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Łukasz Rudnicki

Publications and source records attributed to Łukasz Rudnicki.

At least 37 records · Page 2Linked to original sources
arXiv2023

Practical tests for sub-Rayleigh source discriminations with imperfect demultiplexers

Quantum-optimal discrimination between one and two closely separated light sources can be achieved by ideal spatial-mode demultiplexing, simply monitoring whether a photon is detected in a single antisymmetric mode. However, we show that for any, no matter how small, imperfections of the demultiplexer, this simple statistical test becomes practically useless, i.e. as good as flipping a coin. While we identify a class of separation-independent tests with vanishing error probabilities in the limit of large numbers of detected photons, they are generally unreliable beyond that very limit. As a practical alternative, we propose a simple semi-separation-independent test, which provides a method for designing reliable experiments, through arbitrary control over the maximal probability of error.

quant-ph↗
arXiv2023

Bounds on the breaking time for entanglement-breaking channels

Entanglement-breaking channels are quantum channels transforming entangled states to separable states. Despite a detailed discussion of their operational structure, to be found in the literature, studies on dynamical characteristics of this type of maps are yet limited. We consider one of the basic questions: for Lindblad-type dynamics, when does a given channel break entanglement? We discuss the finite-dimensional case where the quantification of entanglement via entanglement witnesses is utilized. For the general setup, we use the method of quantum speed limit to derive lower bounds on entanglement breaking times in terms of an input state, the dynamical map and the witness operator. Then, with a particular choice of the input state and the entanglement witness, the bounds for the breaking time are turned to solely reflect the characteristics of the dynamics.

quant-ph↗
arXiv2022

Reduced state of the field and classicality of quantum Gaussian evolution

The notion of classicality of quantum evolution of light is an object of both conceptual and practical importance. The main goal of this work is to derive the exact conditions for the classicality of quantum Gaussian evolution, i.e. the evolution of Gaussian states of light and their convex combinations, a model which is of great significance in quantum optics and information. Several examples, ranging from Gaussian thermal operations to entanglement-maximizing dissipative engineering, are discussed. Our results are obtained using the recently introduced mesoscopic theory of the reduced state of the field, which was originally devised as as a description of macroscopic quantum fields. Here, to make the framework suitable for our goal, we redevelop it as a tool for probing classicality, which constitutes our second main contribution.

quant-ph↗
arXiv2022

Dissipative evolution of quantum Gaussian states

Recent works on quantum resource theories of non-Gaussianity, which are based upon the type of tools available in contemporary experimental settings, put Gaussian states and their convex combinations on equal footing. Motivated by this, in this article, we derive a new model of dissipative time evolution based on unitary Lindblad operators which, while does not preserve the set of Gaussian states, preserves the set of their convex combinations, i.e. so-called quantum Gaussian states. As we demonstrate, the considered evolution proves useful both as a description for random scattering and as a tool in dissipator engineering.

quant-ph↗
arXiv2022

Quantum speed limit and stability of coherent states in quantum gravity

Utilizing the program of expectation values in coherent states and its recently developed algorithmic tools, this letter investigates the dynamical properties of cosmological coherent states for Loop Quantum Gravity. To this end, the Quantum Speed Limit is adapted to Quantum Gravity, yielding necessary consistency checks for any proposal of stable families of states. To showcase the strength of the developed tools, they are applied to a prominent model: the Euclidean part of the quantum scalar constraint. We report the variance of this constraint evaluated on a family of coherent states showing that, for short times, this family passes the Quantum Speed Limit test, allowing the transition from one coherent state to another one.

gr-qc↗
arXiv2022

Geophysics and Stuart vortices on a sphere meet differential geometry

We prove new existence criteria relevant for the non-linear elliptic PDE of the form $Δ_{S^2} u=C-he^{u}$, considered on a two dimensional sphere $S^2$, in the parameter regime $2\leq C<4$. We apply this result, as well as several previously known results valid when $C<2$, to discuss existence of solutions of a particular PDE modelling ocean surface currents.

