2307.08405(external)



We present a barycentric decomposition for quantum instruments whose output space is finite-dimensional and input space is separable. As a special case, we obtain a barycentric decomposition for channels between such spaces and for normalized positive-operator-valued measures in separable Hilbert spaces. This extends the known results by Ali and Chiribella et al on decompositions of quantum measurements, and formalizes the fact that every instrument between finite-dimensional Hilbert spaces can be represented using only finite-outcome instruments.

Last updated on 2025-06-03 at 09:43