Joint measurability of quantum effects and the matrix diamond

N/ACitations
Citations of this article
9Readers
Mendeley users who have this article in their library.
Get full text

Abstract

In this work, we investigate the joint measurability of quantum effects and connect it to the study of free spectrahedra. Free spectrahedra typically arise as matricial relaxations of linear matrix inequalities. An example of a free spectrahedron is the matrix diamond, which is a matricial relaxation of the ℓ1-ball. We find that joint measurability of binary positive operator valued measures is equivalent to the inclusion of the matrix diamond into the free spectrahedron defined by the effects under study. This connection allows us to use results about inclusion constants from free spectrahedra to quantify the degree of incompatibility of quantum measurements. In particular, we completely characterize the case in which the dimension is exponential in the number of measurements. Conversely, we use techniques from quantum information theory to obtain new results on spectrahedral inclusion for the matrix diamond.

Cite

CITATION STYLE

APA

Bluhm, A., & Nechita, I. (2018). Joint measurability of quantum effects and the matrix diamond. Journal of Mathematical Physics, 59(11). https://doi.org/10.1063/1.5049125

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free