arXiv subjects

Konrad Schlichtholz

Publications and source records attributed to Konrad Schlichtholz.

18 recordsLinked to original sources

arXiv2026

Multipartite Bell-GHZ nonclassicality from interwoven frustrated down-conversion

We present a theory of an interference process that starts with N coherently pumped two-mode parametric down-conversion (PDC) sources, whose output modes are directed to N observers such that each observer receives modes from two different source crystals. Each observation station is equipped with a locally controlled PDC crystal, coherently pumped with the source crystals, whose output modes are perfectly aligned with the input modes from the source PDCs. By varying the local phases of the input modes, perfect 2N-photon interference can be observed in 2N single-photon registrations, one in each output mode of these N local PDCs. The interference results from the indistinguishability of the origins of the detected 2N photons: either they all originate from the source PDCs or from the local PDCs. Bell-GHZ nonclassicality of the process emerges when one also considers situations in which at least one of the local PDC processes is blocked. In such cases, the 2N-photon interference disappears. A "lifted" Clauser-Horne inequality is violated when its sole negative term, involving all observers with all local pumps active, is tuned to maximal destructive interference, while all other terms involve settings in which one of the local pumps is off.

quant-ph↗

arXiv2026

Unquestionable Bell theorem for interwoven frustrated down conversion processes

Interwoven frustrated parametric down conversion (PDC) processes produce interference effects based on path identity [Phys. Rev. Lett. 118, 080401 (2017)]. In this letter we show Bell nonclassicality of the processes: a proper violation of the Clauser-Horne inequality when the local measurements are controlled by on-off switching of the final local PDC processes. Such a non-standard approach is needed because if only the local phase shifts are used for the measurement settings, as done in the experiment reported in Sci. Adv. 11, 1794 (2025), there exists a local realistic model of the interference, which we present in this letter. Nevertheless, the reported destructive interference is deep enough to violate the inequality when using on-off switching, so our result establishes a firm footing for non-classicality of the new interferometry, in both theory and experiment. The on-off approach to Bell analysis of path-identity-based interference forms a new platform for seeking new highly counterintuitive quantum phenomena.

quant-ph↗

arXiv2026

"Nonlocality-of-a-single-photon" based Quantum Key Distribution and Random Number Generation schemes and their device-independent security analysis

The question of ``non-locality of a single photon'', which started with a paper by Tan, Walls and Collett (TWC, 1991) stirred a thirty years long debate. This hampered attempts to use the TWC interferometric scheme in quantum cryptography. The scheme involves a single photon 50-50 beam-split into two modes propagating to two spatially separated observation stations at which weak homodyne measurements are made. The physics and non-classicality of such an arrangement has been understood only recently, and points out that an unquestionable Bell non-classicality, as was suggested by Hardy (1994), can be observed when the local measurement settings differ by the weak local oscillator being on or off, and additionally the homodyning for the on case is not balanced. Based on that, we present a single-photon based device-independent quantum key distribution scheme secure even against no-signaling eavesdropping. In our protocol the random bits of the cryptographic key are obtained by measurements on the single photon, that is for off settings at both Alice and Bob sides, while the security is positively tested if for eavesdropping testing runs one observes a violation of a specific Bell inequality involving the on and off weak homodyne measurements as alternative local settings. The security analysis presented here is based on a decomposition of the correlations into extreme points of a no-signaling polytope, which allows for identification of the optimal strategy for any eavesdropping constrained only by the no-signaling principle. For this strategy, the key rate is calculated, which is then connected with the violation of a specific Clauser-Horne inequality. We also adapt this analysis to propose a self-testing quantum random number generator based on the old idea that employs the randomness of reflection and transmission events of a quantum light impinged on a 50-50 beamsplitter.

quant-ph↗

arXiv2025

On physicality of electromagnetic potential from causal structure of flux quantization

Recent work by Vaidman [Phys. Rev. A 86,040101 (2012)] showed that Aharonov-Bohm effect can be explained in terms of local fields, thus effectively restating an old problem of physicality of potentials. In this work, we propose an argument demonstrating the physicality of electromagnetic potential (upon the assumption of locality) based on the causal structure in flux quantization setup. Crucially, we discuss the fundamental difference between the considered setup and the Aharonov-Bohm experiment that allows for avoiding Vaidman's loophole in our scenario.

