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.

     

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.     

利用多光子相互作用实现量子信息传递

利用全量子理论,研究了多原子-腔场系统中多光子相互作用的过程,给出了不同情况下系统的一般演化式,发现利用此过程可实现量子纠缠信息的传递:只要控制腔场与原子相互作用的时间即原子以特定速度通过腔场时,处于基态的原子与存储纠缠信息的腔场相互作用的结果使原子获得量子纠缠信息;相反,纠缠原子中的量子纠缠信息也可传递给处于真空态的腔场;基态原子作为"飞行的量子比特"还可将量子纠缠信息从一个腔场传递到另一个腔场。该结论适应于讨论任意多个原子-腔场系统中任意多个光子相互作用的普遍情形。     

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.     

Quantum Capacity under Adversarial Quantum Noise: Arbitrarily Varying Quantum Channels

We investigate entanglement transmission over an unknown channel in the presence of a third party (called the adversary), which is enabled to choose the channel from a given set of memoryless but non-stationary channels without informing the legitimate sender and receiver about the particular choice that he made. This channel model is called an arbitrarily varying quantum channel (AVQC). We derive a quantum version of Ahlswede’s dichotomy for classical arbitrarily varying channels. This includes a regularized formula for the common randomness-assisted capacity for entanglement transmission of an AVQC. Quite surprisingly and in contrast to the classical analog of the problem involving the maximal and average error probability, we find that the capacity for entanglement transmission of an AVQC always equals its strong subspace transmission capacity. These results are accompanied by different notions of symmetrizability (zero-capacity conditions) as well as by conditions for an AVQC to have a capacity described by a single-letter formula. In the final part of the paper the capacity of the erasure-AVQC is computed and some light shed on the connection between AVQCs and zero-error capacities. Additionally, we show by entirely elementary and operational arguments motivated by the theory of AVQCs that the quantum, classical, and entanglement-assisted zero-error capacities of quantum channels are generically zero and are discontinuous at every positivity point.     

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.     

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.     

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.     

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.     

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.     

Remote Quantum Information Concentration Via Weak Cross-Kerr Nonlinearity

By utilizing the quantum parity-check detectors (PCDs) based on the weak cross-Kerr nonlinearities, we propose a scheme for realizing the remote quantum information concentration (RQIC) with the quantum channel of four-photon bound entangled state. After the PCDs and single-photon operations, quantum information initially distributed in three spatially separated photons is concentrated back to a single photon without performing any global operations. The success probability of the scheme is almost a unit. The necessary single-photon unitary operations corresponding to possible measurement outcomes are given detailedly.     

Quantum Key Agreement Via Non-maximally Entangled Cluster States

International Journal of Theoretical Physics - In this paper, we present a quantum key agreement (QKA) protocol with non-maximally entangled four-qubit cluster states. In our scheme, each...