58 research outputs found
Cooperative quantum Parrondo's games
Coordination and cooperation are among the most important issues of game
theory. Recently, the attention turned to game theory on graphs and social
networks. Encouraged by interesting results obtained in quantum evolutionary
game analysis, we study cooperative Parrondo's games in a quantum setup. The
game is modeled using multidimensional quantum random walks with biased coins.
We use the GHZ and W entangled states as the initial state of the coins. Our
analysis shows than an apparent paradox in cooperative quantum games and some
interesting phenomena can be observed.Comment: 13 pages, 10 figure
Distinguishability of generic quantum states
Properties of random mixed states of order distributed uniformly with
respect to the Hilbert-Schmidt measure are investigated. We show that for large
, due to the concentration of measure, the trace distance between two random
states tends to a fixed number , which yields the
Helstrom bound on their distinguishability. To arrive at this result we apply
free random calculus and derive the symmetrized Marchenko--Pastur distribution,
which is shown to describe numerical data for the model of two coupled quantum
kicked tops. Asymptotic values for the fidelity, Bures and transmission
distances between two random states are obtained. Analogous results for quantum
relative entropy and Chernoff quantity provide other bounds on the
distinguishablity of both states in a multiple measurement setup due to the
quantum Sanov theorem.Comment: 13 pages including supplementary information, 6 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
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
Central limit theorem for reducible and irreducible open quantum walks
In this work we aim at proving central limit theorems for open quantum walks
on . We study the case when there are various classes of vertices
in the network. Furthermore, we investigate two ways of distributing the vertex
classes in the network. First we assign the classes in a regular pattern.
Secondly, we assign each vertex a random class with a uniform distribution. For
each way of distributing vertex classes, we obtain an appropriate central limit
theorem, illustrated by numerical examples. These theorems may have application
in the study of complex systems in quantum biology and dissipative quantum
computation.Comment: 20 pages, 4 figure
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