quant-ph↗

arXiv2025

Quantum-inspired exoplanet detection in the presence of experimental imperfections

Ideal spatial demultiplexing (SPADE) is proven to be a quantum-optimal tool for exoplanet detection, i.e., asymmetric source discrimination. However, recent investigations into the related problems of separation estimation and symmetric source discrimination showed its efficiency to be limited in the presence of noise. In this work, we use analytical tools to scrutinize the practical applicability of SPADE and derive the associated optimal decision strategy for exoplanet detection in the presence of experimental imperfections. On the one hand, we find that the probability of detection of noisy SPADE has the same scaling with planet-star separation and relative brightness as conventional techniques, such as direct imaging and coronagraphs. On the other hand, we prove that, due to a superior scaling coefficient under realistic noise conditions, SPADE remains the most efficient method for practical exoplanet detection in the sub-Rayleigh regime.

astro-ph.IM↗

arXiv2025

Unitary operator bases as universal averaging sets

We provide a generalization of the idea of unitary designs to cover finite averaging over much more general operations on quantum states. Namely, we construct finite averaging sets for averaging quantum states over arbitrary reductive Lie groups, on condition that the averaging is performed uniformly over the compact component of the group. Our construction comprises probabilistic mixtures of unitary 1-designs on specific operator subspaces. Provided construction is very general, competitive in the size of the averaging set when compared to other known constructions, and can be efficiently implemented in the quantum circuit model of computation.

quant-ph↗

arXiv2024

Formal relation between Pegg-Barnett and Paul quantum phase frameworks

The problem of defining a hermitian quantum phase operator is nearly as old as quantum mechanics itself. Throughout the years, a number of solutions was proposed, ranging from abstract operator formalisms to phase-space methods. In this work, we make an explicit connection between two of the most prominent approaches, by proving that the probability distribution of phase in the Paul formalism follows exactly from the Pegg-Barnett formalism by combining the latter with the quantum limited amplifier channel. Our findings suggest that the Paul framework may be viewed as a semi-classical limit of the Pegg-Barnett approach.

quant-ph↗

arXiv2024

Superresolving optical ruler based on spatial mode demultiplexing for systems evolving under Brownian motion

The development of superresolution techniques, i.e., allowing for efficient resolution below the Rayleigh limit, became one of the important branches in contemporary optics and metrology. Recent findings show that perfect spatial mode demultiplexing (SPADE) into Hermite-Gauss modes followed by photon counting enables one to reach the quantum limit of precision in the task of estimation of separation between two weak stationary sources in the sub-Rayleigh regime. In order to check the limitations of the method, various imperfections such as misalignment or crosstalk between the modes were considered. Possible applications of the method in microscopy call for the adaptive measurement scheme, as the position of the measured system can evolve in time, causing non-negligible misalignment. In this paper, we examine the impact of Brownian motion of the center of the system of two weak incoherent sources of arbitrary relative brightness on adaptive SPADE measurement precision limits. The analysis is carried out using Fisher information, from which the limit of precision can be obtained by Cramér-Rao bound. As a result, we find that Rayleigh's curse is present in such a scenario; however, SPADE measurement can outperform perfect direct imaging. What is more, a suitable adjustment of the measurement time between alignments allows measurement with near-optimal precision.

quant-ph↗

arXiv2024

Superresolution in separation estimation between two dynamic incoherent sources using spatial demultiplexing

Achieving resolution in the sub-Rayleigh regime (superresolution) is one of the rapidly developing topics in quantum optics and metrology. Recently, it was shown that perfect measurement based on spatial mode demultiplexing (SPADE) in Hermite-Gauss modes allows one to reach the quantum limit of precision for estimation of separation between two weak incoherent stationary sources. Since then, different imperfections such as misalignment or crosstalk between modes have been studied to check how this result translates into more realistic experimental setups. In this paper, we consider another deviation from the perfect setup by discarding the assumption about the stationarity of the sources. This is relevant for example for astrophysical applications where planets necessarily orbit around the star. We analyze two examples of dynamics: rotations and oscillations, showing the robustness of the SPADE-based measurement against them. The analysis is based on Fisher information, which allows one to obtain the precision limit through Cramér-Rao bound. Furthermore, we formulate a measurement algorithm that allows for the reduction of one parameter for estimation (system orientation angle) in the stationary sources scenario, maintaining the measurement precision despite the lack of knowledge about this parameter.

