International Journal of Quantum Information

An asymptotic analytical approach is proposed for bosonic probability amplitudes in unitary linear networks, such as the optical multiport devices for photons. The asymptotic approach applies for large number of bosons N ≫ M in the M-mode network, where M is finite. The probability amplitudes of N bosons unitarily transformed from the input modes to the output modes of a unitary network are approximated by a multidimensional integral with the integrand containing a large parameter (N) in the exponent. The integral representation allows an asymptotic estimate of bosonic probability amplitudes up to a multiplicative error of order 1/N by the saddle point method. The estimate depends on solution of the scaling problem for the M × M-dimensional unitary network matrix: to find the left and right diagonal matrices which scale the unitary matrix to a matrix which has specified row and column sums (equal, respectively, to the distributions of bosons in the input and output modes). The scaled matrices give the saddle points of the integral. For simple saddle points, an explicit formula giving the asymptotic estimate of bosonic probability amplitudes is derived. Performance of the approximation and the scaling of the relative error with N are studied for two-mode network (the beam splitter), where the saddle-points are roots of a quadratic and an exact analytical formula for the probability amplitudes is available, and for three-mode network (the tritter).

State steering and tracking have attracted a lot of interests due to their wide applications. In this paper, we present two concrete examples of trajectory tracking of an open quantum system with time-dependent Lindblad operator which has an eigenstate |ψ_s(t)〉 with eigenvalue 0. We work out the first case analytically while numerically the second case. From both the cases, we find that, if changing the Lindblad operator is sufficiently slow, then the system can follow the trajectory of |ψ_s(t)〉 very well.

The asymmetric CSS construction is extended to the Hermitian dual case. New infinite families of quantum symmetric and asymmetric codes are constructed. In particular, new quantum codes are obtained from binary BCH codes and MDS codes. These codes have known minimum distances and thus the relationship between the rate gain and minimum distance is given explicitly. The codes obtained are shown to have parameters better than those of previous codes. A number of known codes are special cases of the codes given here.

We show that the sudden change of quantum correlation can occur even when only one part of the composite entangled state is exposed to a noisy environment. Our results are illustrated through the action of different noisy environments individually on a single qubit of quantum system. Composite noise on the whole of the quantum system is thus not the necessarily condition for the occurrence of sudden transition for quantum correlation.

In this paper, we propose to directly detect Mott lobes, i.e. the order parameter 〈a〉, describing the Mott insulator (MI) to superfluid (SF) quantum phase transition of the Bose–Hubbard (BH) model. By weakly coupling the system to an environment in the SF phase, the U(1) symmetry breaking of the system is simulated, and the order parameter can be read from the AC Josephson current between the system and the environment. The relation between the order parameter and the Josephson current is obtained from both the mean-field theory approach and an exact numerical simulation of a finite-size example. Our numerical simulations show that the profile of the order parameter read from the Josephson current is different from it predicted by the mean-field theory, but similar to it in a system whose U(1) symmetry is broken by a weak field proportional to a + a^†. This proposal is feasible in optical lattices.

A dipolar coupled spin system can achieve internal thermodynamic equilibrium states at negative absolute temperature. We study analytically and numerically the temperature dependence of the concurrence in a dipolar coupled spin-1/2 system in both nonzero and zero fields and show that, at negative temperatures, entangled states can exist even in zero magnetic field.

A large payload bidirectional quantum secure direct communication (BQSDC) protocol without information leakage is proposed, which is based on entanglement swapping between any two Greenberger–Horne–Zeilinger (GHZ) states. Two remote authorized parties, Alice and Bob, can safely exchange their individual secret messages without worrying about the information leakage problem. Our protocol uses a shared secret GHZ state to overcome the information leakage problem. The shared secret GHZ state plays two roles in the bidirectional communication process: on one hand, it lets Bob know the prepared initial state; on the other hand, it is used for encoding Bob's secret messages. Moreover, our protocol can transmit six bits of secret messages per round communication. Compared with those previous BQSDC protocols, the advantage of our protocol lies in having the following two characters simultaneously: on one hand, it overcomes the information leakage problem; one the other hand, its capacity is as high as six bits per round communication.

Semi-quantum secret sharings (SQSSs), as they are of now, require all the agents choose to measure the received qubits to produce the shared secret key. As a result, to share an n-bit secret key in an (m + 1)-party SQSS, the number of quanta required to transmit is n × 2^m, which increases exponentially with the number of agents (i.e. m). This study proposes a new idea on the construction of the secret key for the existing SQSS such that only 2nm qubits are required to produce an n-bit secret key in the (m + 1)-party SQSS.

A unit evolution step of discrete-time quantum walks (QWs) is determined by both a coin-flip operator and a position-shift operator. The behavior of quantum walkers after many steps delicately depends on the coin-flip operator and an initial condition of the walk. To get the behavior, a lot of long-time limit distributions for the QWs starting with a localized initial state have been derived. In this paper, we compute limit distributions of a 2-state QW with a delocalized initial state, not a localized initial state, and discuss how the walker depends on the coin-flip operator. The initial state induced from the Fourier series expansion, which is called the (α, β) delocalized initial state in this paper, provides different limit density functions from the ones of the quantum walk with a localized initial state.