Controlling the loss of quantum correlations via quantum memory channels

Quantum Information Processing - We consider the support of the limit distribution of the Grover walk on crystal lattices with the linear scaling. The orbit of the Grover walk is denoted by the...     

Quantum coherence of two-qubit over quantum channels with memory

Using the axiomatic definition of the quantum coherence measure, such as the \(l_{1}\) norm and the relative entropy, we study the phenomena of two-qubit system quantum coherence through quantum channels where successive uses of the channels are memory. Different types of noisy channels with memory, such as amplitude damping, phase damping, and depolarizing channels effect on quantum coherence have been discussed in detail. The results show that quantum channels with memory can efficiently protect coherence from noisy channels. Particularly, as channels with perfect memory, quantum coherence is unaffected by the phase damping as well as depolarizing channels. Besides, we also investigate the cohering and decohering power of quantum channels with memory.     

Building with quantum correlations

‘Correlations without correlata’ is an influential way of thinking of quantum entanglement as a form primitive correlation which nonetheless maintains locality of quantum theory. A number of arguments have sought to suggest that such a view leads either to internal inconsistency or to conflict with the empirical predictions of quantum mechanics. Here we explicate and provide a partial defence of the notion, arguing that these objections import unwarranted conceptions of correlation properties as hidden variables. A more plausible account sees the properties in terms of Everettian relative states. The ontological robustness of entanglement is also defended from recent objections.     

Entanglement assisted classical capacity of a class of quantum channels with long-term memory

In this paper we evaluate the entanglement assisted classical capacity of a class of quantum channels with long-term memory, which are convex combinations of memoryless channels. The memory of such channels can be considered to be given by a Markov chain which is aperiodic but not irreducible. This class of channels was introduced by Datta and Dorlas in (J. Phys. A, Math. Theor. 40:8147–8164, 2007), where its product state capacity was evaluated.      

Geometry of quantum state space and quantum correlations

Quantum state space is endowed with a metric structure, and Riemannian monotone metric is an important geometric entity defined on such a metric space. Riemannian monotone metrics are very useful for information-theoretic and statistical considerations on the quantum state space. In this article, considering the quantum state space being spanned by \(2\times 2\) density matrices, we determine a particular Riemannian metric for a state \(\rho \) and show that if \(\rho \) gets entangled with another quantum state, the negativity of the generated entangled state is, upto a constant factor, equal to square root of that particular Riemannian metric . Our result clearly relates a geometric quantity to a measure of entanglement. Moreover, the result establishes the possibility of understanding quantum correlations through geometric approach.     

Quantifying channels output similarity with applications to quantum control

In this work, we aim at quantifying quantum channel output similarity. In order to achieve this, we introduce the notion of quantum channel superfidelity, which gives us an upper bound on the quantum channel fidelity. This quantity is expressed in a clear form using the Kraus representation of a quantum channel. As examples, we show potential applications of this quantity in the quantum control field.     

Real-time system with homogeneous servers and nonidentical channels in steady-state

A real-time multiserver system with homogeneous servers (such as unmanned air vehicles or machine controllers) and several nonidentical channels (such as surveillance regions or assembly lines) working under maximum load regime is studied. We show how to compute steady-state probabilities of such a system, when both maintenance and service times are exponentially distributed. We also compute various important performance parameters, including system availability and loss penalty function.Scope and purposeReal-time systems are responsible for operations management of increasingly sensitive applications, particularly those in which failures to satisfy timing constraints can lead to serious or even catastrophic consequences. In these systems, a job is processed immediately upon arrival (conditional on system availability) without delay. That part of the job which is not executed immediately is lost and cannot be served later. It has become more important to use the analytical methodologies to ensure that the designs and implementations of time-dependent systems are verifiably correct and predictable. This paper shows how to use the methods of stochastic processes and queueing theory in the analysis of multiserver real-time system with different channels, where queueing of jobs is impossible. Failures of some (or even majority) of system components lead only to gradual degradation of the system ability to perform its functions. In the paper this ability is presented by system availability and loss penalty function.     

