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ARBITRARY COHERENCE HOW TO
Marvian, I., Spekkens, R.W.: How to quantify coherence: distinguishing speakable and unspeakable notions. 1, 01LT01 (2016)īaumgratz, T., Cramer, M., Plenio, M.B.: Quantifying coherence. Matera, J.M., Egloff, D., Killoran, N., Plenio, M.B.: Coherent control of quantum systems as a resource theory. (iii) The trade-off between coherence and mixedness still holds in the open system. (ii) The decrease in the coherence is not always accompanied by an increase in the mixedness.
Our results show that (i) Coherence can be completely transferred from the qubit–qubit system to the environment–environment system in the Markovian environment while in non-Markovian scenarios, the coherence between the qubit–qubit system and environment–environment system can be transferred each other. Different types of channels, such as amplitude-damping, phase-damping and bit-phase-flip channels with (non-)Markovian effects, are taken into consideration. At the same time, we also examine the dynamical behaviors of coherence, mixedness and their trade-off for both qubit–qubit system and environment–environment system where a two-qubit composite system is interacting with their own environmental channels. In this paper, we firstly study the geometry of coherence and mixedness for a class of two-qubit X-states and demonstrate new pictures and structures of trade-off between coherence and mixedness. However, whether this relationship holds under the action of decoherence remains to be further investigated. Recently, a relationship between coherence and mixedness for an arbitrary d-dimensional quantum states has been built by Singh et al.
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