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.     

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.

     

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.     

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.     

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.     

Correlation and Information in Quantum Channels

Quantum and classical correlations in quantum channels are investigated by means of an entangled pure state and a separable state which is closest to an entangled pure state. The coherent information and the separable information are used to estimate how much correlation is transmitted through a quantum channel. As the examples, the linear dissipative channel of qubits and the quantum erasure channel are considered.     

Weak Multiplicativity for Random Quantum Channels

It is known that random quantum channels exhibit significant violations of multiplicativity of maximum output p-norms for any p > 1. In this work, we show that a weaker variant of multiplicativity nevertheless holds for these channels. For any constant p > 1, given a random quantum channel ${\mathcal{N}}$ (i.e. a channel whose Stinespring representation corresponds to a random subspace S), we show that with high probability the maximum output p-norm of ${\mathcal{N}^{\otimes n}}$ decays exponentially with n. The proof is based on relaxing the maximum output ∞-norm of ${\mathcal{N}}$ to the operator norm of the partial transpose of the projector onto S, then calculating upper bounds on this quantity using ideas from random matrix theory.     

Revisiting Additivity Violation of Quantum Channels

We prove additivity violation of minimum output entropy of quantum channels by straightforward application of \({\epsilon}\) -net argument and Lévy’s lemma. The additivity conjecture was disproved initially by Hastings. Later, a proof via asymptotic geometric analysis was presented by Aubrun, Szarek and Werner, which uses Dudley’s bound on Gaussian process (or Dvoretzky’s theorem with Schechtman’s improvement). In this paper, we develop another proof along Dvoretzky’s theorem in Milman’s view, showing additivity violation in broader regimes than the existing proofs. Importantly,Dvoretzky’s theorem works well with norms to give strong statements, but these techniques can be extended to functions which have norm-like structures-positive homogeneity and triangle inequality. Then, a connection between Hastings’ method and ours is also discussed. In addition, we make some comments on relations between regularized minimum output entropy and classical capacity of quantum channels.     

Quantum Hall Quantized Cyclotron Entrance Channels

Quantum Hall plateaus are entered via quantized cyclotron (QC) cloud-chamber orbits that have Landau-level (LL) energies and uniquely-defined angular momenta. The conservation of angular momentum in the quantum Hall system requires both canonical and magnetic angular momentum components, which add together to form the invariant kinematic angular momentum. The only LL radial eigenfunctions that satisfy the conservation-law requirements of the QC to LL transition are the u _n,l eigenstates u _n,2n+1, where n = 0, 1, 2, .... These same eigenstates uniquely have the correct scaled sizes to tile the observed families of = 1/(2n + 1) Hall plateaus. Quantum Hall plateau formation is a direct consequence of this tiling.     

A Teleportation with Two Quantum Channels

Recently a quantum teleportation scheme has been analyzed by Wangner et al. (J. Opt. Soc. Am. B 27:A73–A80, 2010) which is based on spatially and temporarily resolved collective spontaneous emission. We study a similar model, which has the two atoms trapped in a resonant cavity instead of in the free vacuum space. It is found that the quantum channel experiences entanglement of sudden death (ESD), yet every time this channel can recover after an interval of time. Surprisingly, we demonstrate there exits another channel to assist the initial channel to complete the teleportation, and the fidelity can be well beyond the classical limit of 2/3, with the increase of dipole-dipole interaction.     

Quantum State Discrimination with Prior Knowledge in Noisy Quantum Channels

Discrimination between two states of a qubit is investigated, which is performed under the influence of noisy quantum channels. When prior knowledge about on the quantum states is available, the detection probability of quantum measurement is compared with that of pure guessing during the irreversible time evolution. In the case of a Markovian channel, the superiority of quantum measurement to pure guessing is lost at finite time which is determined by the prior probability and the fidelity of the quantum states. For a non-Markovian channel, however, it is possible to recover the superiority of quantum measurement even if it is lost. The effect of a system-environment initial correlation on the quantum state discrimination is also investigated.     

Quantum Tasks with Non-maximally Quantum Channels via Positive Operator-Valued Measurement

By using a proper positive operator-valued measure (POVM), we present two new schemes for probabilistic transmission with non-maximally four-particle cluster states. In the first scheme, we demonstrate that two non-maximally four-particle cluster states can be used to realize probabilistically sharing an unknown three-particle GHZ-type state within either distant agent’s place. In the second protocol, we demonstrate that a non-maximally four-particle cluster state can be used to teleport an arbitrary unknown multi-particle state in a probabilistic manner with appropriate unitary operations and POVM. Moreover the total success probability of these two schemes are also worked out.