Martin Plávala

Martin Plávala
  • PhD.
  • Researcher at Leibniz Universität Hannover

About

65
Publications
5,176
Reads
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570
Citations
Current institution
Leibniz Universität Hannover
Current position
  • Researcher
Additional affiliations
July 2024 - present
Leibniz Universität Hannover
Position
  • PostDoc Position
January 2020 - June 2024
University of Siegen
Position
  • PostDoc Position
September 2019 - December 2019
Slovak Academy of Sciences
Position
  • PostDoc Position
Education
April 2017 - November 2018
Comenius University Bratislava
Field of study
  • Mathematical Physics
September 2015 - August 2019
Comenius University Bratislava
Field of study
  • Applied Mathematics
September 2013 - June 2015
Comenius University Bratislava
Field of study
  • Theoretical Physics

Publications

Publications (65)
Preprint
Full-text available
Nonlinear modifications of quantum theory are considered potential candidates for the theory of quantum gravity, with the intuitive argument that since Einstein field equations are nonlinear, quantum gravity should be nonlinear as well. Contextuality is a property of quantum systems that forbids the explanation of prepare-and-measure experiments in...
Preprint
Full-text available
This paper proposes a family of permutation-invariant graph embeddings, generalizing the Skew Spectrum of graphs of Kondor & Borgwardt (2008). Grounded in group theory and harmonic analysis, our method introduces a new class of graph invariants that are isomorphism-invariant and capable of embedding richer graph structures - including attributed gr...
Article
Full-text available
We present a derivation and experimental implementation of a dimension-dependent contextuality inequality to certify both the quantumness and dimensionality of a given system. Existing methods for certification of the dimension of a quantum system can be cheated by using larger classical systems, creating a potential loophole in these benchmarks, o...
Article
Full-text available
Bell nonlocality is a fundamental phenomenon of quantum physics as well as an essential resource for various tasks in quantum information processing. It is known that for the observation of nonlocality the measurements on a quantum system have to be incompatible, but the question of which incompatible measurements are useful, remained open. Here we...
Preprint
Full-text available
Quantum theory exhibits various nonclassical features, such as measurement incompatibility, contextuality, steering, and Bell nonlocality, which distinguish it from classical physics. These phenomena are often studied separately, but they possess deep interconnections. This work introduces a unified mathematical framework based on commuting diagram...
Article
Full-text available
The interface between quantum theory and gravity represents still uncharted territory. Recently, a tabletop experiment has been proposed for witnessing quantum features of gravity: Two masses in an initial superposition of spatially localized states interact only through gravity and it is measured whether the final state is entangled. Here we show...
Preprint
Full-text available
In quantum mechanics, the time evolution of particles is given by the Schr\"odinger equation. It is valid in a nonrelativistic regime where the interactions with the particle can be modelled by a potential and quantised fields are not required. This has been verified in countless experiments when the interaction is of electromagnetic origin, but al...
Preprint
Full-text available
We present a derivation and experimental implementation of a dimension-dependent contextuality inequality to certify both the quantumness and dimensionality of a given system. Existing methods for certification of the dimension of quantum system can be cheated by using larger classical systems, creating a potential loophole in these benchmarks. Our...
Article
Operational contextuality forms a rapidly developing subfield of quantum information theory. However, the characterization of the quantum mechanical entities that fuel the phenomenon has remained unknown with many partial results existing. Here, we present a resolution to this problem by connecting operational contextuality one-to-one with the no-b...
Preprint
Full-text available
Quantum memories are a crucial precondition in many protocols for processing quantum information. A fundamental problem that illustrates this statement is given by the task of channel discrimination, in which an unknown channel drawn from a known random ensemble should be determined by applying it for a single time. In this paper, we characterise t...
Article
Full-text available
We develop the theory of Wigner representations for general probabilistic theories (GPTs), a large class of operational theories that include both classical and quantum theory. The Wigner representations that we introduce are a natural way to describe the theory in terms of some fixed observables; these observables are often picked to be position a...
Article
Full-text available
A separable quantum state shared between parties A and B can be symmetrically extended to a quantum state shared between party A and parties \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69p...
Article
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Quantumness refers to the peculiar and counterintuitive characteristics exhibited by quantum systems. Tsirelson inequalities have emerged as a powerful tool in quantum theory to detect quantumness and entanglement of harmonic oscillators, spins undergoing uniform precession, and anharmonic systems. In this paper we harness the versatility of Tsirel...
Preprint
Full-text available
We construct a convergent family of outer approximations for the problem of optimizing polynomial functions over convex bodies subject to polynomial constraints. This is achieved by generalizing the polarization hierarchy, which has previously been introduced for the study of polynomial optimization problems over state spaces of $C^*$-algebras, to...
