Related papers: A substructural logic for quantum measurements
The fact that there are quantum observables without a simultaneous measurement is one of the fundamental characteristics of quantum mechanics. In this work we expand the concept of joint measurability to all kinds of possible measurement…
The relational interpretation (or RQM, for Relational Quantum Mechanics) solves the measurement problem by considering an ontology of sparse relative events, or "facts". Facts are realized in interactions between any two physical systems…
Coherence is a fundamental notion in quantum mechanics, defined relative to a reference basis. As such, it does not necessarily reveal the locality of interactions nor takes into account the accessible operations in a composite quantum…
Traditional uncertainty relations dictate a minimal amount of noise in incompatible projective quantum measurements. However, not all measurements are projective. Weak measurements are minimally invasive methods for obtaining partial state…
Contextuality is a key signature of quantum non-classicality, which has been shown to play a central role in enabling quantum advantage for a wide range of information-processing and computational tasks. We study the logic of contextuality…
We present two new quantum union bounds for sequential projective measurements. These bounds estimate the disturbance accumulation and probability of outcomes when the measurements are performed sequentially. These results are based on a…
An out of the box intellectual path exploring the foundations of quantum mechanics is discussed in some detail, in order to clarify why a possibly different way to look at the relevant fundamental questions can be identified and can support…
Logical inference leads to one of the major interpretations of probability theory called logical interpretation, in which the probability is seen as a measure of the plausibility of a logical statement under incomplete information. In this…
Projective measurement is a commonly used assumption in quantum mechanics. However, advances in quantum measurement techniques allow for partial measurements, which accurately estimate state information while keeping the wavefunction…
We present a propositional logic with fundamental probabilistic semantics, in which each formula is given a real measure in the interval $[0,1]$ that represents its degree of truth. This semantics replaces the binarity of classical logic,…
In classical physics, a single measurement can in principle reveal the state of a system. However, quantum theory permits numerous non-equivalent measurements on a physical system, each providing only limited information about the state.…
Since the dawn of quantum theory, coherence was attributed as a key to understand the weirdness of fundamental concepts like the wave-particle duality and the Stern-Gerlach experiment. Recently, based on a resource theory approach, the…
Quantum incompatibility, referred as the phenomenon that some quantum measurements cannot be performed simultaneously, is necessary for various quantum information processing tasks, such as nonlocality and steering. When these applications…
We present a way to apply quantum logic to the study of quantum programs. This is made possible by using an extension of the usual propositional language in order to make transformations performed on the system appear explicitly. This way,…
Coinductive reasoning about infinitary structures such as streams is widely applicable. However, practical frameworks for developing coinductive proofs and finding reasoning principles that help structure such proofs remain a challenge,…
It is widely known that `collapse of the wave function' on a quantum system A may be brought about by an interaction with another quantum system B. We will prove that this is not just a possible, but a necessary consequence of information…
This paper presents a minimal formulation of nonrelativistic quantum mechanics, by which is meant a formulation which describes the theory in a succinct, self-contained, clear, unambiguous and of course correct manner. The bulk of the…
To begin with, some of the conundrums concerning Quantum Mechanics and its interpretation(s) are recalled. Subsequently, a sketch of the "ETH-Approach to Quantum Mechanics" is presented. This approach yields a logically coherent quantum…
The most peculiar, specifically quantum, features of quantum mechanics --- quantum nonlocality, indeterminism, interference of probabilities, quantization, wave function collapse during measurement --- are explained on a logical-geometrical…
A logic calculus is presented that is a conservative extension of linear logic. The motivation beneath this work concerns lazy evaluation, true concurrency and interferences in proof search. The calculus includes two new connectives to deal…