15 research outputs found
QuantumInformation.jl---a Julia package for numerical computation in quantum information theory
Numerical investigations are an important research tool in quantum
information theory. There already exists a wide range of computational tools
for quantum information theory implemented in various programming languages.
However, there is little effort in implementing this kind of tools in the Julia
language. Julia is a modern programming language designed for numerical
computation with excellent support for vector and matrix algebra, extended type
system that allows for implementation of elegant application interfaces and
support for parallel and distributed computing. QuantumInformation.jl is a new
quantum information theory library implemented in Julia that provides functions
for creating and analyzing quantum states, and for creating quantum operations
in various representations. An additional feature of the library is a
collection of functions for sampling random quantum states and operations such
as unitary operations and generic quantum channels.Comment: 32 pages, 8 figure
A model for quantum queue
We consider an extension of Discrete Time Markov Chain queueing model to the
quantum domain by use of Discrete Time Quantum Markov Chain. We introduce
methods for numerical analysis of such models. Using this tools we show that
quantum model behaves fundamentally differently from the classical one.Comment: 14 pages, 7 figure
Conditional entropic uncertainty relations for Tsallis entropies
The entropic uncertainty relations are a very active field of scientific
inquiry. Their applications include quantum cryptography and studies of quantum
phenomena such as correlations and non-locality. In this work we find
entanglement-dependent entropic uncertainty relations in terms of the Tsallis
entropies for states with a fixed amount of entanglement. Our main result is
stated as Theorem~\ref{th:bound}. Taking the special case of von Neumann
entropy and utilizing the concavity of conditional von Neumann entropies, we
extend our result to mixed states. Finally we provide a lower bound on the
amount of extractable key in a quantum cryptographic scenario.Comment: 11 pages, 4 figure
Decoherence effects in the quantum qubit flip game using Markovian approximation
We are considering a quantum version of the penny flip game, whose
implementation is influenced by the environment that causes decoherence of the
system. In order to model the decoherence we assume Markovian approximation of
open quantum system dynamics. We focus our attention on the phase damping,
amplitude damping and amplitude raising channels. Our results show that the
Pauli strategy is no longer a Nash equilibrium under decoherence. We attempt to
optimize the players' control pulses in the aforementioned setup to allow them
to achieve higher probability of winning the game compared to the Pauli
strategy.Comment: 19 pages, 7 figure
Quantum Hidden Markov Models based on Transition Operation Matrices
In this work, we extend the idea of Quantum Markov chains [S. Gudder. Quantum
Markov chains. J. Math. Phys., 49(7), 2008] in order to propose Quantum Hidden
Markov Models (QHMMs). For that, we use the notions of Transition Operation
Matrices (TOM) and Vector States, which are an extension of classical
stochastic matrices and probability distributions. Our main result is the Mealy
QHMM formulation and proofs of algorithms needed for application of this model:
Forward for general case and Vitterbi for a restricted class of QHMMs.Comment: 19 pages, 2 figure
Non-stationary departure process in a batch-arrival queue with finite buffer capacity and threshold-type control mechanism
summary:Non-stationary behavior of departure process in a finite-buffer -type queueing model with batch arrivals, in which a threshold-type waking up -policy is implemented, is studied. According to this policy, after each idle time a new busy period is being started with the th message occurrence, where the threshold value is fixed. Using the analytical approach based on the idea of an embedded Markov chain, integral equations, continuous total probability law, renewal theory and linear algebra, a compact-form representation for the mixed double transform (probability generating function of the Laplace transform) of the probability distribution of the number of messages completely served up to fixed time is obtained. The considered queueing system has potential applications in modeling nodes of wireless sensor networks (WSNs) with battery saving mechanism based on threshold-type waking up of the radio. An illustrating simulational and numerical study is attached
Unconditional Security of a -State Quantum Key Distribution Protocol
Quantum key distribution protocols constitute an important part of quantum
cryptography, where the security of sensitive information arises from the laws
of physics. In this paper we introduce a new family of key distribution
protocols and we compare its key with the well-known protocols such as BB84,
PBC0 and generation rate to the well-known protocols such as BB84, PBC0 and
R04. We also state the security analysis of these protocols based on the
entanglement distillation and CSS codes techniques.Comment: 5 pages, 1 figur
Analysis of Non-Steady Queue-Length Distribution in a Finite-Buffer Model with Group Arrivals and Power Saving Mechanism with Setups
In the manuscript, a probability distribution of the queue length is studied in a model with group Markov arrivals, arbitrarily distributed service times and finite waiting room. After the period of suspension of service due to lack of packets, each new busy period is preceded by a random setup time. Integral equations for time-dependent queue-length distribution are derived by identifying renewal moments in the operation of the system and by applying total probability law. The representation for the solution of the system is found in terms of Laplace transforms. Computational examples illustrating the impact of system parameters on the queue-length distribution are included
On Transient Queue-Size Distribution in a Model of WSN Node with Threshold-Type Power-Saving Algorithm
This article proposes a queueing model of the operation of a wireless sensor network node, in which a threshold strategy for starting the node after a period of no transmission is used. In this model, transmission of packets is resumed when the number of packets in the accumulation buffer reaches a predefined level. In the literature, most of the results for models with limited access to the service station are obtained in equilibrium. In this paper, a formula for the Laplace transform of the transient queue-size distribution is obtained and written using the key input parameters of the system. The analytical apparatus uses the concept of the embedded Markov chain, the formula for total probability, renewal theory and some supporting algebraic results. Numerical examples are attached as well