Preprint
Full-text available
Operational contextuality forms a rapidly developing subfield of quantum information theory. However, the characterization of the quantum mechanical entities that fuel the phenomenon has remained unknown with many partial results existing. Here, we present a resolution to this problem by connecting operational contextuality one-to-one with the no-b...
Article
We develop a method for semi-device-independent certification of the number of measurements. We achieve this by testing whether Bob's steering equivalent observables can be simulated by k measurements, which we do by testing whether they are k-compatible with separable joint observable. This test can be performed with the aid of hierarchy of semide...
Article
Encoding and decoding are the two key steps in information processing. In this work, we study the encoding and decoding capabilities of operational theories in the context of information-storability game, where the task is to freely choose a set of states from which one state is chosen at random and by measuring the state it must be identified; a c...
Article
Communication scenarios between two parties can be implemented by first encoding messages into some states of a physical system which acts as the physical medium of the communication and then decoding the messages by measuring the state of the system. We show that already in the simplest possible scenarios it is possible to detect a definite, unbou...
Preprint
Full-text available
We investigate joint probabilistic choice rules describing the behavior of two decision makers, each facing potentially distinct menus. These rules are separable when they can be decomposed into individual choices correlated solely through their respective probabilistic choice rules. Despite its significant interest for the study of peer effects, i...
Article
Quantum theory features several phenomena which can be considered as resources for information processing tasks. Some of these effects, such as entanglement, arise in a nonlocal scenario, where a quantum state is distributed between different parties. Other phenomena, such as contextuality, can be observed if quantum states are prepared and then su...
Article
We show that the phase-space formulation of general probabilistic theories can be extended to include a generalized time evolution and that it can describe a nonquantum hydrogenlike system which is stable, has discrete energy levels, and includes the Zeeman effect. This allows us to study dynamical effects such as excitations of the hydrogenlike sy...
Article
We introduce the framework of general probabilistic theories (GPTs for short). GPTs are a class of operational theories that generalize both finite-dimensional classical and quantum theory, but they also include other, more exotic theories, such as the boxworld theory containing Popescu–Rohrlich boxes. We provide in-depth explanations of the basic...
Preprint
Full-text available
Quantumness refers to the peculiar and counterintuitive characteristics exhibited by quantum systems. Tsirelson inequalities have emerged as a powerful tool in quantum theory to detect quantumness and entanglement of harmonic oscillators, spins undergoing uniform precession, and anharmonic systems. In this paper, we harness the versatility of Tsire...
Preprint
Full-text available
Communication scenarios between two parties can be implemented by first encoding messages into some states of a physical system which acts as the physical medium of the communication and then decoding the messages by measuring the state of the system. We show that already in the simplest possible scenarios it is possible to detect a definite, unbou...
Preprint
Full-text available
We develop a method for semi-device-independent certification of number of measurements. We achieve this by testing whether Bob's steering equivalent observables (SEO) can be simulated by k measurements, which we do by testing whether they are k-compatible with separable joint observable. This test can be performed with the aid of hierarchy of semi...
Article
High-dimensional quantum steering can be seen as a test for the dimensionality of entanglement, where the devices at one side are not characterized. As such, it is an important component in quantum informational protocols that make use of high-dimensional entanglement. Although it has been recently observed experimentally, the phenomenon of high-di...
Preprint
Full-text available
We develop the theory of Wigner representations for a large class of operational theories that include both classical and quantum theory. The Wigner representations that we introduce are a natural way to describe the theory in terms of some fixed observables; these observables are often picked to be position and momentum or spin observables. This a...
Preprint
Full-text available
We analyze choice behavior using Dynamic Random Utility Model (DRUM). Under DRUM, each consumer or decision-maker draws a utility function from a stochastic utility process in each period and maximizes it subject to a menu. DRUM allows for unrestricted time correlation and cross-section heterogeneity in preferences. We fully characterize DRUM when...
Article
Full-text available
No-broadcasting theorem is one of the most fundamental results in quantum information theory; it guarantees that the simplest attacks on any quantum protocol, based on eavesdropping and copying of quantum information, are impossible. Due to the fundamental importance of the no-broadcasting theorem, it is essential to understand the exact boundaries...
Preprint
Full-text available
The success of quantum theory is founded on the ability to model a wide range of physical systems and extract corresponding predictions. While the quantum models are subject to experimental tests and subsequent refinements, the language of quantum theory itself is generally taken as fixed. But quantum theory is only a distinct instance within the c...
Preprint
Full-text available
High-dimensional quantum steering can be seen as a test for the dimensionality of entanglement, where the devices at one side are not characterized. As such, it is an important component in quantum informational protocols that make use of high-dimensional entanglement. Although it has been recently observed experimentally, the phenomenon of high-di...
