Entanglement evolution in multipartite cavity-reservoir systems under local unitary operations

We analyze the entanglement evolution of two cavity photons being affected by the dissipation of two individual reservoirs. Under an arbitrary local unitary operation on the initial state, it is shown that there is only one parameter which changes the entanglement dynamics. For the bipartite subsystems, we show that the entanglement of the cavity photons is correlated with that of the reservoirs, although the local operation can delay the time at which the photon entanglement disappears and advance the time at which the reservoir entanglement appears. Furthermore, via a new defined four-qubit entanglement measure and two three-qubit entanglement measures, we study the multipartite entanglement evolution in the composite system, which allows us to analyze quantitatively both bipartite and multipartite entanglement within a unified framework. In addition, we also discuss the entanglement evolution with an arbitrary initial state.     

Local distinguishability of multipartite unitary operations

We show that any two different unitary operations acting on an arbitrary multipartite quantum system can be perfectly distinguished by local operations and classical communication when a finite number of runs is allowed. Intuitively, this result indicates that the lost identity of a nonlocal unitary operation can be recovered locally. No entanglement between distant parties is required.     

Optimal conversion of nonlocal unitary operations

We study when a nonlocal unitary operation acting on two d-level systems can probabilistically simulate another one when arbitrary local operations and classical communication are allowed. We provide necessary and sufficient conditions for the simulation to be possible. Probabilistic interconvertability is used to define an equivalence relation between gates. We show that this relation induces a finite number of classes that we identify. In the case of two qubits, two classes of nonlocal operations exist. We show how the representatives of these classes, CNOT and SWAP, can be deterministically converted into any operation of its class and calculate the optimal probability of the reverse process.     

Non-Markovian random unitary qubit dynamics

We compare two approaches to non-Markovian quantum evolution: one based on the concept of divisible maps and the other one based on distinguishability of quantum states. The former concept is fully characterized in terms of local generator whereas it is in general not true for the latter one. A simple example of random unitary dynamics of a qubit shows the intricate difference between those approaches. Moreover, in this case both approaches are fully characterized in terms of local decoherence rates.     

Local discrimination scheme for some unitary operations

It has been shown that for two different multipartite unitary operations U_1 and U_2, when tr(U_1~?U_2) = 0, they can always be perfectly distinguished by local operations and classical communication in the single-run scenario. However, how to find the detailed scheme to complete the local discrimination is still a fascinating problem. In this paper, aiming at some U_1 and U_2 acting on the bipartite and tripartite space respectively, especially for U_1~?U_2 locally unitary equivalent to the high dimensional X-type hermitian unitary matrix V with trV = 0, we put forward the explicit local distinguishing schemes in the single-run scenario.     

Multiple multicontrol unitary operations: Implementation and applications

The efficient implementation of computational tasks is critical to quantum computations. In quantum circuits, multicontrol unitary operations are important components. Here, we present an extremely efficient and direct approach to multiple multicontrol unitary operations without decomposition to CNOT and single-photon gates. With the proposed approach, the necessary two-photon operations could be reduced from O(n³) with the traditional decomposition approach to O(n), which will greatly relax the requirements and make large-scale quantum computation feasible. Moreover, we propose the potential application to the (n-k)-uniform hypergraph state.     

Asymptotic solutions of continuous-time random walks

The continuous-time random walk of Montroll and Weiss has a complete separation of time (how long a walker will remain at a site) and space (how far a walker will jump when it leaves a site). The time part is completely described by a pausing time distribution(t). This paper relates the asymptotic time behavior of the probability of being at sitel at timet to the asymptotic behavior of(t). Two classes of behavior are discussed in detail. The first is the familiar Gaussian diffusion packet which occurs, in general, when at least the first two moments of(t) exist; the other occurs when(t) falls off so slowly that all of its moments are infinite. Other types of possible behavior are mentioned. The relationship of this work to solutions of a generalized master equation and to transient photocurrents in certain amorphous semiconductors and organic materials is discussed.This work was partially supported by NSF Grant No. 28501.     

Asymptotic behaviour of the unitary representations of the Poincaré group

The results of R. Jost and K. Hepp [2] and D. Maison [3] concerning the asymptotic behaviour of the translation operators are generalized.     

Entanglement is not necessary for perfect discrimination between unitary operations

We show that a unitary operation (quantum circuit) secretly chosen from a finite set of unitary operations can be determined with certainty by sequentially applying only a finite amount of runs of the unknown circuit. No entanglement or joint quantum operations are required in our scheme. We further show that our scheme is optimal in the sense that the number of the runs is minimal when discriminating only two unitary operations.     

Asymptotic properties of a simple random motion

A random walker in ^N is considered. At each step the walker picks a point in ^N from a fixed finite set of destination points. Having chosen the point, the walker moves a fractionr (r<1) of the distance toward the point along a straight line. Assuming that the successive destination points are chosen independently, it is shown that the asymptotic distribution of the walker's position has the same mean as the destination point distribution. An estimate is obtained for the fraction of time the walker stays within a ball centered at the mean value for almost every destination sequence. Examples show that the asymptotic distribution could have intricate structure.     

Embedding dissipation and decoherence in unitary evolution schemes

Dissipation and decoherence, and the evolution from pure to mixed states in quantum physics, are handled through master equations for the density matrix. By embedding elements of this matrix in a higher-dimensional Liouville-Bloch equation, the methods of unitary integration are adapted to solve for the density matrix as a function of time, including the nonunitary effects of dissipation and decoherence. The input requires only solutions of classical, initial value time-dependent equations. Results are illustrated for a damped, driven two-level system.     

Asymptotic regime in N random interacting species

The asymptotic regime of a complex ecosystem with N random interacting species and in the presence of an external multiplicative noise is analyzed. We find the role of the external noise on the long time probability distribution of the ith density species, the extinction of species and the local field acting on the ith population. We analyze in detail the transient dynamics of this field and the cavity field, which is the field acting on the ith species when this is absent. We find that the presence or the absence of some population give different asymptotic distributions of these fields.     

Evolution of 3D degrees of polarization with random unitary transformations

The irreversible behavior of polarization properties that appears when random unitary transformations are applied to three-dimensional (3D) random optical fields is investigated. The ability of 3D degrees of polarization not to increase and to evolve independently of each other with such transformations is analyzed.     

Asymptotic results on occupancy times of random walks

In this note we derive, using Wald's theorem asymptotic results on mean occupancy time of an interval for random walks with arbitrary transition probabilities. We show that our results are consistent with those obtained (by Weiss, Ref. 2) via the master equation approach, by demonstrating that the resulting infinite series can be summed exactly.     

Asymptotic evolution of weakly collisional Vlasov-Poisson plasmas

We study the role of (weak) numerical diffusion on the long time evolution of the Vlasov-Poisson plasma. We consider the classical problem of phase space vortex formation by particle trapping. We show that the asymptotic macroscopic state is not independent of diffusion even if the dissipative length scale is much shorter than any characteristic physical length scale of the system.     

Gaussian ensembles of random hermitian matrices intermediate between orthogonal and unitary ones

Communications in Mathematical Physics - A Gaussian ensemble of Hermitian matrices depending on a parameter α is considered. When α=0, the ensemble is Gaussian Orthogonal, and when...