Parallelity of mixed quantum ensembles
- URL: http://arxiv.org/abs/2001.06360v1
- Date: Fri, 17 Jan 2020 15:06:26 GMT
- Title: Parallelity of mixed quantum ensembles
- Authors: Erik Sj\"oqvist
- Abstract summary: A unifying framework for identifying distance and holonomy for decompositions of density operators is introduced.
A gauge invariant spectral geometric phase for discrete sequences of mixed quantum states is obtained as the phase of the trace of the spectral holonomy.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: A unifying framework for identifying distance and holonomy for decompositions
of density operators is introduced. Parallelity between quantum ensembles is
defined by minimizing this distance over allowed decompositions. The minimum is
a property of a pair of states and coincides with the Bures distance. The
parallelity condition imposes a connection (rule for parallel transport) that
results in the Uhlmann holonomy for sequences of density operators. A distance
and holonomy for spectral decompositions of density operators is identified as
a sub-group restriction of the full decomposition freedom. These spectral
concepts are gauge invariant (decomposition independent) properties of mixed
quantum ensembles, as long as the corresponding density operators are
non-degenerate. A gauge invariant spectral geometric phase for discrete
sequences of mixed quantum states is obtained as the phase of the trace of the
spectral holonomy. This geometric phase differs from the interferometric mixed
state geometric phase in the continuous limit.
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