Preprint
Full-text available
Quantum theory features several phenomena which can be considered as resources for information processing tasks. Some of these effects, such as entanglement, arise in a non-local scenario, where a quantum state is distributed between different parties. Other phenomena, such as contextuality can be observed, if quantum states are prepared and then s...
Preprint
Full-text available
No-broadcasting theorem is one of the most fundamental results in quantum information theory; it guarantees that the simplest attacks on any quantum protocol, based on eavesdropping and copying of quantum information, are impossible. Due to the fundamental importance of the no-broadcasting theorem, it is essential to understand the exact boundaries...
Preprint
Full-text available
A separable quantum state shared between parties $A$ and $B$ can be symmetrically extended to a quantum state shared between party $A$ and parties $B_1,\ldots ,B_k$ for every $k\in\mathbf{N}$. Quantum states that are not separable, i.e., entangled, do not have this property. This phenomenon is known as "monogamy of entanglement". We show that monog...
Article
We prove that given any two general probabilistic theories (GPTs) the following are equivalent: (i) each theory is nonclassical, meaning that neither of their state spaces is a simplex; (ii) each theory satisfies a strong notion of incompatibility equivalent to the existence of "superpositions"; and (iii) the two theories are entangleable, in the s...
Article
Full-text available
We investigate the connection between steering and contextuality in general probabilistic theories. We show that for a class of bipartite states the steerability of the state by a given set of measurements is equivalent to non-existence of preparation noncontextual hidden variable model for certain restricted theory constructed from the given state...
Article
We show how to construct general probabilistic theories that contain an energy observable dependent on position and momentum. The construction is in accordance with classical and quantum theory and allows for physical predictions, such as the probability distribution for position, momentum, and energy. We demonstrate the construction by formulating...
Preprint
Full-text available
We investigate the connection between steering and contextuality in general probabilistic theories. We show that for a class of bipartite states the steerability of the state by given set of measurements is equivalent to non-existence of preparation noncontextual hidden variable model for certain restricted theory constructed from the given state a...
Preprint
Full-text available
We prove that any two general probabilistic theories (GPTs) are entangleable, in the sense that their composite exhibits either entangled states or entangled measurements, if and only if they are both non-classical, meaning that neither of the state spaces is a simplex. This establishes the universal equivalence of the (local) superposition princip...
Article
Full-text available
Given two quantum channels, we examine the task of determining whether they are compatible—meaning that one can perform both channels simultaneously but, in the future, choose exactly one channel whose output is desired (while forfeiting the output of the other channel). Here, we present several results concerning this task. First, we show it is eq...
Article
Full-text available
We solve a long-standing conjecture by Barker, proving that the minimal and maximal tensor products of two finite-dimensional proper cones coincide if and only if one of the two cones is generated by a linearly independent set. Here, given two proper cones \({\mathcal {C}}_1\), \({\mathcal {C}}_2\), their minimal tensor product is the cone generate...
Preprint
Full-text available
We introduce the framework of general probabilistic theories (GPTs for short). GPTs are a class of operational theories that generalize both finite-dimensional classical and quantum theory, but they also include other, more exotic theories, such as the boxworld theory containing Popescu-Rohrlich boxes. We provide in-depth explanations of the basic...
Preprint
Full-text available
We construct a toy model for the harmonic oscillator that is neither classical nor quantum. The model features a discrete energy spectrum, a ground state with sharp position and momentum, an eigenstate with non-positive Wigner function as well as a state that has tunneling properties. The underlying formalism exploits that the Wigner-Weyl approach...
Article
Full-text available
We construct implementations of the PR-box using quantum and classical channels as state spaces. In both cases our constructions are very similar and they share the same idea taken from general probabilistic theories and the square state space model. We construct all quantum qubit channels that maximally violate a given CHSH inequality, we show tha...
Preprint
Full-text available
Given two quantum channels, we examine the task of determining whether they are compatible - meaning that one can perform both channels simultaneously but, in the future, choose exactly one channel whose output is desired (while forfeiting the output of the other channel). We show several results concerning this task. First, we show it is equivalen...
Article
Full-text available
It is shown that Popescu-Rohrlich nonlocal boxes (beating the Tsirelson bound for Bell inequality) do exist in the existing structures of both quantum and classical theory. In particular, we design an explicit example of measure-and-prepare nonlocal (but no-signaling) channel being the realization of nonlocal and no-signaling Popescu-Rohrlich box w...
Preprint
We solve a long-standing conjecture by Barker, proving that the minimal and maximal tensor products of two finite-dimensional proper cones coincide if and only if one of the two cones is classical (i.e. simplex-based). Here, given two proper cones $C_1$, $C_2$, their minimal tensor product is the cone generated by products of the form $x_1 \otimes...
