Related papers: Leggett-Garg inequalities for multitime processes
We propose an experimental programme to test Leggett--Garg-type temporal correlations in single-neuron dynamics. The goal is to distinguish between diffusive (Wiener/cable-equation) models and non-diffusive persistent stochastic models…
We discuss a scheme for macrorealistic theories of the Leggett-Garg form [A. J. Leggett and A. Garg, Phys. Rev. Lett. 54, 857 (1985)]. Our scheme is based on a hybrid optomechanical system. It seems reasonable to test these inequalities…
We study the macroscopic realism (macrorealism) through the two- and three-time Leggett-Garg inequalities (LGIs) in a two interacting qubits system. The two qubits are coupled either with two bosonic (thermal or photonic) baths or fermionic…
In a recent paper, Chatterjee et al. [Phys. Rev. Lett 135, 220202 (2025)] analyze and experimentally implement a specific unitary evolution of a simple quantum system. The authors refer to this type of dynamics as a "superposition of…
Investigating the relationship, particularly the lead-lag effect, between time series is a common question across various disciplines, especially when uncovering biological process. However, analyzing time series presents several…
Functor coalgebras capture a wide range of transition systems that must however evolve in discrete steps. We introduce graded coalgebras of graded monads and propose them to model continuous-time transition systems. We develop the theory of…
Weak measurement has provided new insight into the nature of quantum measurement, by demonstrating the ability to extract average state information without fully projecting the system. For single qubit measurements, this partial projection…
We prove tail and moment inequalities for multiple stochastic integrals on the Poisson space and for Poisson $U$-statistics. We use them to demonstrate the Law of the Iterated Logarithm for these processes when the intensity of the Poisson…
We study Leggett-Garg inequalities (LGIs) for a two level system (TLS) undergoing Markovian dynamics described by unital maps. We find analytic expression of LG parameter $K_{3}$ (simplest variant of LGIs) in terms of the parameters of two…
Non-orthogonal quantum states pose a fundamental challenge in quantum information processing, as they cannot be distinguished with absolute certainty. Conventionally, the focus has been on minimizing error probability in quantum state…
A generic non-integrable (unitary) out-of-equilibrium quantum process, when interrogated across many times, is shown to yield the same statistics as an (non-unitary) equilibrated process. In particular, using the tools of quantum stochastic…
Tests of local realism and macrorealism have historically been discussed in very similar terms: Leggett-Garg inequalities follow Bell inequalities as necessary conditions for classical behavior. Here, we compare the probability polytopes…
Characterization of quantum devices received from unknown providers is a significant primary task for any quantum information processing protocol. Self-testing protocols are designed for this purpose of certifying quantum components from…
Recently, classification problems of gapped ground state phases attract a lot of attention in quantum statistical mechanics. We explain about our operator algebraic approach to these problems.
We report an experimental study of recently formulated entropic Leggett-Garg inequality (ELGI) by Usha Devi et al. (arXiv: 1208.4491v2 (2012)). This inequality places a bound on the statistical measurement outcomes of dynamical observables…
We review recent results on functional inequalities for systems of orthonormal functions. The key finding is that for various operators the orthonormality leads to a gain over a simple application of the triangle inequality. The operators…
Bell inequalities can be studied both as constraints in the space of probability distributions and as expectation values of multipartite operators. The latter approach is particularly useful when considering outcomes as eigenvalues of…
In this paper, we study the existence of solutions of some kinds of operator equations via operator inequalities. First, we investigate characterizations of operator order $A\geqslant B >0$ and chaotic operator order log $A \geqslant$ log…
Sequential measurements on a single particle play an important role in fundamental tests of quantum mechanics. We provide a general method to analyze temporal quantum correlations, which allows us to compute the maximal correlations for…
We investigate the non-local properties of graph states. To this aim, we derive a family of Bell inequalities which require three measurement settings for each party and are maximally violated by graph states. In turn, for each graph state…