相关论文: The Conditional Probability Interpretation of the …

We study the computational complexity of 2-local Hamiltonian problems generated by a positive-weight symmetric interaction term, encompassing many canonical problems in statistical mechanics and optimization. We show these problems belong…

Coherent states provide a natural connection of quantum systems to their classical limit and are employed in various fields of physics. Here we derive general systematic expansions, with respect to quantum parameters, of expectation values…

Constrained symplectic quantization is a functional formulation of quantum field theory in which quantum fluctuations are sampled through a deterministic Hamiltonian flow in an auxiliary intrinsic time $\tau$. In this paper we extend the…

This paper focuses on inverse problems to identify parameters by incorporating information from measurements. These generally ill-posed problems are formulated here in a probabilistic setting based on Bayes's theorem because it leads to a…

Integrability in string/field theories is known to emerge when considering dynamics in the moduli space of physical theories. This implies that one has to look at the dynamics with respect to unusual time variables like coupling constants…

Here it is shown that the unitary dynamics of a quantum object may be obtained as the conditional expectation of a counting process of object-clock interactions. Such a stochastic process arises from the quantization of the clock, and this…

A value of a CSP instance is typically defined as a fraction of constraints that can be simultaneously met. We propose an alternative definition of a value of an instance and show that, for purely combinatorial reasons, a value of an…

In the literature the $CPT$ theorem has only been established for Hamiltonians that are Hermitian. Here we extend the $CPT$ theorem to quantum field theories with non-Hermitian Hamiltonians. Our derivation is a quite minimal one as it…

Conditional mutual information (CMI) has recently attracted significant attention as a key quantity for characterizing quantum correlations in many-body systems. While it is conjectured that CMI decays rapidly in finite-temperature Gibbs…

We constructed the representation of contextual probabilistic dynamics in the complex Hilbert space. Thus dynamics of the wave function can be considered as Hilbert space projections of realistic dynamics in a ``prespace''. The basic…

This paper presents a categorical account of conditional probability, covering both the classical and the quantum case. Classical conditional probabilities are expressed as a certain "triangle-fill-in" condition, connecting marginal and…

A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define a unitary quantum system, if one modifies the inner product of the Hilbert space properly. We give a comprehensive and essentially self-contained review…

Schaefer's dichotomy theorem [Schaefer, STOC'78] states that a boolean constraint satisfaction problem (CSP) is polynomial-time solvable if one of six given conditions holds for every type of constraint allowed in its instances. Otherwise,…

Applying the theory of self-adjoint extensions of Hermitian operators to Koopman von Neumann classical mechanics, the most general set of probability distributions is found for which entropy is conserved by Hamiltonian evolution. A new…

Conformal prediction is a popular technique for constructing prediction intervals with distribution-free coverage guarantees. The coverage is marginal, meaning it only holds on average over the entire population but not necessarily for any…

The wave-particle duality and its probabilistic interpretation are at the heart of quantum mechanics. Here we show that, in some standard contexts like the double slit experiment, a deterministic interpretation can be provided. This…

In quantum theory, physical systems are usually assumed to evolve relative to a c-number time. This c-number time is unphysical and has turned out to be unnecessary for explaining dynamics: in the timeless approach to quantum theory…

Integrable differential identities, together with ensemble-specific initial conditions, provide an effective approach for the characterisation of relevant observables and state functions in random matrix theory. We develop this approach for…

We explore precision in a measurement process incorporating pure probe states, unitary dynamics and complete measurements via a simple formalism. The concept of `information complement' is introduced. It undermines measurement precision and…

Causal estimands can vary significantly depending on the relationship between outcomes in treatment and control groups, potentially leading to wide partial identification (PI) intervals that impede decision making. Incorporating covariates…