One fundamental feature of quantum entanglement is the monogamy which shows that the entanglement of two systems limits the ability of either system to entangle with a third one. Such an understanding is only well described in the qubit systems, but it remains an open question for high-dimensional quantum systems. Here the relative entropy of entanglement and the negativity are respectively used to quantify the entanglement. Based on the resource theory of coherence, we found that the monogamy inequalities in arbitrarily finite-dimensional systems can be successfully established for the entanglement induced by quantum coherence. Moreover, the similar inequalities are also constructed for the distribution of quantum coherence.

Photon absorption and nonreciprocal photon transmission are studied in a rotating optical resonator coupled with an atomic ensemble. It is demonstrated that the perfect photon absorption is accompanied by optical bistability when the resonator is static. If the spinning detune is adjusted to some particular values, we find that the amplified unidirectional photon transmission can be realized. We have explicitly given the perfect photon absorption conditions and the maximal adjustable amplification rate. It is found that the coupling of the resonator and the atomic ensemble is necessary for perfect photon absorption, and the phase difference of the two input fields only affects the perfect absorption point. It gives new insight into the design of photon absorbers and optical switches.

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Entanglement and photon statistics are investigated in a cavity QED system with three two-level atoms trapped in a modestly driven cavity with weak dissipation. It is shown that the local maximal steady-state entanglement of any two atoms perfectly corresponds to the strongest photon antibunching point. In particular, the local maximal entanglement of two atoms is also consistent with the strongest photon bunching point. It provides a new angle to understand both photon statistics and entanglement. Our work gives strong support for employing extremal photon statistics to signal the extremal atomic entanglement in this system.

Approximating a quantum state by the convex mixing of some given states has strong experimental significance and provides alternative understandings of quantum resource theory. It is essentially a complex optimal problem which, up to now, has only partially solved for qubit states. Here, the most general case is focused on that the approximation of a d-dimensional objective quantum state by the given state set consisting of any number of (mixed-) states. The problem is thoroughly solved with a closed solution of the minimal distance in the sense of l 2 norm between the objective state and the set. In particular, the minimal number of states in the given set is presented to achieve the optimal distance. The validity of this closed solution is further verified numerically by several randomly generated quantum states.