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

Perfect quantum-state synchronization

We investigate the most general mechanisms that lead to perfect synchronization of the quantum states of all subsystems of an open quantum system starting from an arbitrary initial state. We provide a necessary and sufficient condition for such "quantum-state synchronization", prove tight lower bounds on the dimension of the environment's Hilbert space in two main classes of quantum-state synchronizers, and give an analytical solution for their construction. The functioning of the found quantum-state synchronizer of two qubits is demonstrated experimentally on an IBM quantum computer and we show that the remaining asynchronicity is a sensitive measure of the quantum computer's imperfection.Comment: 10 pages, 4 figure

Trade--off relations for operation entropy of complementary quantum channels

The entropy of a quantum operation, defined as the von Neumann entropy of the corresponding Choi-Jamio{\l}kowski state, characterizes the coupling of the principal system with the environment. For any quantum channel $\Phi$ acting on a state of size $N$ one defines the complementary channel $\tilde \Phi$, which sends the input state into the state of the environment after the operation. Making use of subadditivity of entropy we show that for any dimension $N$ the sum of both entropies, $S(\Phi)+ S(\tilde \Phi)$, is bounded from below. This result characterizes the trade-off between the information on the initial quantum state accessible to the principal system and the information leaking to the environment. For one qubit maps, $N=2$, we describe the interpolating family of depolarising maps, for which the sum of both entropies gives the lower boundary of the region allowed in the space spanned by both entropies.Comment: 16 pages, 5 figure

Relating compatibility and divisibility of quantum channels

We connect two key concepts in quantum information: compatibility and divisibility of quantum channels. Two channels are compatible if they can be both obtained via marginalization from a third channel. A channel divides another channel if it reproduces its action by sequential composition with a third channel. (In)compatibility is of central importance for studying the difference between classical and quantum dynamics. The relevance of divisibility stands in its close relationship with the onset of Markovianity. We emphasize the simulability character of compatibility and divisibility, and, despite their structural difference, we find a set of channels -- self-degradable channels -- for which the two notions coincide. We also show that, for degradable channels, compatibility implies divisibility, and that, for anti-degradable channels, divisibility implies compatibility. These results motivate further research on these classes of channels and shed new light on the meaning of these two largely studied notions.Comment: Suggestions are welcome! =

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

DNA molecular recognition specificity : pairwise and in competition

Despite its importance in biological systems, the molecular recognition of DNA hybridization within complex, competitive environments is poorly understood. The present thesis investigates DNA hybridization in thermal equilibrium for DNA strands bound to the surface of a microarray as well as in solution in presence of one or more competitors. For the latter we employ fluorescence anisotropy and fluorescence correlation spectroscopy to determine binding affinities of two DNA strands in a pairwise manner and in presence of a single competitor. Our results reveal that there must be a non-trivial interaction between the competing strands that extends beyond simple double helix formation. This is a signature of cooperative behavior, which can lead to more complex binding phenomena than previously thought. Moreover, we find surprising differences between the results of both techniques, which we attribute to differing sensitivities to distinct microstates of double helix formation. The second part of this work is performed with surface-bound DNA and devoted to experimentally determine a sufficient number of differing bases between two sequences to avoid cross-hybridization. We construct a set of 23 non-interacting sequences with a length of 7 bases. We conclude that for systems of increasing complexity a high level of discrimination between many competitors is essential for accurate recognition.Trotz der Relevanz für biologische Systeme sind die Mechanismen molekularer Erkennung bei der Hybridisierung von DNA in komplexen Umgebungen kaum verstanden. Die vorliegende Arbeit untersucht DNA Hybridisierung im thermischen Gleichgewicht mit DNA-Strängen sowohl an die Oberfläche eines Microarrays gebunden als auch in Lösung in Gegenwart von Konkurrenten. Für letztere verwenden wir Fluoreszenzanisotropie sowie -korrelationsspektroskopie, um Bindungsaffinitäten zweier DNA-Stränge paarweise und in Anwesenheit einzelner Konkurrenten zu bestimmen. Unsere Ergebnisse zeigen, dass es nicht triviale Wechselwirkungen zwischen den beteiligten Strängen geben muss, die über die einfache Bildung einer Doppelhelix hinausgehen. Diese Beobachtung deutet auf kooperatives Verhalten hin und zeigt, dass DNA-Hybridisierung komplexer abläuft als bisher angenommen. Außerdem finden wir eine unerwartete Diskrepanz beider Methoden, die auf unterschiedliche Sensitivitäten für bestimmte Mikrozustände der gebundenen DNA zurückgeht. Im zweiten Teil der Arbeit widmen wir uns Experimenten mit oberflächengebundener DNA. Wir bestimmen eine ausreichende Anzahl sich unterscheidender Basenpaare zweier Stränge, um nicht spezifische Hybridisierung zu vermeiden, und zeigen, dass sich damit ein Satz aus 23 nicht interagierenden Strängen á 7 Basen konstruieren lässt. Wir schließen, dass für zunehmend komplexe Systeme ein hoher Diskriminierungsgrad zwischen vielen Konkurrenten unabdingbar für präzise Erkennung ist