Quantum Information Processing

In this paper, we again discuss quantum search by partial adiabatic evolution, which was first proposed by Zhang et al. In contrast to previous conclusions, we show that partial adiabatic search does not improve the time complexity of a local adiabatic algorithm. Firstly, we show a variant of this algorithm and find that it is equivalent to the original partial adiabatic algorithm, in the sense of the same time complexity. But we give two alternate viewpoints on this “new” adiabatic algorithm—“global” adiabatic evolution and local adiabatic evolution approaches, respectively. Then, we discuss how global and local adiabatic quantum search can be recast in the framework of partial adiabatic search algorithm. It is found here that the former two algorithms could be considered as special cases of the later one when appropriately tuning the evolution interval of it. Also this implies the flexibility of quantum search based on partial adiabatic evolution.

Quantum secure multi-party summation is a specific primitive of classical secure multi-party computation. Compared with classical secure multi-party summation based on mathematical difficulty problems such as integer factorization and discrete logarithm which has been threatened by potential quantum computers, the quantum version can provide unconditional security for the computing tasks. A quantum protocol based on the entanglement swapping between d-level Bell state and d-level cat state is constructed to perform secure multi-party summation. With the aid of a semi-honest third party who does not conspire with any participant, the proposed protocol can calculate the non-modular sum of the secret integers held by the participants who do not trust each other. Not only can the protocol resist the attacks from both outside and semi-honest third party, but also resist participants’ attack, even though there are at most $$n-2$$ participants colluding together. (n is the number of participants.) This protocol only needs $$O(\log M)$$ (M is the maximum value of all secret integers) quantum resources to complete the computing task. Specially, under the condition of computing the sum of larger integers for a small number of participants, this protocol utilizes fewer quantum resources and has higher efficiency than other proposed protocols.

Quantum Key Recycling (QKR) is a quantum cryptographic primitive that allows one to reuse keys in an unconditionally secure way. By removing the need to repeatedly generate new keys, it improves communication efficiency. Škorić and de Vries recently proposed a QKR scheme based on 8-state encoding (four bases). It does not require quantum computers for encryption/decryption but only single-qubit operations. We provide a missing ingredient in the security analysis of this scheme in the case of noisy channels: accurate upper bounds on the required amount of privacy amplification. We determine optimal attacks against the message and against the key, for 8-state encoding as well as 4-state and 6-state conjugate coding. We provide results in terms of min-entropy loss as well as accessible (Shannon) information. We show that the Shannon entropy analysis for 8-state encoding reduces to the analysis of quantum key distribution, whereas 4-state and 6-state suffer from additional leaks that make them less effective. From the optimal attacks we compute the required amount of privacy amplification and hence the achievable communication rate (useful information per qubit) of qubit-based QKR. Overall, 8-state encoding yields the highest communication rates.

In this paper, several new protocols for the controlled remote state preparation (CRSP) by using the Brown state as the quantum channel are proposed. Firstly, we propose a CRSP protocol of an arbitrary two qubit state. Then, the CRSP protocol of an arbitrary three qubit state, which has rarely been considered by the previous papers, is investigated. The coefficients of the prepared states can be not only real, but also complex. To design these protocols, some useful and general measurement bases are constructed, which can greatly reduce the restrictions for the coefficients of the prepared states. The security analysis is provided in detail. Moreover, receiver’s all recovery operations are summarized into a concise formula.

