scholarly journals Computing Classical-Quantum Channel Capacity Using Blahut–Arimoto Type Algorithm: A Theoretical and Numerical Analysis

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 222
Author(s):  
Haobo Li ◽  
Ning Cai
Keyword(s):  
Quantum Channel ◽  
Accurate Solution ◽  
Matrix Space ◽  
Output State ◽  
Finite Dimensional ◽  
Input Alphabet ◽  
Geometric Convergence ◽  
Classical Quantum ◽  
Theoretical And Numerical Analysis ◽  
Output Dimension

Based on Arimoto’s work in 1972, we propose an iterative algorithm for computing the capacity of a discrete memoryless classical-quantum channel with a finite input alphabet and a finite dimensional output, which we call the Blahut–Arimoto algorithm for classical-quantum channel, and an input cost constraint is considered. We show that, to reach ε accuracy, the iteration complexity of the algorithm is upper bounded by log n log ε ε where n is the size of the input alphabet. In particular, when the output state { ρ x } x ∈ X is linearly independent in complex matrix space, the algorithm has a geometric convergence. We also show that the algorithm reaches an ε accurate solution with a complexity of O ( m 3 log n log ε ε ) , and O ( m 3 log ε log ( 1 − δ ) ε D ( p * | | p N 0 ) ) in the special case, where m is the output dimension, D ( p * | | p N 0 ) is the relative entropy of two distributions, and δ is a positive number. Numerical experiments were performed and an approximate solution for the binary two-dimensional case was analysed.

Performance characterization of Pauli channels assisted by indefinite causal order and post-measurement

2020 ◽  
Vol 20 (15&16) ◽  
pp. 1261-1280
Author(s):  
Francisco Delgado ◽  
Carlos Cardoso-Isidoro
Keyword(s):  
Quantum Channel ◽  
Communication Channel ◽  
Quantum Communication ◽  
Quantum Channels ◽  
Causal Order ◽  
Combined Process ◽  
Performance Characterization ◽  
Output State ◽  
Transmission Of Information

Indefinite causal order has introduced disruptive procedures to improve the fidelity of quantum communication by introducing the superposition of { orders} on a set of quantum channels. It has been applied to several well characterized quantum channels as depolarizing, dephasing and teleportation. This work analyses the behavior of a parametric quantum channel for single qubits expressed in the form of Pauli channels. Combinatorics lets to obtain affordable formulas for the analysis of the output state of the channel when it goes through a certain imperfect quantum communication channel when it is deployed as a redundant application of it under indefinite causal order. In addition, the process exploits post-measurement on the associated control to select certain components of transmission. Then, the fidelity of such outputs is analysed to characterize the generic channel in terms of its parameters. As a result, we get notable enhancement in the transmission of information for well characterized channels due to the combined process: indefinite causal order plus post-measurement.

Classical-Quantum Channel Coding

2014 ◽  
pp. 205-229
Author(s):  
Masahito Hayashi ◽  
Satoshi Ishizaka ◽  
Akinori Kawachi ◽  
Gen Kimura ◽  
Tomohiro Ogawa
Keyword(s):  
Channel Coding ◽  
Quantum Channel ◽  
Classical Quantum

On Quantum Capacity and its Bound

2003 ◽  
Vol 06 (02) ◽  
pp. 301-310 ◽  
Author(s):  
Masanori Ohya ◽  
Igor V. Volovich
Keyword(s):  
Quantum Channel ◽  
Quantum Mechanical ◽  
Quantum Capacity ◽  
Classical Quantum ◽  
Mutual Entropy

The quantum capacity of a pure quantum channel and that of classical-quantum-classical channel are discussed in detail based on the fully quantum mechanical mutual entropy. It is proved that the quantum capacity generalizes the so-called Holevo bound.

scholarly journals Infinite dimensional generalizations of Choi’s Theorem

2019 ◽  
Vol 7 (1) ◽  
pp. 67-77
Author(s):  
Shmuel Friedland
Keyword(s):  
Hilbert Spaces ◽  
Quantum Channel ◽  
Trace Class ◽  
Natural Generalization ◽  
Linear Operators ◽  
Completely Positive Map ◽  
Completely Positive ◽  
Bounded Linear ◽  
Positive Map ◽  
Finite Dimensional

