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2017 ; 7
(1
): 14806
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Coherence transformations in single qubit systems
#MMPMID29093505
Shi HL
; Wang XH
; Liu SY
; Yang WL
; Yang ZY
; Fan H
Sci Rep
2017[Nov]; 7
(1
): 14806
PMID29093505
show ga
We investigate the single qubit transformations under several typical
coherence-free operations, such as, incoherent operation (IO), strictly
incoherent operation (SIO), physically incoherent operation (PIO), and
coherence-preserving operation (CPO). Quantitative connection has been built
between IO and SIO in single qubit systems. Moreover, these coherence-free
operations have a clear hierarchical relationship in single qubit systems: CPO ?
PIO ? SIO=IO. A new and explicit proof for the necessary and sufficient condition
of single qubit transformation via IO or SIO has been provided, which indicates
that SIO with only two Kraus operators are enough to realize this transformation.
The transformation regions of single qubits via CPO and PIO are also given. Our
method provides a geometric illustration to analyze single qubit coherence
transformations by introducing the Bloch sphere depiction of the transformation
regions, and tells us how to construct the corresponding coherence-free
operations.