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Abstract
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.
Highlights
Quantum resource theory has become a powerful tool in quantitatively describing many intriguing and novel characteristics of quantum systems[1]
We have systematically studied the single qubit transformations under incoherent operation (IO), strictly incoherent operation (SIO), coherence-preserving operation (CPO), and physically incoherent operation (PIO)
By introducing the Bloch sphere depiction, we show that the transformation ability of single qubit via IO, SIO, CPO or PIO has rotational symmetry around z-axis
Summary
Quantum resource theory has become a powerful tool in quantitatively describing many intriguing and novel characteristics of quantum systems[1]. We discuss how to implement single qubit transformations via four kinds of incoherent operations, namely, IO, SIO, PIO, and CPO. New method to construct the map for realization of single qubit transformation via IO, where the intermediate state ρ′max is no longer necessary and only two special Kraus operators are needed.
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