quant-ph↗

arXiv2024

Open dynamics of entanglement in mesoscopic bosonic systems

A key issue in Quantum Information is finding an adequate description of mesoscopic systems that is simpler than full quantum formalism yet retains crucial information about non-classical phenomena like entanglement. In particular, the study of fully bosonic systems undergoing open evolution is of great importance for the advancement of photonic quantum computing and communication. In this paper, we propose a mesoscopic description of such systems based on boson number correlations. This description allows for tracking Markovian open evolution of entanglement of both non-Gaussian and Gaussian states and their sub-Poissonian statistics. It can be viewed as a generalization of the reduced state of the field formalism [Entropy 2019, 21(7), 705], which by itself does not contain information about entanglement. As our approach adopts the structure of the description of two particles in terms of first quantization, it allows for broad intuitive usage of known tools. Using the proposed formalism, we show the robustness of entanglement against low-temperature damping for four-mode bright squeezed vacuum state and beam-splitted single photon. We also present a generalization of the Mandel Q parameter. Building upon this, we show that the entanglement of the state obtained by beam splitting of a single occupied mode is fully inherited from sub-Poissonian statistics of the input state.

quant-ph↗

arXiv2024

Relativistically invariant encoding of quantum information revisited

In this work, we provide a detailed analysis of the issue of encoding of quantum information which is invariant with respect to arbitrary Lorentz transformations. We significantly extend already known results and provide compliments where necessary. In particular, we introduce novel schemes for invariant encoding which utilize so-called pair-wise helicity -- a physical parameter characterizing pairs of electric-magnetic charges. We also introduce new schemes for ordinary massive and massless particles based on states with fixed total momentum, in contrast to all protocols already proposed, which assumed equal momenta of all the particles involved in the encoding scheme. Moreover, we provide a systematic discussion of already existing protocols and show directly that they are invariant with respect to Lorentz transformations drawn according to any distribution, a fact which was not manifestly shown in previous works.

quant-ph↗

arXiv2023

Application range of crosstalk-affected spatial demultiplexing for resolving separations between unbalanced sources

Superresolution is one of the key issues at the crossroads of contemporary quantum optics and metrology. Recently, it was shown that for an idealized case of two balanced sources, spatial mode demultiplexing (SPADE) achieves resolution better than direct imaging even in the presence of measurement crosstalk [Phys. Rev. Lett. 125, 100501 (2020)]. In this work, we consider arbitrarily unbalanced sources and provide a systematic analysis of the impact of crosstalk on the resolution obtained from SPADE. As we dissect, in this generalized scenario, SPADE's effectiveness depends non-trivially on the strength of crosstalk, relative brightness and the separation between the sources. In particular, for any source imbalance, SPADE performs worse than ideal direct imaging in the asymptotic limit of vanishing source separations. Nonetheless, for realistic values of crosstalk strength, SPADE is still the superior method for several orders of magnitude of source separations.

quant-ph↗

arXiv2023

Generalization of Gisin's Theorem to Quantum Fields

We generalize Gisin's theorem on the relation between the entanglement of pure states and Bell non-classicality to the case of mode entanglement of separated groups of modes of quantum fields extending the theorem to cover also states with undefined particle number. We show that any pure state of the field which contains entanglement between two groups of separated modes violates some Clauser-Horne inequality. In order to construct the observables leading to a violation in the first step, we show an isomorphism between the Fock space built from a single-particle space involving two separated groups of modes and a tensor product of two abstract separable Hilbert spaces spanned by formal monomials of creation operators. In the second step, we perform a Schmidt decomposition of a given entangled state mapped to this tensor product space and then we map back the obtained Schmidt decomposition to the original Fock space of the system under consideration. Such obtained Schmidt decomposition in Fock space allows for construction of observables leading to a violation of the Clauser-Horne inequality. We also show that our generalization of Gisin's theorem holds for the case of states on non-separable Hilbert spaces, which physically represent states with actually infinite number of particles. Such states emerge, for example, in the discussion of quantum phase transitions. Finally, we discuss the experimental feasibility of constructed Bell test and provide a necessary condition for realizability of this test within the realm of passive linear optics.