Problem of quantifying quantum correlations with non-commutative discord

In this work we analyze a non-commutativity measure of quantum correlations recently proposed by Guo (Sci Rep 6:25241, 2016). By resorting to a systematic survey of a two-qubit system, we detected an undesirable behavior of such a measure related to its representation-dependence. In the case of pure states, this dependence manifests as a non-satisfactory entanglement measure whenever a representation other than the Schmidt’s is used. In order to avoid this basis-dependence feature, we argue that a minimization procedure over the set of all possible representations of the quantum state is required. In the case of pure states, this minimization can be analytically performed and the optimal basis turns out to be that of Schmidt’s. In addition, the resulting measure inherits the main properties of Guo’s measure and, unlike the latter, it reduces to a legitimate entanglement measure in the case of pure states. Some examples involving general mixed states are also analyzed considering such an optimization. The results show that, in most cases of interest, the use of Guo’s measure can result in an overestimation of quantum correlations. However, since Guo’s measure has the advantage of being easily computable, it might be used as a qualitative estimator of the presence of quantum correlations.     

Uncertainty under quantum measures and quantum memory

The uncertainty principle restricts potential information one gains about physical properties of the measured particle. However, if the particle is prepared in entanglement with a quantum memory, the corresponding entropic uncertainty relation will vary. Based on the knowledge of correlations between the measured particle and quantum memory, we have investigated the entropic uncertainty relations for two and multiple measurements and generalized the lower bounds on the sum of Shannon entropies without quantum side information to those that allow quantum memory. In particular, we have obtained generalization of Kaniewski–Tomamichel–Wehner’s bound for effective measures and majorization bounds for noneffective measures to allow quantum side information. Furthermore, we have derived several strong bounds for the entropic uncertainty relations in the presence of quantum memory for two and multiple measurements. Finally, potential applications of our results to entanglement witnesses are discussed via the entropic uncertainty relation in the absence of quantum memory.     

Dynamics of quantum entanglement in quantum channels

Based on the von Neumann entropy, we give a computational formalism of the quantum entanglement dynamics in quantum channels, which can be applied to a general finite systems coupled with their environments in quantum channels. The quantum entanglement is invariant in the decoupled local unitary quantum channel, but it is variant in the non-local coupled unitary quantum channel. The numerical investigation for two examples, two-qubit and two-qutrit models, indicates that the quantum entanglement evolution in the quantum non-local coupling channel oscillates with the coupling strength and time, and depends on the quantum entanglement of the initial state. It implies that quantum information loses or gains when the state of systems evolves in the quantum non-local coupling channel.     

Generation of synthetic spike trains with defined pairwise correlations

Recent technological advances as well as progress in theoretical understanding of neural systems have created a need for synthetic spike trains with controlled mean rate and pairwise cross-correlation. This report introduces and analyzes a novel algorithm for the generation of discretized spike trains with arbitrary mean rates and controlled cross correlation. Pairs of spike trains with any pairwise correlation can be generated, and higher-order correlations are compatible with common synaptic input. Relations between allowable mean rates and correlations within a population are discussed. The algorithm is highly efficient, its complexity increasing linearly with the number of spike trains generated and therefore inversely with the number of cross-correlated pairs.     

Categories of quantum and classical channels

We introduce a construction that turns a category of pure state spaces and operators into a category of observable algebras and superoperators. For example, it turns the category of finite-dimensional Hilbert spaces into the category of finite-dimensional C*-algebras and completely positive maps. In particular, the new category contains both quantum and classical channels, providing elegant abstract notions of preparation and measurement. We also consider nonstandard models that can be used to investigate which notions from algebraic quantum information theory are operationally justifiable.     

Classical capacities of quantum channels with environment assistance

A quantum channel physically is a unitary interaction between an information carrying system and an environment, which is initialized in a pure state before the interaction. Conventionally, this state, as also the parameters of the interaction, is assumed to be fixed and known to the sender and receiver. Here, following the model introduced by us earlier [1], we consider a benevolent third party, i.e., a helper, controlling the environment state, and show how the helper’s presence changes the communication game. In particular, we define and study the classical capacity of a unitary interaction with helper, in two variants: one where the helper can only prepare separable states across many channel uses, and one without this restriction. Furthermore, two even more powerful scenarios of pre-shared entanglement between helper and receiver, and of classical communication between sender and helper (making them conferencing encoders) are considered.     