Preprint
Full-text available
We construct implementations of PR boxes using quantum and classical channels as state spaces. In both cases our constructions are very similar and they share the same idea taken from general probabilistic theories and the square state space model. We construct all quantum qubit channels that maximally violate a given CHSH inequality, we show that...
Article
Full-text available
In quantum theory, the no-information-without-disturbance and no-free-information theorems express that those observables that do not disturb the measurement of another observable and those that can be measured jointly with any other observable must be trivial, i.e., coin tossing observables. We show that in the framework of general probabilistic t...
Article
Full-text available
The aim of this paper is to show that there can be either only one or uncountably many contexts in any spectral effect algebra, answering a question posed in [S. Gudder, Convex and Sequential Effect Algebras, (2018), arXiv:1802.01265]. We also provide some results on the structure of spectral effect algebras and their state spaces and investigate t...
Preprint
Full-text available
The aim of this paper is to show that there can be either only one or uncountably many contexts in any spectral effect algebra, answering a question posed in [S. Gudder, Convex and Sequential Effect Algebras, (2018), arXiv:1802.01265]. We also provide some results on the structure of spectral effect algebras and their state spaces and investigate t...
Preprint
Full-text available
In quantum theory, the no-information-without-disturbance and no-free-information theorems express that those observables that do not disturb the measurement of another observable and those that can be measured jointly with any other observable must be trivial, i.e., coin tossing observables. We show that in the framework of general probabilistic t...
Article
The incompatibility of measurements is a strange feature of Quantum theory that forbids us from performing two measurements at the same time. Usually presented in the form of Heisenberg’s uncertainty principle, it is one of the more inexplicable and counterintuitive features of quantum theory. In the following article I will show you a simple model...
Article
Full-text available
We derive general conditions for the compatibility of channels in general probabilistic theory. We introduce formalism that allows us to easily formulate steering by channels and Bell nonlocality of channels as generalizations of the well-known concepts of steering by measurements and Bell nonlocality of measurements. The generalization does not fo...
Preprint
Full-text available
It is shown that Popescu-Rohrlich nonlocal boxes (beating the Tsirelson bound for Bell inequality) do exist in the existing structures of both quantum and classical theory. In particular, we design an explicit example of measure-and-prepare nonlocal (but no-signaling) channel being the realization of nonlocal and no-signaling Popescu-Rohrlich box w...
Article
Full-text available
We formulate the necessary and sufficient conditions for the existence of a pair of maximally incompatible two-outcome measurements in a finite-dimensional general probabilistic theory. The conditions are on the geometry of the state space; they require the existence of two pairs of parallel exposed faces with an additional condition on their inter...
Preprint
Full-text available
We derive general conditions for the compatibility of channels in general probabilistic theory. We introduce formalism that allows us to easily formulate steering by channels and Bell nonlocality of channels as generalizations of the well-known concepts of steering by measurements and Bell nonlocality of measurements. The generalization does not fo...
Preprint
Full-text available
We formulate the necessary and sufficient conditions for the existence of a pair of maximally incompatible two-outcome measurements in a finite dimensional General Probabilistic Theory. The conditions are on the geometry of the state space, they require existence of two pairs of parallel exposed faces with additional condition on their intersection...
Article
Full-text available
We find optimality conditions for testers in discrimination of quantum channels. These conditions are obtained using semidefinite programming and are similar to optimality conditions for POVMs obtained by Holevo for ensembles of quantum states. We get a simple condition for existence of an optimal tester with any given input state with maximal Schm...
Article
Full-text available
We study the compatibility of measurements on finite-dimensional compact convex state space in the framework of general probabilistic theory. Our main emphasis is on formulation of necessary and sufficient conditions for two-outcome measurements to be compatible and we use these conditions to show that there exist incompatible measurements whenever...
Preprint
Full-text available
We study the compatibility of measurements on finite-dimensional compact convex state space in the framework of general probabilistic theory. Our main emphasis is on formulation of necessary and sufficient conditions for two-outcome measurements to be compatible and we use these conditions to show that there exist incompatible measurements whenever...
Preprint
We find optimality conditions for testers in discrimination of quantum channels. These conditions are obtained using semidefinite programming and are similar to optimality conditions for POVMs obtained by Holevo for ensembles of quantum states. We get a simple condition for existence of an optimal tester with any given input state with maximal Schm...
Article
Full-text available
We show that the solution of the Friedmann equation for a universe with matter and cosmological constant is stable with respect to small changes in the density parameter Ω0. We find an expression for the difference of the solution with Ω0 = 1 and with Ω0 = 1+ε. We use the estimate of the difference to obtain an upper bound on the difference of ages...

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