31 research outputs found

### Entropy of quantum channel in the theory of quantum information

Quantum channels, also called quantum operations, are linear, trace
preserving and completely positive transformations in the space of quantum
states. Such operations describe discrete time evolution of an open quantum
system interacting with an environment. The thesis contains an analysis of
properties of quantum channels and different entropies used to quantify the
decoherence introduced into the system by a given operation. Part I of the
thesis provides a general introduction to the subject. In Part II, the action
of a quantum channel is treated as a process of preparation of a quantum
ensemble. The Holevo information associated with this ensemble is shown to be
bounded by the entropy exchanged during the preparation process between the
initial state and the environment. A relation between the Holevo information
and the entropy of an auxiliary matrix consisting of square root fidelities
between the elements of the ensemble is proved in some special cases. Weaker
bounds on the Holevo information are also established. The entropy of a
channel, also called the map entropy, is defined as the entropy of the state
corresponding to the channel by the Jamiolkowski isomorphism. In Part III of
the thesis, the additivity of the entropy of a channel is proved. The minimal
output entropy, which is difficult to compute, is estimated by an entropy of a
channel which is much easier to obtain. A class of quantum channels is
specified, for which additivity of channel capacity is conjectured. The last
part of the thesis contains characterization of Davies channels, which
correspond to an interaction of a state with a thermal reservoir in the week
coupling limit, under the condition of quantum detailed balance and
independence of rotational and dissipative evolutions. The Davies channels are
characterized for one-qubit and one-qutrit systems

### Non-Markovianity of Gaussian Channels

We introduce a necessary and sufficient criterion for the non-Markovianity of
Gaussian quantum dynamical maps based on the violation of divisibility. The
criterion is derived by defining a general vectorial representation of the
covariance matrix which is then exploited to determine the condition for the
complete positivity of partial maps associated to arbitrary time intervals.
Such construction does not rely on the Choi-Jamiolkowski representation and
does not require optimization over states.Comment: 5 pages, 1 figure. Published versio

### 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

### Security against jamming and noise exclusion in imaging

We describe a protocol by which an imaging system could be protected against jamming by a malevolent party. Our protocol not only allows recognition of the jamming, but also allows for the recovery of the true image from the jammed one. We apply the method to jamming of quantum ghost imaging, for which the jamming detection probability is increased when the imaging light is entangled. The method can also be used to provide image recovery in general noisy environments

### Security against jamming in imaging with partially-distinguishable photons

We describe a protocol in which we detect intercept-resend jamming of imaging and can reverse its effects. The security is based on control of the polarization states of photons that are sent to interrogate an object and form an image at a camera. The scheme presented here is a particular implementation of a general anti-jamming protocol established by Roga and Jeffers in Ref. 5. It is applied here to imaging by photons with partially distinguishable polarisation states. The protocol in this version is easily applicable as only single photon states are involved, however the efficiency is traded off against the intrusion detectability because of a leak of information to the intruder

### Device-independent quantum reading and noise-assisted quantum transmitters

In quantum reading, a quantum state of light (transmitter) is applied to read classical information. In the presence of noise or for sufficiently weak signals, quantum reading can outperform classical reading by reason of enhanced state distinguishability. Here we show that enhanced quantum efficiency depends on the presence in the transmitter of a particular type of quantum correlations, the discord of response. Different encodings and transmitters give rise to different levels of efficiency. Considering noisy quantum probes, we show that squeezed thermal transmitters with non-symmetrically distributed noise among the field modes yield higher quantum efficiency compared with coherent thermal quantum states. The noise-enhanced quantum advantage is a consequence of the discord of response being a non-decreasing function of increasing thermal noise under constant squeezing, a behavior that leads to increased state distinguishability. We finally show that, for non-symmetric squeezed thermal states, the probability of error, as measured by the quantum Chernoff bound, vanishes asymptotically with increasing local thermal noise with finite global squeezing. Therefore, with fixed finite squeezing, noisy but strongly discordant quantum states with a large noise imbalance between the field modes can outperform noisy classical resources as well as pure entangled transmitters with the same finite level of squeezing

### Matrices of fidelities for ensembles of quantum states and the Holevo quantity

The entropy of the Gram matrix of a joint purification of an ensemble of K
mixed states yields an upper bound for the Holevo information Chi of the
ensemble. In this work we combine geometrical and probabilistic aspects of the
ensemble in order to obtain useful bounds for Chi. This is done by constructing
various correlation matrices involving fidelities between every pair of states
from the ensemble. For K=3 quantum states we design a matrix of root fidelities
that is positive and the entropy of which is conjectured to upper bound Chi.
Slightly weaker bounds are established for arbitrary ensembles. Finally, we
investigate correlation matrices involving multi-state fidelities in relation
to the Holevo quantity.Comment: 24 pages, 3 figure