Geometric phase induced by quantum nonlocality

By analyzing an instructive example, for testing many concepts and approaches in quantum mechanics, of a one-dimensional quantum problem with moving infinite square-well, we define geometric phase of the physical system. We find that there exist three dynamical phases from the energy, the momentum and local change in spatial boundary condition respectively, which is different from the conventional computation of geometric phase. The results show that the geometric phase can fully describe the nonlocal character of quantum behavior.     

Investigation of continuous-time quantum walk via spectral distribution associated with adjacency matrix

Using the spectral distribution associated with the adjacency matrix of graphs, we introduce a new method of calculation of amplitudes of continuous-time quantum walk on some rather important graphs, such as line, cycle graph C_n, complete graph K_n, graph G_n, finite path and some other finite and infinite graphs, where all are connected with orthogonal polynomials such as Hermite, Laguerre, Tchebichef, and other orthogonal polynomials. It is shown that using the spectral distribution, one can obtain the infinite time asymptotic behavior of amplitudes simply by using the method of stationary phase approximation (WKB approximation), where as an example, the method is applied to star, two-dimensional comb lattices, infinite Hermite and Laguerre graphs. Also by using the Gauss quadrature formula one can approximate the infinite graphs with finite ones and vice versa, in order to derive large time asymptotic behavior by WKB method. Likewise, using this method, some new graphs are introduced, where their amplitudes are proportional to the product of amplitudes of some elementary graphs, even though the graphs themselves are not the same as the Cartesian product of their elementary graphs. Finally, by calculating the mean end to end distance of some infinite graphs at large enough times, it is shown that continuous-time quantum walk at different infinite graphs belong to different universality classes which are also different from those of the corresponding classical ones.     

Spin bath decoherence of quantum entanglement

We study an analytically solvable model for decoherence of a two spin system embedded in a large spin environment. As a measure of entanglement, we evaluate the concurrence for the Bell states (Einstein-Podolsky-Rosen pairs). We find that while for two separate spin baths all four Bell states lose their coherence with the same time dependence, for a common spin bath, two of the states decay faster than the others. We explain this difference by the relative orientation of the individual spins in the pair. We also examine how the Bell inequality is violated in the coherent regime. Both for one bath and two bath cases, we find that while two of the Bell states always obey the inequality, the other two violate the inequality at early times.     

The effect and control on remaining the quantum correlation by the coupling symmetry between qubits and the bath

We study the dynamic evolution of quantum correlation of two interacting coupled qubits system in non-Markov environment, and quantify the quantum correlation using concurrence and quantum discord. We find that although both of them are physical quantities which measure the system characteristics of the quantum correlations, the quantum discord is more robust than concurrence, since it can keep a positive value even when the ESD happens. The quantum correlation of quantum system not only depends on the initial state but also strongly depends on the coupling ways between qubits and environment. For the given initial state, by keeping the coupling between qubits and environment in completely symmetric, we can completely avoid the effect the decoherence influenced on the quantum correlation and effectively prolong the survival time of quantum discord and concurrence. We also find that the stronger the interaction between qubits is, the more conducive the death of the quantum correlation is resisted.     

Controlled quantum secure direct communication using a non-symmetric quantum channel with quantum superdense coding

We present a controlled quantum secure direct communication protocol that uses a 2-dimensional Greenberger–Horne–Zeilinger (GHZ) entangled state and a 3-dimensional Bell-basis state and employs the high-dimensional quantum superdense coding, local collective unitary operations and entanglement swapping. The proposed protocol is secure and of high source capacity. It can effectively protect the communication against a destroying-travel-qubit-type attack. With this protocol, the information transmission is greatly increased. This protocol can also be modified, so that it can be used in a multi-party control system.     

Eavesdropping on secure quantum telephone protocol with dishonest server

The crucial issue of quantum communication protocol is its security. In this paper, we show that in secure quantum telephone protocol proposed by Wen et al. [X. Wen et al., Opt. Commun. 275 (2007) 278-282] the dishonest server can obtain full information of the communication with zero risk of being detected.     

