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We consider the additive white Gaussian noise channels. We prove that the error probability of decoding tends to one exponentially for rates above the capacity and derive the optimal exponent function. We shall demonstrate that the…
We consider the quantum measurement properties of a driven cavity with a Kerr-type nonlinearity which is used to amplify a dispersively coupled input signal. Focusing on an operating regime which is near a bifurcation point, we derive…
Adaptive measurements were recently shown to significantly improve the performance of quantum state tomography. Utilizing information about the system for the on-line choice of optimal measurements allows to reach the ultimate bounds of…
Searching for a weak signal at an unknown frequency is a canonical task in experiments probing fundamental physics such as gravitational-wave observatories and ultra-light dark matter haloscopes. These state-of-the-art sensors are limited…
In this article, I show that a recent family of quantum algorithms, based on the quantum amplitude amplification algorithm, can be used to describe a cognitive heuristic called availability bias. The amplitude amplification algorithm is…
The necessary and sufficient conditions of optimality of the decoding of quantum signals minimizing the Bayesian risk are generalized for the Shannon mutual information criteria. It is shown that for a linear channel with Gaussian boson…
We consider two variants of a quantum-statistical generalization of the Cramer-Rao inequality that establishes an invariant lower bound on the mean square error of a generalized quantum measurement. The proposed complex variant of this…
There are processes that cannot generate entanglement but may, nevertheless, amplify entanglement already present in a system. Here, we show that a non-entangling operation can increase the Schmidt number of a quantum state only if it can…
Quantum estimation theory is a reformulation of random statistical theory with the modern language of quantum mechanics. In fact, the density operator plays a role similar to that of probability distribution functions in classical…
Squeezing experiments which are capable of creating a minimum uncertainty state during the nonlinear process, for example optical parametric amplification, are commonly used to produce light far below the quantum noise limit. This report…
The certification of randomness is essential for both fundamental science and information technologies. Unlike traditional random number generators, randomness obtained from nonlocal correlations is fundamentally guaranteed to be…
The maximum-likelihood principle unifies inference of quantum states and processes from experimental noisy data. Particularly, a generic quantum process may be estimated simultaneously with unknown quantum probe states provided that…
We develop generalized bounds for quantum single-parameter estimation problems for which the coupling to the parameter is described by intrinsic multi-system interactions. For a Hamiltonian with $k$-system parameter-sensitive terms, the…
Boson sampling, a computational problem conjectured to be hard to simulate on a classical machine, is a promising candidate for an experimental demonstration of quantum advantage using bosons. However, inevitable experimental noise and…
Overcoming the influence of noise and imperfections in quantum devices is one of the main challenges for viable quantum applications. In this article, we present different protocols, which we denote as "superposed quantum error mitigation",…
The Einstein-Podolsky-Rosen nonlocality puzzle has been recognized as one of the most important unresolved issues in the foundational aspects of quantum mechanics. We show that the problem is resolved if the quantum correlations are…
In this paper, a modified formulation of generalized probabilistic theories that will always give rise to the structure of Hilbert space of quantum mechanics, in any finite outcome space, is presented and the guidelines to how to extend…
In a Bayesian setting, inverse problems and uncertainty quantification (UQ) - the propagation of uncertainty through a computational (forward) model - are strongly connected. In the form of conditional expectation the Bayesian update…
Even though measurement results obtained in the real world are generally both noisy and continuous, quantum measurement theory tends to emphasize the ideal limit of perfect precision and quantized measurement results. In this article, a…
Finding solid and practical quantum advantages via noisy quantum devices without error correction is a critical but challenging problem. Conversely, comprehending the fundamental limitations of the state-of-the-art is equally crucial. In…