quant-ph↗

arXiv2023

No-go for fully unitary quantum mechanics from Bell's Theorem; comment on "Physics and Metaphysics of Wigner's Friends: Even performed pre-measurements have no results''

The purpose of this comment is to show that a reinterpretation of the results from the Letter: "Physics and Metaphysics of Wigner's Friends: Even performed pre-measurements have no results" allows for reaching the conclusion "pre-measurements have no resul" [arXiv:2003.07464] based only on postulates of quantum mechanics without additional assumptions on irreversibility. Additionally, with supplementary reasoning based on Bell's theorem, one can show that unitary decoherence cannot be solely responsible for the quantum-to-classical transition, and an additional irreversibility model is required for its full description. Consequently, the black hole information paradox has no physical basis.

quant-ph↗

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↗

arXiv2022

Bosonic fields in states with undefined particle numbers possess detectable non-contextuality features, plus more

Most of the paradoxical, for the classical intuition, features of quantum theory were formulated for situations which involve a fixed number of particles. While one can now find a formulation of Bell's theorem for quantum fields, a Kochen-Specker-type reasoning is usually formulated for just one particle, or like in the case of Peres-Mermin square for two. A question emerges. Is it possible to formulate a contextuality proof for situation in which the numbers of particles are fundamentally undefined? We address this problem for bosonic fields. We introduce a representation of the $\mathfrak{su}(2)$ algebra in terms of boson number states in two modes that allows us to assess nonclassicality of states of bosonic fields. As a figure of merit of a nonclassical behaviour we analyze first of all contextuality, and we show that the introduced observables are handy and efficient to reveal violation of local realism, and to formulate entanglement indicators. We construct a method which extends the Kochen-Specker contextuality to bosonic quantum fields. A form of an inequality is derived using a suitable version of the Peres-Mermin square. The entanglement indicators use a witness built with specially defined Pauli-like observables. Finally, Bell-nonclassicality is discussed: an inequality that involves the expectation values of pairs of the Pauli-like operators is presented. The introduced indicators are shown to be effective, e.g. they reveal nonclassicality in situaations involving undefined boson numbers. This is shown via quantum optical examples of the $2\times 2$ bright squeezed vacuum state, and a recently discussed bright-GHZ state resulting from multiple three photon emissions in a parametric process.

quant-ph↗

arXiv2021

Simplified Quantum Optical Stokes observables and Bell's Theorem

We introduce a simplified form of Stokes operators for quantum optical fields that involve the known concept of binning. Behind polarization analyzer photon numbers (more generally intensities) are measured. If the value obtained in one of the outputs, say H, is greater the than in the other one, V, then the value of the simplified Stokes operator is, say, 1, otherwise it is -1. For equal photon numbers we put 0. Such observables do not have all properties of the Stokes operators, but surprisingly can be employed in Bell type measurements, involving polarization analyzers. They are especially handy for states of undefined number of photons, e.g. squeezed vacuum. We show that surprisingly they can lead to quite robust violations of associated Bell inequalities.

quant-ph↗

arXiv2020

Non-classicality of bright GHZ-like radiation of an optical parametric source

With the emerging possibility to obtain emissions of triples of GHZ-entangled photons via a direct parametric generation we study here bright emissions of this kind which involve higher order emissions of two triples, three triples, etc. Such states would constitute a natural generalization of the four mode (two beams plus polarization) squeezed vacuum. We have three beam process of emission generalized bright GHZ states, which a are superpositions of one, two, three, and so on GHZ entangled triples of photons. We show how to avoid technical difficulties related with straight ahead generalization of the usual description of parametric down conversion. Using Pade approximation we turn first terms of the non-converging perturbation expansion into elements of conversing series. This allows us to study non-classicality of the new bright generalized GHZ states.

quant-ph↗