Secure quantum sealed-bid auction

A new experimentally feasible and secure quantum sealed-bid auction protocol using quantum secure direct communication based on GHZ states is proposed. In this scheme all bidders Bob, Charlie, … , and Zach use M groups n-particle GHZ states to represent their bids. Here, an auctioneer gives the auction outcome by performing a sequence of n-particle GHZ-basis measurements on the final quantum states. It has been shown that using this method guarantees the honesty of the protocol, and malicious bidders can not collude with the auctioneers.     

Newton-Leibniz integration for ket-bra operators in quantum mechanics and derivation of entangled state representations

Newton-Leibniz integration rule only applies to commuting functions of continuum variables, while operators made of Dirac’s symbols (ket versus bra, e.g., |q〉〈q| of continuous parameter q) in quantum mechanics are usually not commutative. Therefore, integrations over the operators of type |〉〈| cannot be directly performed by Newton-Leibniz rule. We invented an innovative technique of integration within an ordered product (IWOP) of operators that made the integration of non-commutative operators possible. The IWOP technique thus bridges this mathematical gap between classical mechanics and quantum mechanics, and further reveals the beauty and elegance of Dirac’s symbolic method and transformation theory. Various applications of the IWOP technique, including constructing the entangled state representations and their applications, are presented.     

Monogamy and entanglement in tripartite quantum states

We present an interesting monogamy equation for (2⊗2⊗n)-dimensional pure states, by which a quantity is found to characterize the tripartite entanglement with the GHZ type and W type entanglements as a whole. In particular, we, for the first time, reveals that for any quantum state of a pair of qubits, the difference between the two remarkable entanglement measures, concurrence and negativity, characterizes the W type entanglement of tripartite pure states with the two-qubit state as reduced density.     

Bidirectional quantum secure communication based on a shared private Bell state

We propose a secure bidirectional quantum communication protocol, which is based on a shared private quantum entangled channel, the highlight of our protocol is that the drawback “information leakage” is eliminated. Our protocol is similar but more efficient than a bidirectional quantum communication based on QKD & OTP (One-time pad).     

Large-capability quantum key distribution with entangled qutrits

A secure quantum key distribution protocol is proposed to distribute the three-dimensional secret message in a two-way quantum channel based on the entanglement of two-qutrit quantum system. The present protocol has an advantage over transmitting directly the secret message with large capacity since the distributed message has been imposed on nonorthogonal two-qutrit-entangled states by the sender using the superdense coding via local unitary operations. The security is ensured by the entanglement of the two-qutrit quantum system and the secure transmission of the traveling-particle sequence in the lossless and noiseless channel.     

Disentanglement of atom-photon via quantum interference in driven three-level atoms

In this paper, the effect of quantum interference on the entanglement of a driven V-type three-level atom and its spontaneous emission field was investigated by using the quantum entropy. The results indicate that, in the absence of quantum interference the atom and its spontaneous emission field are always entangled at the steady-state. But, in the presence of full quantum interference their steady-state entanglement depends on the atomic parameters. Specifically, with appropriate atomic parameters they can be entangled or disentangled at the steady-state. We realized that the steady-state entanglement is due to completely destructive nature of quantum interference. On the contrary, the steady-state disentanglement is due to instructive nature of quantum interference.     

Comment on “Multiparty secret sharing of quantum information via cavity QED”

In a recent paper [Z.J. Zhang, Opt. Commun. 261 (2006) 199], a scheme on secret sharing of quantum information in cavity QED has been discussed. The author claims that he has improved the success probability of teleportation from 6.25% in our original paper [Y.Q. Zhang, X.R. Jin, S. Zhang, Phys. Lett. A 341 (2005) 380] to 100%. However, in this comment, we show that it is not the case and the author has mistakenly understood our original paper [Y.Q. Zhang, X.R. Jin, S. Zhang, Phys. Lett. A 341 (2005) 380].     

