Classical Capacity of Quantum Channels with General Markovian Correlated Noise

The classical capacity of a quantum channel with arbitrary Markovian correlated noise is evaluated. For the general case of a channel with long-term memory, which corresponds to a Markov chain which does not converge to equilibrium, the capacity is expressed in terms of the communicating classes of the Markov chain. For an irreducible and aperiodic Markov chain, the channel is forgetful, and one retrieves the known expression (Kretschmann and Werner in Phys. Rev. A 72:062323, 2005) for the capacity.     

Quantum Network Coding on Networks with Arbitrarily Distributed Hidden Channels

Although perfect quantum network coding has been proved to be achievable,it is still puzzling whether it is feasible whenever one or more of the channels are replaced by the hidden ones emerging from quantum entanglement.The question is answered in this paper.First,we propose a quantum network coding protocol over a butterfly network with two hidden channels.Second,we investigate a more general situation,where d-level quantum letters are transmitted through the network containing arbitrarily distributed hidden channels,and prove that quantum network coding on such networks is still achievable.     

Quantum Network Coding on Networks with Arbitrarily Distributed Hidden Channels

Although perfect quantum network coding has been proved to be achievable, it is still puzzling whether it is feasible whenever one or more of the channels are replaced by the hidden ones emerging from quantum entanglement. The question is answered in this paper. First, we propose a quantum network coding protocol over a butterfly network with two hidden channels. Second, we investigate a more general situation, where d-level quantum letters are transmitted through the network containing arbitrarily distributed hidden channels, and prove that quantum network coding on such networks is still achievable.     

一般泡利信道量子容量的逼近

量子编码定理证明信道在没有辅助资源的情况下其量子容量等于规整化相干信息的最大值。一般泡利信道是最普遍使用的信道模型,其量子容量目前无法准确计算,只能用多信道相干信息去逼近。本文应用量子图态级联编码,得到一般泡利信道在该编码输入下的多信道相干信息的公式,能够有效计算一般泡利信道量子容量的逼近值和信道传输量子信息的噪声容限。计算速度比Monte Carlo算法提高三个数量级。     

量子热噪声信道在纠缠辅助下的容量

研究了量子纠缠辅助下输入功率受限时的单模热辐射噪声信道传输经典信息的容量问题，和带有放大或衰减的单模热噪声信道的相应问题。对热噪声信道，表明了容量在输入信号为热噪声信号时达到，压缩态无助于达到信道容量CE；对带有放大或衰减的单模热噪声信道，说明了容量同样在输入为热噪声态时达到。     

Dividing Quantum Channels

We investigate the possibility of dividing quantum channels into concatenations of other channels, thereby studying the semigroup structure of the set of completely-positive trace-preserving maps. We show the existence of ‘indivisible’ channels which can not be written as non-trivial products of other channels and study the set of ‘infinitesimal divisible’ channels which are elements of continuous completely positive evolutions. For qubit channels we obtain a complete characterization of the sets of indivisible and infinitesimal divisible channels. Moreover, we identify those channels which are solutions of time-dependent master equations for both positive and completely positive evolutions. For arbitrary finite dimension we prove a representation theorem for elements of continuous completely positive evolutions based on new results on determinants of quantum channels and Markovian approximations.     

Quantum Coherence in Non-Markovian Quantum Channels

We numerically simulate quantum coherence in a system of two qubits interacting with a reservoir for non-Markovian channels. The explicit form of the master equation is taken in terms of density-operator elements and is solved according to the initial conditions. In particular, we consider the effect of an Ohmic reservoir (OR) with Lorentz–Drude regularization (LDR) on the extent of coherence during dynamics. We describe the dynamical behavior of the coherence for low, intermediate, and high-temperature reservoirs. We explain the effect of the ratio of the cutoff frequency (CF) to the quantum system frequency and the effect of temperature on the quantum coherence. We show that a decreasing ratio enhances coherence, while an increasing temperature decreases it.

     

Dynamics of Quantum Coherence in Bell-Diagonal States under Markovian Channels

We study the curves of coherence for the Bell-diagonal states including l_1-norm of coherence and relative entropy of coherence under the Markovian channels in the first subsystem once. For a special Bell-diagonal state under bit-phase flip channel, we find frozen coherence under l_1 norm occurs, but relative entropy of coherence decrease. It illustrates that the occurrence of frozen coherence depends on the type of the measure of coherence. Also, we study the coherence evolution of Bell-diagonal states under Markovian channels in the first subsystem n times and find that coherence under depolarizing channel decreases initially then increases for small n and tends to zero for large n. The dynamics of coherence of the Bell-diagonal state under two independent same type local Markovian channels is discussed.     

