arXiv subjects

Peter Rapčan

Publications and source records attributed to Peter Rapčan.

4 recordsLinked to original sources

arXiv2026

Exact Resource Laws for Passive Wavelength Routing in Entanglement Networks

Entanglement-based networks provide a scalable framework for multiuser quantum communication by passively routing spectrally correlated photon pairs across interconnected nodes. Several wavelength-allocation schemes have been demonstrated experimentally, but these designs do not yet give a general way to determine how spectral use, receiver load, repeated connections, and fan-out constrain one another. We address this problem through the network's connectivity graph, where the wavelength assignment becomes a resource-optimization problem. For one-sided fan-out, assigning each link to a center and grouping links with the same center gives an exact optimization for arbitrary networks and fan-out limits. We solve this for complete networks and for complete networks in which every user has one excluded partner. Allowing both conjugate wavelengths to fan out changes the resource landscape: a balanced binary hierarchy attains the minimum spectral-layer count for a complete network while reducing the maximum receiver load to logarithmic in the number of users. An eight-user complete network then makes explicit the competing roles of spectral efficiency, receiver load, redundancy, and fan-out. We include the passive-splitter loss and the dependence of the key rate on the delivered pair flux to determine the minimum total pair-generation rate required to meet the prescribed targets. Finally, we formulate the corresponding BBM92 quantum key distribution (QKD) secret-key-rate analysis for a continuous-wave-pumped broadband source, with true and accidental coincidences evaluated between detector channels at the two endpoint users and relative layer pair-generation rates fixed by the source spectrum. This framework, therefore, provides a direct route from exact network resource laws to the design and comparison of passive entanglement architectures under experimentally specified hardware constraints.

quant-ph↗

arXiv2025

Quantum Potts Models on the Sierpiński Pyramid

Phase transition of the two- and three-state quantum Potts models on the Sierpiński pyramid are studied by means of a tensor network framework, the higher-order tensor renormalization group method. Critical values of the transverse magnetic field and the magnetic exponent $β$ are evaluated. Despite the fact that the Hausdorff dimension of the Sierpiński pyramid is exactly two $( = \log_2^{~} 4)$, the obtained critical properties show that the effective dimension is lower than two.

cond-mat.stat-mech↗

arXiv2017

Entanglement can preserve the compact nature of the phase-space occupancy

We study the one-dimensional transverse-field spin-1/2 Ising ferromagnet at its critical point. We consider an $L$-sized subsystem of a $N$-sized ring, and trace over the states of $(N-L)$ spins, with $N\to\infty$. The full $N$-system is in a pure state, but the $L$-system is in a statistical mixture. As well known, for $L >>1$, the Boltzmann-Gibbs-von Neumann entropy violates thermodynamical extensivity, namely $S_{BG}(L) \propto \log L$, whereas the nonadditive entropy $S_q$ is extensive for $q=q_c=\sqrt{37}-6 $, namely $S_{q_c}(L) \propto L$. When this problem is expressed in terms of independent fermions, we show that the usual thermostatistical sums emerging within Fermi-Dirac statistics can, for $L>>1$, be indistinctively taken up to $L$ terms or up to $\log L$ terms. This is interpreted as a compact occupancy of phase-space of the $L$-system, hence standard BG quantities with an effective length $V \equiv \log L$ are appropriate and are explicitly calculated. In other words, the calculations are to be done in a phase-space whose effective dimension is $2^{\log L}$ instead of $2^L$. The whole scenario is strongly reminiscent of a usual phase transition of a spin-1/2 $d$-dimensional system, where the phase-space dimension is $2^{L^d}$ in the disordered phase, and effectively $2^{L^d/2}$ in the ordered one.

cond-mat.stat-mech↗

arXiv2016

Nonlinear inhomogeneous Fokker-Planck equations: entropy and free-energy time evolution

We extend a recently introduced free-energy formalism for homogeneous Fokker-Planck equations to a wide, and physically appealing, class of inhomogeneous nonlinear Fokker-Planck equations. In our approach, the free-energy functional is expressed in terms of an entropic functional and an auxiliary potential, both derived from the coefficients of the equation. With reference to the introduced entropic functional, we discuss the entropy production in a relaxation process towards equilibrium. The properties of the stationary solutions of the considered Fokker-Planck equations are also discussed.

cond-mat.stat-mech↗