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Łukasz Pawela

Publications and source records attributed to Łukasz Pawela.

53 records · Page 3Linked to original sources
arXiv2018

Unconditional Security of a $K$-State Quantum Key Distribution Protocol

Quantum key distribution protocols constitute an important part of quantum cryptography, where the security of sensitive information arises from the laws of physics. In this paper we introduce a new family of key distribution protocols and we compare its key with the well-known protocols such as BB84, PBC0 and generation rate to the well-known protocols such as BB84, PBC0 and R04. We also state the security analysis of these protocols based on the entanglement distillation and CSS codes techniques.

quant-ph↗
arXiv2017

Almost all quantum channels are equidistant

In this work we analyze properties of generic quantum channels in the case of large system size. We use random matrix theory and free probability to show that the distance between two independent random channels converges to a constant value as the dimension of the system grows larger. As a measure of the distance we use the diamond norm. In the case of a flat Hilbert-Schmidt distribution on quantum channels, we obtain that the distance converges to $\frac12 + \frac{2}π$, giving also an estimate for the maximum success probability for distinguishing the channels. We also consider the problem of distinguishing two random unitary rotations.

quant-ph↗
arXiv2017

Properties of quantum stochastic walks from the asymptotic scaling exponent

This work focuses on the study of quantum stochastic walks, which are a generalization of coherent, i. e. unitary quantum walks. Our main goal is to present a measure of a coherence of the walk. To this end, we utilize the asymptotic scaling exponent of the second moment of the walk i. e. of the mean squared distance covered by a walk. As the quantum stochastic walk model encompasses both classical random walks and quantum walks, we are interested how the continuous change from one regime to the other influences the asymptotic scaling exponent. Moreover this model allows for behavior which is not found in any of the previously mentioned model -- the model with global dissipation. We derive the probability distribution for the walker, and determine the asymptotic scaling exponent analytically, showing that ballistic regime of the walk is maintained even at large dissipation strength.

quant-ph↗
arXiv2016

Distinguishability of generic quantum states

Properties of random mixed states of order $N$ distributed uniformly with respect to the Hilbert-Schmidt measure are investigated. We show that for large $N$, due to the concentration of measure, the trace distance between two random states tends to a fixed number ${\tilde D}=1/4+1/π$, 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.

quant-ph↗
arXiv2016

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 $\mathbb{Z}^d$. 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.

quant-ph↗
arXiv2015

Quantum games on evolving random networks

We study the advantages of quantum strategies in evolutionary social dilemmas on evolving random networks. We focus our study on the two-player games: prisoner's dilemma, snowdrift and stag-hunt games. The obtained result show the benefits of quantum strategies for the prisoner's dilemma game. For the other two games, we obtain regions of parameters where the quantum strategies dominate, as well as regions where the classical strategies coexist.

physics.soc-ph↗
arXiv2015

Quantifying channels output similarity with applications to quantum control

In this work we aim at quantifying quantum channel output similarity. In order to achieve this, we introduce the notion of quantum channel superfidelity, which gives us an upper bound on the quantum channel fidelity. This quantity is expressed in a clear form using the Kraus representation of a quantum channel. As examples, we show potential applications of this quantity in the quantum control field.

quant-ph↗
arXiv2014

Real numerical shadow and generalized B-splines

Restricted numerical shadow $P^X_A(z)$ of an operator $A$ of order $N$ is a probability distribution supported on the numerical range $W_X(A)$ restricted to a certain subset $X$ of the set of all pure states - normalized, one-dimensional vectors in ${\mathbb C}^N$. Its value at point $z \in {\mathbb C}$ equals to the probability that the inner product $< u |A| u >$ is equal to $z$, where $u$ stands for a random complex vector from the set $X$ distributed according to the natural measure on this set, induced by the unitarily invariant Fubini-Study measure. For a Hermitian operator $A$ of order $N$ we derive an explicit formula for its shadow restricted to real states, $P^{\mathbb R}_A(x)$, show relation of this density to the Dirichlet distribution and demonstrate that it forms a generalization of the $B$-spline. Furthermore, for operators acting on a space with tensor product structure, ${\cal H}_A \otimes {\cal H}_B$, we analyze the shadow restricted to the set of maximally entangled states and derive distributions for operators of order N=4.

math.FA↗
arXiv2014

Relativistic quantum pseudo-telepathy

We analyze the impact of the Unruh effect on the quantum Magic Square game. We find the values of acceleration parameter for which quantum strategy yields higher players' winning probability than classical strategy.

quant-ph↗
arXiv2014

Various methods of optimizing control pulses for quantum systems with decoherence

We study three methods of obtaining an approximation of unitary evolution of a quantum system under decoherence. We use three methods of optimizing the control pulses: genetic optimization, approximate evolution method and approximate gradient method. To model the noise in the system we use the Lindblad equaiton. We obtain results showing that genetic optimization may give a better approximation of a unitary evolution in the case of high noise.

quant-ph↗
arXiv2014

General model for a entanglement-enhanced composed quantum game on a two-dimensional lattice

We introduce a method of analyzing entanglement enhanced quantum games on regular lattices of agents. Our method is valid for setups with periodic and non-periodic boundary conditions. To demonstrate our approach we study two different types games, namely the prisoner's dilemma game and a cooperative Parrondo's game. In both cases we obtain results showing, that entanglement is a crucial resource necessary for the agents to achieve positive capital gain.

quant-ph↗
arXiv2013

Quantum control robust with coupling with an external environment

We study coherent quantum control strategy which is robust with respect to coupling with an external environment. We model this interaction by appending an additional subsystem to the initial system and we choose the strength of the coupling to be proportional to the magnitude of the control pulses. Therefore, to minimize the interaction we impose $L_1$ norm restrictions on the control pulses. In order to efficiently solve this optimization problem we employ the BFGS algorithm. We use three different functions as the derivative of the $L1$ norm of control pulses: the signum function, a fractional derivative $\frac{\dd^α|x|}{\dd x^α}$, where $0<α<1$, and the Fermi-Dirac distribution. We show that our method allows to efficiently obtain the control pulses which neglect the coupling with an external environment.

quant-ph↗
arXiv2013

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.

quant-ph↗
arXiv2013

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.

quant-ph↗
arXiv2013

Enhancing pseudo-telepathy in the Magic Square game

We study the possibility of reversing an action of a quantum channel. Our principal objective is to find a specific channel that reverses as accurately as possible an action of a given quantum channel. To achieve this goal we use semidefinite programming. We show the benefits of our method using the quantum pseudo-telepathy Magic Square game with noise. Our strategy is to move the pseudo-telepathy region to higher noise values. We show that it is possible to reverse the action of a noise channel using semidefinite programming.

quant-ph↗
arXiv2012

Quantum control with spectral constraints

Various constraints concerning control fields can be imposed in the realistic implementations of quantum control systems. One of the most important is the restriction on the frequency spectrum of acceptable control parameters. It is important to consider the limitations of experimental equipment when trying to find appropriate control parameters. Therefore, in this paper we present a general method of obtaining a piecewise-constant controls, which are robust with respect to spectral constraints. We consider here a Heisenberg spin chain, however the method can be applied to a system with more general interactions. To model experimental restrictions we apply an ideal low-pass filter to numerically obtained control pulses. The usage of the proposed method has negligible impact on the control quality as opposed to the standard approach, which does not take into account spectral limitations.

quant-ph↗