Protection of quantum correlations against decoherence

The protection of different quantum correlations, such as Bell nonlocality, quantum discord, and geometric quantum discord as trace distance against noise, is explored. By weak measurement and quantum measurement reversal, we show that the mentioned quantum correlations can be effectively preserved probabilistically from the decoherence due to amplitude damping. The results will play an important role in the experiments using the quantum correlations as resource.     

Robust sequence memory in sparsely-connected networks with controllable steady-state period

A novel sparsely-connected neural network for sequence memory with controllable steady-state period is proposed in this study. By introducing a new exponential kernel sampling function and the sampling interval parameter, the steady-state period can be controlled, and the steady-state time steps is equal to the sampling interval parameter. Ascribing to the exponential kernel sampling function, the sequence storage capacity is enlarged compared with the existing sequence memory models. Owning to the sparsely-connected of Gaussian distribution, the model produces the efficient use of synapse resources, but the sequence storage capacity is decreased compared with the fully-connected networks. The study also gives a significant result that the networks of different dimensions have the same synapse connection efficiency if they are with the same connection mean degree.     

One-mode quantum Gaussian channels: Structure and quantum capacity

A complete classification of one-mode Gaussian channels is given up to canonical unitary equivalence. We also comment on the quantum capacity of these channels. A channel complementary to the quantum channel with additive classical Gaussian noise is described, providing an example of a one-mode Gaussian channel which is neither degradable nor antidegradable.     

Efficient multi-sequence memory with controllable steady-state period and high sequence storage capacity

Sequential information processing, for instance the sequence memory, plays an important role on many functions of brain. In this paper, multi-sequence memory with controllable steady-state period and high sequence storage capacity is proposed. By introducing a novel exponential kernel sampling function and the sampling interval parameter, the steady-state period can be controlled, and the steady-state time steps are equal to the sampling interval parameter. Furthermore, we explained this phenomenon theoretically. Ascribing to the nonlinear function constitution for local field, the conventional Hebbian learning rule with linear outer product method can be improved. Simulation results show that neural network with nonlinear function constitution can effectively increase sequence storage capacity.     

Quantum privacy and quantum wiretap channels

Following Schumacher and Westmoreland, we address the problem of the capacity of a quantum wiretap channel. We first argue that, in the definition of the so-called quantum privacy, Holevo quantities should be used instead of classical mutual informations. The argument actually shows that the security condition in the definition of a code should limit the wiretappers Holevo quantity. Then we show that this modified quantum privacy is the optimum achievable rate of secure transmission.Translated from Problemy Peredachi Informatsii, No. 4, 2004, pp. 26–47. Original Russian Text Copyright © 2004 by Cai, Winter, Yeung.     

Pairwise quantum correlations of a three-qubit XY chain with phase decoherence

Quantum correlations, including entanglement and discord with its geometric measure in a three-qubit Heisenberg XY chain, with phase decoherence, are investigated when a nonuniform magnetic field is applied. When the qubits are initially in an unentangled state, the nearest neighbor pairwise correlations are destroyed by phase decoherence, but stationary correlations appear for next-to-neighbor qubits. With an inhomogeneous magnetic field, the stationary correlations appear for nearest neighbor qubits and they disappear for next-to-nearest neighbor qubits. But when the qubits are initially in an entangled state, an inhomogeneous magnetic field can enhance the stationary correlations of next-to-neighbor qubits, but it cannot do so for nearest neighbor qubits. The decoherence effect on stationary correlations is much stronger for next-to-nearest neighbor qubits than it is for nearest neighbor qubits. Finally, a uniform magnetic field can affect the correlations when the qubits are initially in an entangled state, but it cannot affect them when the qubits are initially in an unentangled state.