Conditional probabilities of measurements, quantum time and the Wigner's
friend case
- URL: http://arxiv.org/abs/2103.08903v4
- Date: Mon, 7 Mar 2022 21:51:30 GMT
- Title: Conditional probabilities of measurements, quantum time and the Wigner's
friend case
- Authors: Martino Trassinelli
- Abstract summary: conditional probabilities are derived for subsequent measurements in the non-relativistic regime.
One-time conditional probabilities are unambiguously derived via the Gleason-Bush theorem.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Considering a minimal number of assumptions and in the context of the
timeless formalism, conditional probabilities are derived for subsequent
measurements in the non-relativistic regime. Only unitary transformations are
considered with detection processes described by generalized measurements
(POVM). One-time conditional probabilities are unambiguously derived via the
Gleason-Bush theorem, including for puzzling cases like the Wigner's friend
scenario where their form underlines the relativity aspect of measurements. No
paradoxical situations emerge and the roles of Wigner and Wigner can be seen by
his friend as being in a superposition.
Related papers
- Certifying measurement incompatibility in prepare-and-measure and Bell scenarios [0.6249768559720122]
We consider the problem of certifying measurement incompatibility in a prepare-and-measure (PM) scenario.
We present different families of sets of qubit measurements which are incompatible, but cannot lead to any quantum over classical advantage.
Our examples are obtained via a general theorem which proves a set of qubit dichotomic measurements can have their incompatibility certified in a PM scenario.
arXiv Detail & Related papers (2024-07-09T11:58:19Z) - Making sense of relativistic Wigner friend scenarios: a problem for
unitary accounts of quantum measurements ? [0.0]
Wigner-friend scenarios highlight the difficulties inherent to quantum theory when accounting for measurements.
In non-relativistic scenarios, the difficulty is to accommodate unitary evolution for a closed system.
In relativistic scenarios the tensions between quantum theory and relativity induce additional constraints.
arXiv Detail & Related papers (2023-10-06T11:32:03Z) - Measurement events relative to temporal quantum reference frames [49.1574468325115]
We compare two approaches to the Page-Wootters formalism to clarify the operational meaning of evolution and measurements.
We show that for non-ideal clocks, the purified measurement approach yields time non-local, non-unitary evolution.
arXiv Detail & Related papers (2023-08-21T18:26:12Z) - Logic meets Wigner's Friend (and their Friends) [49.1574468325115]
We take a fresh look at Wigner's Friend thought-experiment and some of its more recent variants and extensions.
We discuss various solutions proposed in the literature, focusing on a few questions.
arXiv Detail & Related papers (2023-07-04T13:31:56Z) - Witnessing superpositions of causal orders before the process is completed [0.0]
What is the most general representation of a quantum state at a single point in time?
Can we adapt the current formalisms to situations where the order of quantum operations is coherently or incoherently superposed?
arXiv Detail & Related papers (2022-09-19T16:47:53Z) - Events in quantum mechanics are maximally non-absolute [0.9176056742068814]
We prove that quantum correlations can be maximally non-absolute according to both quantifiers.
We show that chained Bell inequalities (and relaxations thereof) are also valid constraints for Wigner's experiment.
arXiv Detail & Related papers (2021-12-19T21:15:16Z) - Experimentally determining the incompatibility of two qubit measurements [55.41644538483948]
We describe and realize an experimental procedure for assessing the incompatibility of two qubit measurements.
We demonstrate this fact in an optical setup, where the qubit states are encoded into the photons' polarization degrees of freedom.
arXiv Detail & Related papers (2021-12-15T19:01:44Z) - Optimal Adaptive Strategies for Sequential Quantum Hypothesis Testing [87.17253904965372]
We consider sequential hypothesis testing between two quantum states using adaptive and non-adaptive strategies.
We show that these errors decrease exponentially with decay rates given by the measured relative entropies between the two states.
arXiv Detail & Related papers (2021-04-30T00:52:48Z) - The Variational Method of Moments [65.91730154730905]
conditional moment problem is a powerful formulation for describing structural causal parameters in terms of observables.
Motivated by a variational minimax reformulation of OWGMM, we define a very general class of estimators for the conditional moment problem.
We provide algorithms for valid statistical inference based on the same kind of variational reformulations.
arXiv Detail & Related papers (2020-12-17T07:21:06Z) - Equivalence of approaches to relational quantum dynamics in relativistic
settings [68.8204255655161]
We show that the trinity' of relational quantum dynamics holds in relativistic settings per frequency superselection sector.
We ascribe the time according to the clock subsystem to a POVM which is covariant with respect to its (quadratic) Hamiltonian.
arXiv Detail & Related papers (2020-07-01T16:12:24Z) - Symmetric Informationally Complete Measurements Identify the Irreducible
Difference between Classical and Quantum Systems [0.0]
We describe a general procedure for associating a minimal informationally-complete quantum measurement (or MIC) with a set of linearly independent post-measurement quantum states.
We prove that the representation of the Born Rule obtained from a symmetric informationally-complete measurement (or SIC) minimizes this distinction in at least two senses.
arXiv Detail & Related papers (2018-05-22T16:27:27Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.