In this paper, we investigate the behavior of bipartite entanglement of fermionic systems when one of the parties is traveling with a uniform acceleration. For the ordering problem in fermionic systems, we apply the recent result of Montero and Mart\'\in-Mart\'\inez [Phys. Rev. A 83, 052306 (2011)]. Based on the approach, we consider both pure and mixed entangled states, and we show that the behavior in terms of the entanglement measure (negativity) allows one to obtain physical results, i.e., its convergence in the infinite acceleration. The behavior shows that the ordering employed is relevant to derive physical results for fermionic entanglement. This also corrects the previous analysis of Mart\'\in-Mart\'\inez and Fuentes.

Quantum state discrimination is a fundamental task having many applications in quantum information processing. However up to now there has been no rigorous formulation for discriminating $N$-qudit states. In this article we provide a geometric method to obtain minimum error discrimination for $N$-qudit states. By using the geometric approach to minimum-error discrimination for $N$-qudit states, we supply the condition for the existence of optimal measurement that can be composed of null operators, which gives a key understanding for discriminating $N$-qudit states. Furthermore we present how the number of nonzero operators for optimal measurement can be reduced. Applying our method to symmetric $N$-qudit states we obtain optimal measurements, which are different from known ones.

We consider unambiguous discrimination of three pure quantum states. Necessary and sufficient conditions to decide which states should be detected for optimal measurement of unambiguous discrimination are provided in terms of inner products and the geometric phase $\mathrm{\Phi }$. We get the optimal measurement and the optimal failure probability when the optimal unambiguous discrimination does not require the detection of every given quantum state. When at least two quantum states are orthogonal to each other, we supply the optimal measurement and optimal failure probability in analytic form. When all three quantum states are not orthogonal to each other and $\mathrm{\Phi }\ne 0$, we find an analytic condition to determine the zero and nonzero elements for an optimal positive operator valued measure. We explain how to determine the solution in a geometric manner. Using the known solution of a case where the mutual inner products are real, we check the necessary and sufficient conditions when $\mathrm{\Phi }=\pi$ and analyze the property of the singular point when $\mathrm{\Phi }=0$ and the relation between the optimal points.

Recently, Schmid and Spekkens studied the quantum contextuality in terms of state discrimination. By dealing with the minimum error discrimination of two quantum states with identical prior probabilities, they reported that quantum contextual advantage exists. Meanwhile, if one notes a striking observation that the selection of prior probability can affect the quantum properties of the system, it is necessary to verify whether the quantum contextual advantage depends on the prior probabilities of the given states. In this paper, we consider the minimum error discrimination of two states with arbitrary prior probabilities, in which both states are pure or mixed. We show that the quantum contextual advantage in state discrimination may depend on the prior probabilities of the given states. In particular, even though the quantum contextual advantage always exists in the state discrimination of two nonorthogonal $\mathit{pure}$ states with nonzero prior probabilities, the quantum contextual advantage depends on prior probabilities in the state discrimination of two $\mathit{mixed}$ states.

Recently, J. A. Bergou et al. proposed sequential state discrimination as a new quantum state discrimination scheme. In the scheme, by the successful sequential discrimination of a qubit state, receivers Bob and Charlie can share the information of the qubit prepared by a sender Alice. A merit of the scheme is that a quantum channel is established between Bob and Charlie, but a classical communication is not allowed. In this report, we present a method for extending the original sequential state discrimination of two qubit states to a scheme of N linearly independent pure quantum states. Specifically, we obtain the conditions for the sequential state discrimination of N = 3 pure quantum states. We can analytically provide conditions when there is a special symmetry among N = 3 linearly independent pure quantum states. Additionally, we show that the scenario proposed in this study can be applied to quantum key distribution. Furthermore, we show that the sequential state discrimination of three qutrit states performs better than the strategy of probabilistic quantum cloning.

Recently, sequential state discrimination, as a quantum-key distribution protocol, has been proposed for multiple receivers. A previous study [J. A. Bergou et al., Phys. Rev. Lett. 111, 100501 (2013)] showed that every receiver could successfully perform a sequential state discrimination of two pure states with identical prior probabilities. In this study, we extend the sequential state discrimination to mixed states with arbitrary prior probability. First, we analytically obtain the condition of the receiver's optimal measurement. In addition, we show that the optimal probability for every receiver to share the mixed state prepared by the sender is not zero. Furthermore, we compare the sequential state discrimination to the strategies of quantum reproducing and quantum broadcasting. We find that there are cases in which, unlike that of the pure state, the sequential state discrimination of mixed states shows a better performance than the other strategies.