Unitary dilation of freely independent contractions

Scott Atkinson; Christopher Ramsey

doi:10.1090/proc/13345

Unitary dilation of freely independent contractions

Proceedings of the American Mathematical Society ◽

10.1090/proc/13345 ◽

2016 ◽

Vol 145 (4) ◽

pp. 1729-1737

Author(s):

Scott Atkinson ◽

Christopher Ramsey

Keyword(s):

Unitary Dilation

Download Full-text

Unitary dilation for polar decompositions of p-hyponormal operators

10.4064/bc67-0-11 ◽

2005 ◽

Author(s):

Muneo Chō ◽

Tadasi Huruya ◽

Kôtarô Tanahashi

Keyword(s):

Hyponormal Operators ◽

Unitary Dilation

Download Full-text

Quantum clocks and the temporal localisability of events in the presence of gravitating quantum systems

Nature Communications ◽

10.1038/s41467-020-16013-1 ◽

2020 ◽

Vol 11 (1) ◽

Cited By ~ 4

Author(s):

Esteban Castro-Ruiz ◽

Flaminia Giacomini ◽

Alessio Belenchia ◽

Časlav Brukner

Keyword(s):

Reference Frame ◽

Reference Frames ◽

Quantum Systems ◽

Indefinite Metric ◽

Causal Order ◽

Quantum Operations ◽

Unitary Dilation ◽

Local Quantum ◽

Fixed Space ◽

Quantum Clocks

AbstractThe standard formulation of quantum theory relies on a fixed space-time metric determining the localisation and causal order of events. In general relativity, the metric is influenced by matter, and is expected to become indefinite when matter behaves quantum mechanically. Here, we develop a framework to operationally define events and their localisation with respect to a quantum clock reference frame, also in the presence of gravitating quantum systems. We find that, when clocks interact gravitationally, the time localisability of events becomes relative, depending on the reference frame. This relativity is a signature of an indefinite metric, where events can occur in an indefinite causal order. Even if the metric is indefinite, for any event we can find a reference frame where local quantum operations take their standard unitary dilation form. This form is preserved when changing clock reference frames, yielding physics covariant with respect to quantum reference frame transformations.

Download Full-text