A Query about an article on quantum synchronization

Query in attached paper on quantum synchronization.
I am currently studying this paper on quantum synchronization. The first page gives an introduction to synchronization and the basic setup of the ensembles in the cavity. My query is on the second page where the following statements are made.

Because of the ##U(1)## symmetry, ##\langle \hat{\sigma}^{\pm}_{(A,B)j} \rangle = 0##. Therefore, all nonzero observables can be expressed in terms of ##\langle \hat{\sigma}^{z}_{(A,B)j} \rangle, \langle \hat{\sigma}^{+}_{(A,B)i}\hat{\sigma}^{-}_{(A,B)j} \rangle## and ##\langle \hat{\sigma}^{z}_{(A,B)i}\hat{\sigma}^{z}_{(A,B)j} \rangle.##
Can anyone see why the implication is that all observables can be expressed by these terms?

Thanks for any assistance.


Last edited by a moderator:

Want to reply to this thread?

"Query about an article on quantum synchronization" You must log in or register to reply here.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Hot Threads