Quantum Information Processing

In this paper, we study the relation among quantum coherence, uncertainty, steerability of quantum coherence based on skew information and quantum phase transition in the spin model by employing quantum renormalization-group method. Interestingly, the results show that the value of the local quantum uncertainty is equal to the local quantum coherence corresponding to local observable $$\sigma _z$$ in XXZ model, and unlikely in XY model, local quantum uncertainty is minimal optimization of the local quantum coherence over local observable $$\sigma _x$$ and this proposition can be generalized to a multipartite system. Therefore, one can directly achieve quantum correlation measured by local quantum uncertainty and coherence by choosing different local observables $$\sigma _x$$ , $$\sigma _z$$ , corresponding to the XY model and XXZ model separately. Meanwhile, steerability of quantum coherence in XY and XXZ model is investigated systematically, and our results reveal that no matter what times the QRG iterations are carried out, the quantum coherence of the state of subsystem cannot be steerable, which can also be suitable for block–block steerability of local quantum coherence in both XY and XXZ models. On the other hand, we have illustrated that the quantum coherence and uncertainty measure can efficiently detect the quantum critical points associated with quantum phase transitions after several iterations of the renormalization. Moreover, the nonanalytic and scaling behaviors of steerability of local quantum coherence have been also taken into consideration.

In this paper, we propose a quantum version of the differential cryptanalysis which offers a quadratic speedup over the existing classical one and show the quantum circuit implementing it. The quantum differential cryptanalysis is based on the quantum minimum/maximum-finding algorithm, where the values to be compared and filtered are obtained by calling the quantum counting algorithm. Any cipher which is vulnerable to the classical differential cryptanalysis based on counting procedures can be cracked more quickly under this quantum differential attack.

We use one of the influential quantum game models, the Marinatto–Weber model, to investigate quantum Bayesian game. We show that in a quantum Bayesian game which has more than one Nash equilibrium, one equilibrium stands out as the compelling solution, whereas two Nash equilibria seem equally compelling in the classical Bayesian game.

The non-equilibrium thermal entanglement and quantum discord in a two-qubit Heisenberg XYZ model subjected to two thermal baths with different temperatures are investigated. The dynamical behaviors of entanglement and quantum discord under the influences of the initial states of the two-qubit system, the temperature of the thermal baths and the coupling constant $$J_z$$ are discussed. A special emphasis is devoted to study the effects of the thermal baths on the steady quantum correlation between the two qubits. Our results show that the temperature difference $$\Delta T$$ plays a key role for the appearance of steady quantum correlation, which can be enhanced by coupling constant $$J_z$$, DM interaction and non-uniform magnetic field.

Mutual convertibility of bound entangled states under local quantum operations and classical communication (LOCC) is studied. We focus on states associated with unextendible product bases (UPB) in a system of three qubits. A complete classification of such UPBs is suggested. We prove that for any pair of UPBs S and T the associated bound entangled states ρ S and ρ T cannot be converted to each other by LOCC, unless S and T coincide up to local unitaries. More specifically, there exists a finite precision ε (S,T) > 0 such that for any LOCC protocol mapping ρ S into a probabilistic ensemble (pα, ρα), the fidelity between ρ T and any possible final state ρα satisfies F(ρ T , ρα) = 1 - ε(S,T). PACS: 03.65.Bz; 03.67.-a; 89.70+c.

Semiquantum cryptography was proposed to deal with the issue that some players require only partial quantum power, such as preparing or measuring quantum states in the classical basis, which simplifies the implementations of quantum cryptography. However, the efficiency of the existing semiquantum cryptographic protocols was relatively low from a practical point of view. In this paper, we devise improved semiquantum key distribution (SQKD) protocols to improve the efficiency of SQKD protocols. Our improved SQKD protocols utilize the discarded X-SIFT bits in the previous SQKD protocols for improving the efficiency of previous SQKD protocols (Boyer et al. in Phys Rev Lett 99:140501, 2007; Zou et al. in Phys Rev A 79:052312, 2009). Besides, the efficiency of our new protocols can be made asymptotically close to 100% by letting players select their actions asymmetrically. We prove the information theoretical secure of the proposed SQKD protocols against the most general attacks. Our security proof is suitable for the single-state SQKD protocol (Zou et al. in Phys Rev A 79:052312, 2009).

We construct new stabilizer quantum error-correcting codes from generalized monomial-Cartesian codes. Our construction uses an explicitly defined twist vector, and we present formulas for the minimum distance and dimension. Generalized monomial-Cartesian codes arise from polynomials in m variables. When $$m=1$$ our codes are MDS, and when $$m=2$$ and our lower bound for the minimum distance is 3, the codes are at least Hermitian almost MDS. For an infinite family of parameters, when $$m=2$$ we prove that our codes beat the Gilbert–Varshamov bound. We also present many examples of our codes that are better than any known code in the literature.

In this paper, we introduce a remote state preparation protocol for the case of a known four-qubit entangled state in which there are two possible receivers and the sender has the option of choosing one of the two possible parties for a preparation of the intended state at the end of the chosen party. The sender begins with a measurement on a two-qubit system in which the measurement basis is chosen by using the known information of the state. After that she exercises her option which is exclusively her own prerogative. The protocol has four components depending on the four different measurement results of the sender. The scheme is compared in terms of efficiency with other contemporary remote state preparation protocols for similar purposes.