Abstract In this paper we give a simple sequence of necessary and sufficient finite dimensional conditions for a positive map between certain subspaces of bounded linear operators on separable Hilbert spaces to be completely positive. These criterions are natural generalization of Choi’s characterization for completely positive maps between pairs of linear operators on finite dimensional Hilbert spaces. We apply our conditions to a completely positive map between two trace class operators on separable Hilbert spaces. A completely positive map μ is called a quantum channel, if it is trace preserving, and μ is called a quantum subchannel if it decreases the trace of a positive operator.We give simple neccesary and sufficient condtions for μ to be a quantum subchannel.We show that μ is a quantum subchannel if and only if it hasHellwig-Kraus representation. The last result extends the classical results of Kraus and the recent result of Holevo for characterization of a quantum channel.

scholarly journals Imprinting Complete Information about a Quantum Channel on its Output State

2003 ◽  
Vol 91 (4) ◽  
Author(s):  
Giacomo Mauro D’Ariano ◽  
Paoloplacido Lo Presti
Keyword(s):  
Quantum Channel ◽  
Complete Information ◽  
Output State

Diffusive wave-absorbing control: example of the boundary stabilization of a thin flexible beam

2011 ◽  
Vol 18 (11) ◽  
pp. 1708-1721 ◽  
Author(s):  
Gérard Montseny
Keyword(s):  
Continuous Semigroup ◽  
Semigroup Theory ◽  
Flexible Beam ◽  
Convolution Operators ◽  
Controlled System ◽  
Reflected Waves ◽  
Output State ◽  
Finite Dimensional ◽  
Euler Bernoulli Beam ◽  
The Ideal

In this paper we deal with the boundary control of the Euler–Bernoulli beam by means of wave-absorbing feedback. Such controls are based upon the reduction of reflected waves and involve long memory non-rational convolution operators resulting from specific properties of the system. These operators are reformulated under so-called diffusive input–output state-space realizations, which allow us to represent the global closed-loop system under the abstract form d X/d t = A X with A the infinitesimal generator of a continuous semigroup. So, well-posedness and stability of the controlled system result from classical semigroup theory. Finite-dimensional approximations of the diffusive realizations are then studied, with the aim of providing implementable controls close to the ideal ones. Finally, significant numerical simulations are presented.

scholarly journals The classical-quantum channel with random state parameters known to the sender

2016 ◽  
Vol 49 (19) ◽  
pp. 195302 ◽  
Author(s):  
Holger Boche ◽  
Ning Cai ◽  
Janis Nötzel
Keyword(s):  
Quantum Channel ◽  
Classical Quantum ◽  
Random State

Geometric Convergence of Iterative Methods for a Problem with M-matrices and Diagonal Multivalued Operators

2002 ◽  
Vol 2 (1) ◽  
pp. 26-40 ◽  
Author(s):  
Alexander Lapin
Keyword(s):  
Iterative Methods ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Mesh Approximation ◽  
Finite Dimensional ◽  
Multivalued Operators ◽  
Geometric Convergence ◽  
Parallel Iterative ◽  
A Free Boundary Problem

Abstract A finite-dimensional problem with several M-matrices and diagonal maximal monotone operators is studied. This problem includes variational inequalities with M-matrices as a partial case and appears, in particular, as a mesh approximation for a free boundary problem with several constraints and nonlinear relations. The existence of an unique solution for the problem is studied, as well as the convergence and geometric rate of the convergence for a class of the iterative methods, the Schwarz alternating-type methods among them. The application of the general results to a mesh scheme for a dam problem is considered. Parallel iterative methods are constructed on the basis of the domain decomposition, geometric convergence of these methods is justified.

Few-photon routing via chiral light-matter couplings

2021 ◽  
Author(s):  
Ya Yang ◽  
Jing Lu ◽  
Lan Zhou
Keyword(s):  
Quantum Channel ◽  
Active Element ◽  
Single Photon ◽  
Essential Elements ◽  
Quantum Network ◽  
Photon Scattering ◽  
Output State ◽  
Two Photon ◽  
Quantum Router ◽  
The One

Abstract Quantum router is one of the essential elements in the quantum network. Conventional routers only direct a single photon from one quantum channel into another. Here, we proposed a few-photon router. The active element of the router is a single qubit chirally coupled to two independent waveguides simultaneously, where each waveguide mode provides a quantum channel. By introducing the operators of the scatter-free space and the controllable space, the output state of the one-photon and two-photon scattering are derived analytically. It is found that the qubit can direct one and two photons from one port of the incident waveguide to an arbitrarily selected port of the other waveguide with unity, respectively. However, two photons cannot be simultaneously routed to the same port due to the anti-bunch effect.

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