math.AP↗
arXiv2021

Thermodynamics of Reduced State of the Field

Recent years have seen the flourishing of research devoted to quantum effects on mesoscopic and macroscopic scales. In this context, in Entropy 2019, 21, 705, a formalism aiming at describing macroscopic quantum fields, dubbed Reduced State of the Field (RSF), was envisaged. While, in the original work, a proper notion of entropy for macroscopic fields, together with their dynamical equations, was derived, here, we expand thermodynamic analysis of the RSF, discussing the notion of heat, solving dynamical equations in various regimes of interest, and showing the thermodynamic implications of these solutions.

quant-ph↗
arXiv2021

Entropic uncertainty relations for mutually unbiased periodic coarse-grained observables resemble their discrete counterparts

One of the most important and useful entropic uncertainty relations concerns a $d$ dimensional system and two mutually unbiased measurements. In such a setting, the sum of two information entropies is lower bounded by $\ln d$. It has recently been shown that projective measurements subject to operational mutual unbiasedness can also be constructed in a continuous domain, with the help of periodic coarse graining. Here we consider the whole family of Rényi entropies applied to these discretized observables and prove that such a scheme does also admit the uncertainty relation mentioned above.

quant-ph↗
arXiv2021

Periodic discretized continuous observables are neither continuous nor discrete

Most of the fundamental characteristics of quantum mechanics, such as non-locality and contextuality, are manifest in discrete, finite-dimensional systems. However, many quantum information tasks that exploit these properties cannot be directly adapted to continuous-variable systems. To access these quantum features, continuous quantum variables can be made discrete by binning together their different values, resulting in observables with a finite number "$d$" of outcomes. While direct measurement indeed confirms their manifestly discrete character, here we employ a salient feature of quantum physics known as mutual unbiasedness to show that such coarse-grained observables are in a sense neither continuous nor discrete. Depending on $d$, the observables can reproduce either the discrete or the continuous behavior, or neither. To illustrate these results, we present an example for the construction of such measurements and employ it in an optical experiment confirming the existence of four mutually unbiased measurements with $d = 3$ outcomes in a continuous variable system, surpassing the number of mutually unbiased continuous variable observables.

quant-ph↗
arXiv2021

Comment on "Fluctuations in Extractable Work Bound the Charging Power of Quantum Batteries"

In the abstract of~[Phys. Rev. Lett. {\bf 125}, 040601 (2020)] one can read that: [...]{\it to have a nonzero rate of change of the extractable work, the state $ρ_\mathcal{W}$ of the battery cannot be an eigenstate of a "free energy operator", defined by $\mathcal{F}=H_\mathcal{W}+β^{-1}\log ρ_\mathcal{W}$, where $H_\mathcal{W}$ is the Hamiltonian of the battery and $β$ is the inverse temperature} [...]. Contrarily to what is presented below Eq.~(17) of the paper, we observe that the above conclusion does not hold when the battery is subject to nonunitary dynamics.

quant-ph↗
arXiv2020

Five open problems in quantum information

We identify five selected open problems in the theory of quantum information, which are rather simple to formulate, were well-studied in the literature, but are technically not easy. As these problems enjoy diverse mathematical connections, they offer a huge breakthrough potential. The first four concern existence of certain objects relevant for quantum information, namely a family of symmetric informationally complete generalized measurements in an infinite sequence of dimensions, mutually unbiased bases in dimension six, absolutely maximally entangled states for four subsystems with six levels each and bound entangled states with negative partial transpose. The fifth problem requires checking whether a certain state of a two-ququart system is 2-copy distillable. An award for solving each of them is announced.

