2,549 research outputs found
Generating and using truly random quantum states in Mathematica
The problem of generating random quantum states is of a great interest from
the quantum information theory point of view. In this paper we present a
package for Mathematica computing system harnessing a specific piece of
hardware, namely Quantis quantum random number generator (QRNG), for
investigating statistical properties of quantum states. The described package
implements a number of functions for generating random states, which use
Quantis QRNG as a source of randomness. It also provides procedures which can
be used in simulations not related directly to quantum information processing.Comment: 12 pages, 3 figures, see http://www.iitis.pl/~miszczak/trqs.html for
related softwar
Employing online quantum random number generators for generating truly random quantum states in Mathematica
We present a new version of TRQS package for Mathematica computing system.
The package allows harnessing quantum random number generators (QRNG) for
investigating the statistical properties of quantum states. It implements a
number of functions for generating random states. The new version of the
package adds the ability to use the on-line quantum random number generator
service and implements new functions for retrieving lists of random numbers.
Thanks to the introduced improvements, the new version provides faster access
to high-quality sources of random numbers and can be used in simulations
requiring large amount of random data.Comment: New version of the package described in arXiv:1102.4598. Software
available at http://www.iitis.pl/~miszczak/trq
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
Symbolic integration with respect to the Haar measure on the unitary group
We present IntU package for Mathematica computer algebra system. The
presented package performs a symbolic integration of polynomial functions over
the unitary group with respect to unique normalized Haar measure. We describe a
number of special cases which can be used to optimize the calculation speed for
some classes of integrals. We also provide some examples of usage of the
presented package.Comment: 7 pages, two columns, published version, software available at:
https://github.com/iitis/Int
Generating random density matrices
We study various methods to generate ensembles of random density matrices of
a fixed size N, obtained by partial trace of pure states on composite systems.
Structured ensembles of random pure states, invariant with respect to local
unitary transformations are introduced. To analyze statistical properties of
quantum entanglement in bi-partite systems we analyze the distribution of
Schmidt coefficients of random pure states. Such a distribution is derived in
the case of a superposition of k random maximally entangled states. For another
ensemble, obtained by performing selective measurements in a maximally
entangled basis on a multi--partite system, we show that this distribution is
given by the Fuss-Catalan law and find the average entanglement entropy. A more
general class of structured ensembles proposed, containing also the case of
Bures, forms an extension of the standard ensemble of structureless random pure
states, described asymptotically, as N \to \infty, by the Marchenko-Pastur
distribution.Comment: 13 pages in latex with 8 figures include
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