LAUSR

AbstractIn this paper, we discuss the coherence of the reduced state in system HA ⊗HB under taking different quantum operations acting on subsystem HB. Firstly, we show that for a pure bipartite state, the coherence of the final subsystem HA under the sum of two orthonormal rank 1 projections acting on HB is less than or equal to the sum of the coherence of the state after two orthonormal projections acting on HB, respectively. Secondly, we obtain that the coherence of reduced state in subsystem HA under random unitary channel Φ(ρ)=∑sλsUsρUs∗${\Phi }(\rho )={\sum }_{s}\lambda _{s}U_{s}\rho U_{s}^{\ast }$ acting on HB, is equal to the coherence of the state after each operation Φs(ρ)=λsUsρUs∗${\Phi }_{s}(\rho )=\lambda _{s}U_{s}\rho U_{s}^{\ast }$ acting on HB for every s. In addition, for general quantum operation Φ(ρ)=∑sFsρFs∗${\Phi }(\rho )={\sum }_{s}F_{s}\rho F_{s}^{\ast }$ on HB, we get the relation C(I⊗Φ)ρABA≤∑sC(I⊗Φs)ρABA.$ C\left (\left ((I\otimes {\Phi })\rho ^{AB}\right )^{A}\right )\leq \sum \limits _{s}C\left (\left ((I\otimes {\Phi }_{s})\rho ^{AB}\right )^{A}\right ). $