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Classical chaos is marked by an extreme sensitivity to initial conditions, where infinitesimally close trajectories separate exponentially over time. In quantum mechanics, however, unitary evolution and the uncertainty principle preclude…
A standard method to obtain information on a quantum state is to measure marginal distributions along many different axes in phase space, which forms a basis of quantum state tomography. We theoretically propose and experimentally…
In this paper, we use the characteristic function, i.e., the Fourier transform of the Glauber-Sudarshan phase-space distribution, to find the degree of nonclassicality of a given state. This degree of nonclassicality quantifies the…
The D-CTC condition, introduced by David Deutsch as a condition to be fulfilled by analogues for processes of quantum systems in the presence of closed timelike curves, is investigated for classical statistical (non-quantum) bi-partite…
Continuous-variable quantum systems are foundational to quantum computation, communication, and sensing. While traditional representations using wave functions or density matrices are often impractical, the tomographic picture of quantum…
We develop a general framework to investigate fluctuations of non-commuting observables. To this end, we consider the Keldysh quasi-probability distribution (KQPD). This distribution provides a measurement-independent description of the…
We devise a method to certify nonclassical features via correlations of phase-space distributions by unifying the notions of quasiprobabilities and matrices of correlation functions. Our approach complements and extends recent results that…
We study the local indistinguishability problem of quantum states. By introducing an easily calculated quantity, non-commutativity, we present an criterion which is both necessary and sufficient for the local indistinguishability of a…
In chaotic quantum systems, an initially localized quantum state can deviate strongly from the corresponding classical phase-space distribution after the Ehrenfest time $t_{\mathrm{E}} \sim \log(\hbar^{-1})$, even in the limit $\hbar \to…
As currently understood since its discovery, the bare Klein-Gordon theory consists of negative quantum probabilities which are considered to be physically meaningless if not outright obsolete. Despite this annoying setback, these negative…
What is the minimal time until a quantum system can exhibit genuine quantum features? To answer this question we derive quantum speed limits for two-time correlation functions arising from statistics of measurements. Generally, these…
The notion of (non)contextuality pertains to sets of properties measured one subset (context) at a time. We extend this notion to include so-called inconsistently connected systems, in which the measurements of a given property in different…
In quantum optics, measurement statistics -- for example, photocounting statistics -- are considered nonclassical if they cannot be reproduced with statistical mixtures of classical radiation fields. We have formulated a necessary and…
We employ the operational quasiprobability (OQ) as a work distribution, which reproduces the Jarzynski equality and yields the average work consistent with the classical definition. The OQ distribution can be experimentally implemented…
The use of quantum information in technology promises to supersede the so-called classical devices used nowadays. Understanding what features are inherently non-classical is crucial for reaching better-than-classical performance. This…
This thesis discusses the young fields of quantum pseudo-randomness and quantum learning algorithms. We present techniques for derandomising algorithms to decrease randomness resource requirements and improve efficiency. One key object in…
We show that postselection offers a nonclassical advantage in metrology. In every parameter-estimation experiment, the final measurement or the postprocessing incurs some cost. Postselection can improve the rate of Fisher information (the…
We report two fundamental experiments on three-level quantum systems (qutrits). The first one tests the simplest task for which quantum mechanics provides an advantage with respect to classical physics. The quantum advantage is certified by…
Nonclassicality, defined in the quantum optical sense, serves as a resource for photon-based quantum technologies. Therefore, certifying the nonclassicality of a quantum state is crucial for gauging its potential for quantum advantage.…
We compare the power of quantum and classical physics in terms of randomness certification from devices which are only partially characterised. We study randomness certification based on state discrimination and take noncontextuality as the…