arXiv subjects

Mikołaj Czechlewski

Publications and source records attributed to Mikołaj Czechlewski.

5 recordsLinked to original sources

arXiv2026

Benchmarking weak randomness in Quantum and Natural Sources

Private randomness is a fundamental resource for cryptography, security proofs, and information processing. Quantum devices offer a unique advantage by amplifying weak randomness sources in regimes unattainable by classical means. A central theoretical model for such sources is the Santha-Vazirani (SV) model, yet identifying natural processes that satisfy this model remains a major challenge. Here we take three steps toward addressing this problem. First, we introduce an axiomatic framework for quantifying weak randomness, providing a unified basis for estimating an SV-type source. Second, we develop SVTest, a general-purpose software tool for estimating the SV parameter of an arbitrary data sequence. Third, we apply this framework to both engineered and natural sources. Using data from a self-certifying commercial quantum random number generator with guaranteed min-entropy as a benchmark, we validate the accuracy and limitations of our estimation method. We then analyze geophysical signals associated with seismic activity and find that, depending on the discretization, both earthquakes and local seismic noise can exhibit SV-type randomness. Our results indicate that geophysical phenomena may constitute viable sources of cryptographic randomness, establishing an unexpected connection between quantum information theory and geophysics.

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arXiv2025

Quantification of the energy consumption of entanglement distribution

Inspired by environmental sciences, we develop a framework to quantify the energy needed to generate quantum entanglement via noisy quantum channels, focusing on the hardware-independent, i.e. fundamental cost. Within this framework, we define a measure of the minimal fundamental energy consumption rate per distributed entanglement (expressed in Joule per ebit). We then derive a lower bound on the energy cost of distributing a maximally entangled state via a quantum channel, which yields a quantitative estimate of energy investment per entangled bit for future quantum networks. We thereby show that irreversibility in entanglement theory implies a non-zero energy cost in standard entanglement distribution protocols. We further establish an upper bound on the fundamental energy consumption rate of entanglement distribution by determining the minimal energy required to implement quantum operations via classical control. To this end, we formulate the axioms for an energy cost measure and introduce a Hamiltonian model for classically-controlled quantum operations. The fundamental cost is then defined as the infimum energy over all such Hamiltonian protocols, with or without specific hardware constraints. The study of the energy cost of a quantum operation is general enough to be naturally applicable to quantum computing and is of independent interest. Finally, we evaluate the energy demands of three entanglement distillation protocols for photonic polarization qubits, finding that, due to entanglement irreversibility, their required energy exceeds the fundamental lower bound by many orders of magnitude. The introduced paradigm can be applied to other quantum resources, with appropriate changes depending on their nature.

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arXiv2019

Device independent witness of arbitrary dimensional quantum systems employing binary outcome measurements

Device independent dimension witnesses (DW) are a remarkable way to test the dimension of a quantum system in a prepare-and-measure scenario imposing minimal assumptions on the internal features of the devices. However, as the dimension increases, the major obstacle in the realization of DW arises due to the requirement of many outcome quantum measurements. In this article, we propose a new variant of a widely studied communication task (random access code) and take its average payoff as the DW. The presented DW applies to arbitrarily large quantum systems employing only binary outcome measurements.

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arXiv2017

The influence of the choice of post-processing method on Bell inequalities

In every experimental test of a Bell inequality, we are faced with the problem of inefficient detectors. How we treat the events when no particle was detected has a big influence on the properties of the inequality. In this work, we study this influence. We show that the choice of post-processing can change the critical detection efficiency, the equivalence between different inequalities or the applicability of the non-signaling principle. We also consider the problem of choosing the optimal post-processing strategy. We show that this is a non-trivial problem and that different strategies are optimal for different ranges of detector efficiencies.

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arXiv2011

Distillation of entanglement by projection on permutationally invariant subspaces

We consider distillation of entanglement from two qubit states which are mixtures of three mutually orthogonal states: two pure entangled states and one pure product state. We distill entanglement from such states by projecting n copies of the state on permutationally invariant subspace and then applying one-way hashing protocol. We find analytical expressions for the rate of the protocol. We also generalize this method to higher dimensional systems. To get analytical expression for two qubit case, we faced a mathematical problem of diagonalizing a family of matrices enjoying some symmetries w.r.t. to symmetric group. We have solved this problem in two ways: (i) directly, by use of Schur-Weyl decomposition and Young symmetrizers (ii) showing that the problem is equivalent to a problem of diagonalizing adjacency matrices in a particular instance of a so called algebraic association scheme.

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