quant-ph↗
arXiv2020

Algorithmic approach to Cosmological Coherent State Expectation Values in LQG

In the lattice approach to Loop Quantum Gravity on a fixed graph computations tend to be involved and are rarely analytically manageable. But, when interested in the expectation values of coherent states on the lattice which are sharply peaked on isotropic, flat cosmology several simplifications are possible which reduce the computational effort. We present a step-by-step algorithm resulting in an analytical expression including up to first order corrections in the spread of the state. The algorithm is developed in such a way that it makes the computation straightforward and easy to be implementable in programming languages such as Mathematica. Exemplarily, we demonstrate how the algorithm streamlines the road to obtain the expectation value of the euclidean part of the scalar constraint and as a consistency check perform the analytic computation as well. To showcase further applications of the algorithm, we investigate the fate of the effective dynamics program custom in Loop Cosmology and find that the next-to-leading order corrections can {\it not} be used as corrections for an effective Hamiltonian.

gr-qc↗
arXiv2020

Stabilizing entanglement in two-mode Gaussian states

We analyze the stabilizability of entangled two-mode Gaussian states in three benchmark dissipative models: local damping, dissipators engineered to preserve two-mode squeezed states, and cascaded oscillators. In the first two models, we determine principal upper bounds on the stabilizable entanglement, while in the last model, arbitrary amounts of entanglement can be stabilized. All three models exhibit a tradeoff between state entanglement and purity in the entanglement maximizing limit. Our results are derived from the Hamiltonian-independent stabilizability conditions for Gaussian systems. Here, we sharpen these conditions with respect to their applicability.

quant-ph↗
arXiv2019

Bounding the sets of classical and quantum correlations in networks

We present a method that allows the study of classical and quantum correlations in networks with causally-independent parties, such as the scenario underlying entanglement swapping. By imposing relaxations of factorization constraints in a form compatible with semidefinite programming, it enables the use of the Navascués-Pironio-Acín hierarchy in complex quantum networks. We first show how the technique successfully identifies correlations not attainable in the entanglement-swapping scenario. Then we use it to show how the nonlocal power of measurements can be activated in a network: there exist measuring devices that, despite being unable to generate nonlocal correlations in the standard Bell scenario, provide a classical-quantum separation in an entanglement swapping configuration.

quant-ph↗
arXiv2019

Gravitational mass of composite systems

The equivalence principle in combination with the special relativistic equivalence between mass and energy, $E=mc^2$, is one of the cornerstones of general relativity. However, for composite systems a long-standing result in general relativity asserts that the passive gravitational mass is not simply equal to the total energy. This seeming anomaly is supported by all explicit derivations of the dynamics of bound systems, and is only avoided after time-averaging. Here we rectify this misconception and derive from first principles the correct gravitational mass of a generic bound system in an external gravitational field. Our results clarify a lasting conundrum in general relativity and show how the weak and strong equivalence principles naturally manifest themselves for composite systems. The results are crucial for describing new effects due to the quantization of the interaction between gravity and composite systems.

gr-qc↗
arXiv2019

Quantum correlations and complementarity of vectorial light fields

We explore quantum correlations of general vector-light fields in multislit interference and show that the $n$th-order field-coherence matrix is directly linked with the reduced $n$-photon density matrix. The connection is utilized to examine photon wave-particle duality in the double-slit configuration, revealing that there is a hidden information-theoretic contribution that complements the standard inequality associated with such duality by transforming it into a strict equality, a triality identity. We also establish a general quantum complementarity relation among the field correlations and the particle correlations which holds for any number of slits, correlation orders, and vector-light states. The framework that we advance hence uncovers fundamental physics about quantum interference.

quant-ph↗
arXiv2019

Pauli semigroups and unistochastic quantum channels

We adopt the perspective of similarity equivalence, in gate set tomography called the gauge, to analyze various properties of quantum operations belonging to a semigroup, $Φ= e^{{\cal L}t}$,and therefore given through the Lindblad operator. We first observe that the non unital part of the channel decouples from the time evolution. Focusing on unital operations we restrict our attention to the single-qubit case, showing that the semigroup embedded inside the tetrahedron of Pauli channels is bounded by the surface composed of product probability vectors and includes the identity map together with the maximally depolarizing channel. Consequently, every member of the Pauli semigroup is unitarily equivalent to a unistochastic map, describing a coupling with one-qubit environment initially in the maximally mixed state, determined by a unitary matrix of order four.

quant-ph↗