Requirement of dissonance in assisted optimal state discrimination

Unambiguous State Discrimination with Intrinsic Coherence

We investigate the discrimination of pure-mixed (quantum filtering) and mixed-mixed states and compare their optimal success probability with the one for discriminating other pairs of pure states superposed by the vectors included in the mixed states. We prove that under the equal-fidelity condition, the pure-pure state discrimination scheme is superior to the pure-mixed (mixed-mixed) one. With respect to quantum filtering, the coherence exists only in one pure state and is detrimental to the state discrimination for lower dimensional systems; while it is the opposite for the mixed-mixed case with symmetrically distributed coherence. Making an extension to infinite-dimensional systems, we find that the coherence which is detrimental to state discrimination may become helpful and vice versa.

Mutual Information and Quantum Discord in Quantum State Discrimination with a Fixed Rate of Inconclusive Outcomes

We studied the mutual information and quantum discord that Alice and Bob share when Bob implements a discrimination with a fixed rate of inconclusive outcomes (FRIO) onto two pure non-orthogonal quantum states, generated with arbitrary a priori probabilities. FRIO discrimination interpolates between minimum error (ME) and unambiguous state discrimination (UD). ME and UD are well known discrimination protocols with several applications in quantum information theory. FRIO discrimination provides a more general framework where the discrimination process together with its applications can be studied. In this setting, we compared the performance of optimum probability of discrimination, mutual information, and quantum discord. We found that the accessible information is obtained when Bob implements the ME strategy. The most (least) efficient discrimination scheme is ME (UD), from the point of view of correlations that are lost in the initial state and remain in the final state, after Bob’s measurement.

Understanding of Various Type of Unambiguous Discrimination in View of Coherence Distribution

Unambiguous quantum state discrimination is a strategy where the conclusive result can always be trusted. This strategy is very important, since it can be used for various quantum information protocols, including quantum key distribution. However, in the view of quantumness, it is not clear what is going on in performing unambiguous quantum state discrimination. To answer the question, we investigate coherence distribution when unambiguous discrimination is performed by generalized measurement. Specially, we study coherence distribution in three cases, which consist of unambiguous quantum state discrimination, sequential quantum state discrimination, and assisted optimal discrimination, which are considered to be a family of unambiguous quantum state discrimination. In this investigation, we show that the structure of generalized measurements performing various types of unambiguous quantum state discrimination can be understood in terms of coherence distribution. Our result is not limited to the discrimination of two pure quantum states, but it is extended to the discrimination of two mixed states.

Coherence and Entanglement Dynamics in Training Variational Quantum Perceptron

In quantum computation, what contributes supremacy of quantum computation? One of the candidates is known to be a quantum coherence because it is a resource used in the various quantum algorithms. We reveal that quantum coherence contributes to the training of variational quantum perceptron proposed by Y. Du et al., arXiv:1809.06056 (2018). In detail, we show that in the first part of the training of the variational quantum perceptron, the quantum coherence of the total system is concentrated in the index register and in the second part, the Grover algorithm consumes the quantum coherence in the index register. This implies that the quantum coherence distribution and the quantum coherence depletion are required in the training of variational quantum perceptron. In addition, we investigate the behavior of entanglement during the training of variational quantum perceptron. We show that the bipartite concurrence between feature and index register decreases since Grover operation is only performed on the index register. Also, we reveal that the concurrence between the two qubits of index register increases as the variational quantum perceptron is trained.

Quantum dissonance in chiral graphene nanoribbons

Based on the effective spin-ladder model, we study the properties of quantum dissonance (Q) between two edge spins in chiral graphene nanoribbons (CGNRs) thermalized with a reservoir at temperature T, and discuss the influences of relative location between two edge spins, ribbon width, temperature, and on-site Coulomb repulsion (U) on Q. The results show that Q is widely present in Wannier edge states. For intra-edge coupled spin pairs, quantum entanglement (E) is zero, but there still exists considerable value of Q. Interestingly, Q always keeps a constant for entangled edge spin pairs. Considering the thermal effect, it shows that Q always decays with the increasing temperature T, and the decay rate is very sensitive to the intensity of U. Compared Q with E and total quantum correlation (quantum discord, denoted by D), we conjecture that the quantum correlations for a bipartite Wannier edge state in CGNRs satisfy the relation Q  ⩽  D-E.

Quantum Discord, Thermal Discord, and Entropy Generation in the Minimum Error Discrimination Strategy

We study the classical and quantum correlations in the minimum error discrimination (ME) of two non-orthogonal pure quantum states. In particular, we consider quantum discord, thermal discord and entropy generation. We show that ME allows one to reach the accessible information between the two involved parties, Alice and Bob, in the discrimination process. We determine the amount of quantum discord that is consumed in the ME and show that the entropy generation is, in general, higher than the thermal discord. However, in certain cases the entropy generation is very close to thermal discord, which indicates that, in these cases, the process generates the least possible entropy. Moreover, we also study the ME process as a thermodynamic cycle and we show that it is in agreement with the second law of thermodynamics. Finally, we study the relation between the accessible information and the optimum success probability in ME.

Universal quantum correlation close to quantum critical phenomena

We study the ground state quantum correlation of Ising model in a transverse field (ITF) by implementing the quantum renormalization group (QRG) theory. It is shown that various quantum correlation measures and the Clauser-Horne-Shimony-Holt inequality will highlight the critical point related with quantum phase transitions, and demonstrate nonanalytic phenomena and scaling behavior when the size of the systems becomes large. Our results also indicate a universal behavior of the critical exponent of ITF under QRG theory that the critical exponent of different measures is identical, even when the quantities vary from entanglement measures to quantum correlation measures. This means that the two kinds of quantum correlation criterion including the entanglement-separability paradigm and the information-theoretic paradigm have some connections between them. These remarkable behaviors may have important implications on condensed matter physics because the critical exponent directly associates with the correlation length exponent.

Linear monogamy of entanglement in three-qubit systems

For any three-qubit quantum systems ABC, Oliveira et al. numerically found that both the concurrence and the entanglement of formation (EoF) obey the linear monogamy relations in pure states. They also conjectured that the linear monogamy relations can be saturated when the focus qubit A is maximally entangled with the joint qubits BC. In this work, we prove analytically that both the concurrence and EoF obey linear monogamy relations in an arbitrary three-qubit state. Furthermore, we verify that all three-qubit pure states are maximally entangled in the bipartition A|BC when they saturate the linear monogamy relations. We also study the distribution of the concurrence and EoF. More specifically, when the amount of entanglement between A and B equals to that of A and C, we show that the sum of EoF itself saturates the linear monogamy relation, while the sum of the squared EoF is minimum. Different from EoF, the concurrence and the squared concurrence both saturate the linear monogamy relations when the entanglement between A and B equals to that of A and C.