Capacity of Multivariate Channels with Multiplicative Noise: Random Matrix Techniques and Large-N Expansions (2)

We study memoryless, discrete time, matrix channels with additive white Gaussian noise and input power constraints of the form Y i = ∑ _j H _ij X _j + Z _i , where Y _i , X _j and Z _i are complex, i = 1… m, j = 1… n, and H is a complex m× n matrix with some degree of randomness in its entries. The additive Gaussian noise vector is assumed to have uncorrelated entries. Let H be a full matrix (non-sparse) with pairwise correlations between matrix entries of the form E[H ik H ^* jl] = 1/n C ij D kl, where C, D are positive definite Hermitian matrices. Simplicities arise in the limit of large matrix sizes (the so called large-n limit) which allow us to obtain several exact expressions relating to the channel capacity. We study the probability distribution of the quantity f(H) = log (1+PH ^† SH) . S is non-negative definite and hermitian, with TrS = n and P being the signal power per input channel. Note that the expectation E[f(H)], maximised over S, gives the capacity of the above channel with an input power constraint in the case H is known at the receiver but not at the transmitter. For arbitrary C, D exact expressions are obtained for the expectation and variance of f(H) in the large matrix size limit. For C = D = I, where I is the identity matrix, expressions are in addition obtained for the full moment generating function for arbitrary (finite) matrix size in the large signal to noise limit. Finally, we obtain the channel capacity where the channel matrix is partly known and partly unknown and of the form α; I+ β H, α,β being known constants and entries of H i.i.d. Gaussian with variance 1/n. Channels of the form described above are of interest for wireless transmission with multiple antennae and receivers.     

Dequantization Via Quantum Channels

For a unital completely positive map \({\Phi}\) (“quantum channel”) governing the time propagation of a quantum system, the Stinespring representation gives an enlarged system evolving unitarily. We argue that the Stinespring representations of each power \({\Phi^m}\) of the single map together encode the structure of the original quantum channel and provide an interaction-dependent model for the bath. The same bath model gives a “classical limit” at infinite time \({m\to\infty}\) in the form of a noncommutative “manifold” determined by the channel. In this way, a simplified analysis of the system can be performed by making the large-m approximation. These constructions are based on a noncommutative generalization of Berezin quantization. The latter is shown to involve very fundamental aspects of quantum-information theory, which are thereby put in a completely new light.     

Quantum Correlations Evolution Asymmetry in Quantum Channels

It was demonstrated that the entanglement evolution of a specially designed quantum state in the bistochastic channel is asymmetric. In this work, we generalize the study of the quantum correlations, including entanglement and quantum discord, evolution asymmetry to various quantum channels. We found that the asymmetry of entanglement and quantum discord only occurs in some special quantum channels, and the behavior of the entanglement evolution may be quite different from the behavior of the quantum discord evolution. To quantum entanglement, in some channels it decreases monotonously with the increase of the quantum channel intensity. In some other channels, when we increase the intensity of the quantum channel, it decreases at first, then keeps zero for some time, and then rises up. To quantum discord, the evolution becomes more complex and you may find that it evolutes unsmoothly at some points. These results illustrate the strong dependence of the quantum correlations evolution on the property of the quantum channels.     

量子噪音与量子Langevin方程

介绍了量子噪音和量子Langevin方程 ,并与经典噪音和经典Langevin方程进行了比较 .量子噪音来源于两种途径 ,第一种与经典噪音相似 ,第二种则起源于Heisengberg测不准原理 .同时 ,也简略给出了量子Langevin方程的推导.The properties of quantum noise and Langevin equation are discussed. Comparisons between the quantum noise and Langevin eqution and the classic one are presented. A brief derivation for quantum Langevin equation is showed. The quantum noise comes from two ways, namely, the way as same as that of classic noise and the Heisenberg uncertainty.     

Protecting Quantum Fisher Information in Correlated Quantum Channels

Quantum Fisher information (QFI) has potential applications in quantum metrology tasks. QFI is investigated when the consecutive actions of a quantum channel on the sequence of qubits have partial classical correlations. The results showed that while the decoherence effect is detrimental to QFI, effects of such classical correlations on QFI are channel-dependent. For the Bell-type probe states, the classical correlations on consecutive actions of the depolarizing and phase flip channels can be harnessed to improve QFI, while the classical correlations in the bit flip and bit-phase flip channels induce a slight decrease of QFI. For a more general parameterization form of the probe states, the advantage of using the initial correlated system on improving QFI can also remain in a wide regime of the correlated quantum channels.     

Relating Entropies of Quantum Channels

In this work, we study two different approaches to defining the entropy of a quantum channel. One of these is based on the von Neumann entropy of the corresponding Choi–Jamiołkowski state. The second one is based on the relative entropy of the output of the extended channel relative to the output of the extended completely depolarizing channel. This entropy then needs to be optimized over all possible input states. Our results first show that the former entropy provides an upper bound on the latter. Next, we show that for unital qubit channels, this bound is saturated. Finally, we conjecture and provide numerical intuitions that the bound can also be saturated for random channels as their dimension tends to infinity.     

Multipartite Quantum Clock Synchronization under The Influence of Unruh Thermal Noise

A protocol for multipartite quantum clock synchronization is performed under the influence of Unruh thermal noise. The dynamics of multipartite quantum system consisting of Unruh–DeWitt detectors when one of the detectors is accelerated are obtained. To estimate the time difference between the clocks, the time probability is calculated and how the probability is influenced by the Unruh thermal noise and other factors is analyzed. It is shown that both relativistic motion and interaction between the atom and the external scalar field affect the choice of optimal number of excited atoms in the initial state, which leads to a higher clock adjustment accuracy. Time probabilities for different types of initial states approach the same value in the limit of infinite acceleration, while tend to different minimums with increasing number of atoms. In addition, the accuracy of clock synchronization using a pair of entangled clocks in two‐party system is always higher than in a multipartite system, while the optimal Z‐type multipartite initial state always performs better than the W‐type state.