Measurement-induced nonlocality and geometric quantum discord in two SC-charge qubits

By using geometric quantum discord and measurement-induced nonlocality, quantum correlations are investigated for two superconducting (SC) charge qubits that share a large Josephson junction where the field is assumed to be prepared initially in a coherent state. It is found that the difference between measure measurement-induced nonlocality and geometric quantum discord, of the final state of the two SC-charge qubits system which is especial case of X-states, is equal to a constant value. It is found that the quantum correlations and entanglement of the qubits are very sensitive to the mean number of the coherent photons. The entanglement exists in small intervals of death quantum discord and measurement-induced nonlocality. This is further evidence in support of the fact that quantum correlation and entanglement are not synonymous.     

Continuous-time quantum walks on Erdös-Rényi networks

We study the coherent exciton transport of continuous-time quantum walks (CTQWs) on Erdös-Rényi networks. We numerically investigate the transition probability between two nodes of the networks, and compare the classical and quantum transport efficiency on networks of different connectivity. In the long time limiting, we find that there is a high probability to find the exciton at the initial node. We also study how the network parameters affect such high return probability.     

Persistence of quantum information

We study the flip-processes in a two-level system, which is triggered by the coupling to a classical bath. When the bath is represented by a stochastic field, the time evolution of the density matrix leads to a stochastic equation with a multiplicative noise. Accordingly the Fokker–Planck-equation (FPE) depends on the matrix elements of the underlying density operator. The solution of the FPE can be parametrized in terms of an inherent conserved quantity α, which is interpreted as a measure for the persistence of quantum information. We show that the FPE exhibits a single unique steady state solution different from Boltzmann's law. The exactly computable discrete spectrum of the relaxation times is characterized by two quantum numbers and the ratio of Planck's constant and the coupling strength to the bath. The total entropy is analyzed as function of the quantum number α  . In case of α=1$\alpha =1$ the system is in a pure state whereas for α≠1$\alpha \ne 1$ a mixed state is realized. In case of two, two-level systems, immersed in the common bath, the two noninteracting two-level systems become mutually entangled. The annealed entropy is in that case non-extensive.     

Improving the total efficiency of quantum key distribution by comparing Bell states

A protocol for quantum key distribution by comparing Bell states [G. Gao, Opt. Commun. 281 (2008) 876] is recently proposed by Gan Gao. Gan Gao claimed that his protocol has the advantage of high total efficiency and its total efficiency is 50%. In this paper, by giving a little modification to the original one, we introduce an improved version of Gao’s protocol, which can make the total efficiency of the communication come up to 100%.     

Secure quantum telephone

A quantum telephone protocol including the dialing process and the talking one is proposed. In the dialing process, with their respective secret keys, the legitimate communicators Alice and Bob can pass the authentication by Charlie acting as a telephone company. In the talking process, Charlie provides the authenticated Alice and Bob with a quantum channel sequence, on which Alice and Bob can communicate with each other directly and privately by virtue of some encoding operations. Different from the insecure classical telephone having been used in our lives, the proposed quantum telephone protocol has asymptotically security and the communicators cannot disavow having used the quantum channels.     

Remote preparation of the N-particle GHZ state using quantum statistics

We present a remote preparation of the N-particle GHZ state protocol in which only the effects of quantum statistics of indistinguishable particles are used. The N-particle GHZ state can be successfully prepared in the limit of N → ∞.     

Macroscopic entanglement on a hybrid quantum circuit

A scheme is proposed to deterministically create maximal entanglement between hybrid artificial atoms: superconducting charge and flux qubits. By tuning the circuit, the two qubits are dynamically decoupled and entanglement can be long-lived. This provides a new version of the Einstein-Podolsdy-Rosen (EPR) situation where the components of a macroscopic EPR pair are in opposite regimes.