Quantum correlation is a key component in various quantum information processing tasks. Decoherence process imposes limitations on achieving these quantum tasks. Therefore, understanding the behavior of quantum correlations in dissipative noisy systems is of paramount importance. Here, on the basis of the Gaussian Rényi-2 entropy, we analyze entanglement and quantum discord in a two-mode Gaussian state $$\rho _{AB}$$ . The mode A(B) is generated within the first (second) transition of a nondegenerate three-level cascade laser. Using realistic experimental parameters, we show that both entanglement and discord could be generated and enhanced by inducing more quantum coherence. Under thermal noise, entanglement is found more fragile having a tendency to disappear rapidly, while quantum discord exhibits a freezing behavior, where it can be captured within a wide range of temperature. Surprisingly, we find that entanglement can exceed quantum discord in contrary to the expectation based on the assumption that the former is only a part of the later. Finally, we show numerically as well as analytically that optimal quantum discord can be captured by performing Gaussian measurements on mode B. The obtained results suggest that nondegenerate three-level lasers may be a valuable resource for some quantum information tasks, especially for those who do not require entanglement.

We analyze two identical qubits interacting with a single-mode quantized radiation field, taking into account the influence of phase damping. The qubits are assumed to be initially in a superposition of the excited and the ground states, and the field is in a coherent state. The effects of the damping on the purity loss of the system and different bipartite partitions of the system [field-two qubits, qubit–(field + qubit)] through the tangles are considered. The effect of the damping on the entanglement of field qubits state is evaluated by the negativity. It is noted that the phenomenon of death and rebirth of the entanglement appears. With the increase in the phase parameter, this phenomenon disappears.

In spite of a long history, the quantification of entanglement still calls for exploration. What matters about entanglement depends on the situation, and so presumably do the numbers suitable for its quantification. Regardless of situational complications, a necessary first step is to make available for calculation some quantitative measure of entanglement. Here we define a geometric degree of entanglement, distinct from earlier definitions, but in the case of bipartite pure states related to that proposed by Shimony (Ann N Y Acad Sci 755:675–679, 1995). The definition offered here applies also to multipartite mixed states, and a variational method simplifies the calculation. We analyze especially states that are invariant under permutation of particles, states that we call bosonic. Of interest to quantum sensing, for bosonic states, we show that no partial trace can increase a degree of entanglement. For some sample cases we quantify the degree of entanglement surviving a partial trace. As a function of the degree of entanglement of a bosonic 3-qubit pure state, we show the range of degree of entanglement for the 2-qubit reduced density matrix obtained from it by a partial trace. Then we calculate an upper bound on the degree of entanglement of the mixed state obtained as a partial trace over one qubit of a 4-qubit bosonic state. As a reminder of the situational dependence of the advantage of entanglement, we review the way in which entanglement combines with scattering theory in the example of light-based radar.

Quantum annealing has the potential to find low energy solutions of NP-hard problems that can be expressed as quadratic unconstrained binary optimization problems. However, the hardware of the quantum annealer manufactured by D-Wave Systems, which we consider in this work, is sparsely connected and moderately sized (on the order of thousands of qubits), thus necessitating a minor-embedding of a logical problem onto the physical qubit hardware. The combination of relatively small hardware sizes and the necessity of a minor-embedding can mean that solving large optimization problems is not possible on current quantum annealers. In this research, we show that a hybrid approach combining parallel quantum annealing with graph decomposition allows one to solve larger optimization problem accurately. We apply the approach to the Maximum Clique problem on graphs with up to 120 nodes and 6395 edges.

We examine coherent processes in a two-state quantum system that is strongly coupled to a mesoscopic spin bath and weakly coupled to other environmental degrees of freedom. Our analysis is specifically aimed at understanding the quantum dynamics of solid-state quantum bits such as electron spins in semiconductor structures and superconducting islands. The role of mesoscopic degrees of freedom with long correlation times (local degrees of freedom such as nuclear spins and charge traps) in qubit-related dephasing is discussed in terms of a quasi-static bath. A mathematical framework simultaneously describing coupling to the slow mesoscopic bath and a Markovian environment is developed and the dephasing and decoherence properties of the total system are investigated. The model is applied to several specific examples with direct relevance to current experiments. Comparisons to experiments suggests that such quasi-static degrees of freedom play an important role in current qubit implementations. Several methods of mitigating the bath-induced error are considered.