4 research outputs found
Composition of quantum operations and products of random matrices
Spectral properties of evolution operators corresponding to random maps and
quantized chaotic systems strongly interacting with an environment can be
described by the ensemble of non-hermitian random matrices from the real
Ginibre ensemble. We analyze evolution operators Psi=Psi_s...Psi_1 representing
the composition of s random maps and demonstrate that their complex eigenvalues
are asymptotically described by the law of Burda et al. obtained for a product
of s independent random complex Ginibre matrices. Numerical data support the
conjecture that the same results are applicable to characterize the
distribution of eigenvalues of the s-th power of a random Ginibre matrix.
Squared singular values of Psi are shown to be described by the Fuss-Catalan
distribution of order s. Results obtained for products of random Ginibre
matrices are also capable to describe the s-step evolution operator for a model
deterministic dynamical system - a generalized quantum baker map subjected to
strong interaction with an environment.Comment: 19 pages, 7 figure
Selfcomplementary quantum channels
Selfcomplementary quantum channels are characterized by such an interaction
between the principal quantum system and the environment that leads to the same
output states of both interacting systems. These maps can describe approximate
quantum copy machines, as perfect copying of an unknown quantum state is not
possible due to the celebrated no-cloning theorem. We provide here a
parametrization of a large class of selfcomplementary channels and analyze
their properties. Selfcomplementary channels preserve some residual coherences
and residual entanglement. Investigating some measures of non-Markovianity we
show that time evolution under selfcomplementary channels is highly
non-Markovian.Comment: 23 pages, 4 figure
Tensor Products of Random Unitary Matrices
Tensor products of M random unitary matrices of size N from the circular
unitary ensemble are investigated. We show that the spectral statistics of the
tensor product of random matrices becomes Poissonian if M=2, N become large or
M become large and N=2.Comment: 23 pages, 2 figure
Universality of spectra for interacting quantum chaotic systems
We analyze a model quantum dynamical system subjected to periodic interaction
with an environment, which can describe quantum measurements. Under the
condition of strong classical chaos and strong decoherence due to large
coupling with the measurement device, the spectra of the evolution operator
exhibit an universal behavior. A generic spectrum consists of a single
eigenvalue equal to unity, which corresponds to the invariant state of the
system, while all other eigenvalues are contained in a disk in the complex
plane. Its radius depends on the number of the Kraus measurement operators, and
determines the speed with which an arbitrary initial state converges to the
unique invariant state. These spectral properties are characteristic of an
ensemble of random quantum maps, which in turn can be described by an ensemble
of real random Ginibre matrices. This will be proven in the limit of large
dimension.Comment: 11 pages, 10 figure