Most of the fundamental characteristics of quantum mechanics, such as nonlocality and contextuality, are manifest in discrete, finite-dimensional systems. However, many quantum information tasks that exploit these properties cannot be directly adapted to continuous variable systems. To access these quantum features, continuous quantum variables can be made discrete by binning together their different values, resulting in observables with a finite number, $d$ , of outcomes. While direct measurement indeed confirms their manifestly discrete character, here we employ a salient feature of quantum physics known as mutual unbiasedness to show that such coarse-grained observables are in a sense neither continuous nor discrete. Depending on $d$ , the observables can reproduce either the discrete or the continuous behavior, or neither. To illustrate these results, we present an example for the construction of such measurements and employ it in an optical experiment confirming the existence of four mutually unbiased measurements with $d=3$ outcomes in a continuous variable system, surpassing the number of mutually unbiased continuous variable observables.Most of the fundamental characteristics of quantum mechanics, such as nonlocality and contextuality, are manifest in discrete, finite-dimensional systems. However, many quantum information tasks that exploit these properties cannot be directly adapted to continuous variable systems. To access these quantum features, continuous quantum variables can be made discrete by binning together their different values, resulting in observables with a finite number, $d$, of outcomes. While direct measurement indeed confirms their manifestly discrete character, here we employ a salient feature of quantum physics known as mutual unbiasedness to show that such coarse-grained observables are in a sense neither continuous nor discrete. Depending on $d$, the observables can reproduce either the discrete or the continuous behavior, or neither. To illustrate these results, we present an example for the construction of such measurements and employ it in an optical experiment confirming the existence of four mutually unbiased measurements with $d=3$ outcomes in a continuous variable system, surpassing the number of mutually unbiased continuous variable observables.

arXiv:2009.05062Physical Review ResearchJan 28, 20223 citations

Continuous measurements in quantum systems

Carlo Presilla A, Ubaldo Tambini

arXiv:cond-mat/9711007Hyperfine InteractionsNov 1, 19980 citations

The Situated Continuity Framework™

Elyse Meagan Estes

The Situated Continuity Framework™ is a working philosophical paper within Red Tape Theory™ examining how observers recognize systems across changing conditions of perceptual access. The paper connects two thought experiments: a boat whose identity is considered across successive states, and an observer inside a fig whose developmental history and wider surroundings are only partially accessible. It distinguishes continuity within a system, perceptibility to an observer, and the observer’s recognition of identity. The framework introduces 1 and 0 as condition-relative indicators of perceptibility rather than existence. It argues that an interruption in observation does not, by itself, establish an interruption in continuity. Conversely, continuous observation does not guarantee that a system remains unchanged. Its method distinguishes changes within a system, changes in observational access, and changes produced by participation or measurement. The paper also addresses competing explanations, explicit identity criteria, and the difference between a state being new to an observer and being new under a stated system criterion. The guiding principle is: “A boundary in observation is not, by itself, a boundary in continuity.” Version 1.0 presents a philosophical framework for interpretation under limited access. It does not propose a physical mechanism, explain quantum interference, or claim to provide a complete solution to identity persistence.The Situated Continuity Framework™ is a working philosophical paper within Red Tape Theory™ examining how observers recognize systems across changing conditions of perceptual access. The paper connects two thought experiments: a boat whose identity is considered across successive states, and an observer inside a fig whose developmental history and wider surroundings are only partially accessible. It distinguishes continuity within a system, perceptibility to an observer, and the observer’s recognition of identity. The framework introduces 1 and 0 as condition-relative indicators of perceptibility rather than existence. It argues that an interruption in observation does not, by itself, establish an interruption in continuity. Conversely, continuous observation does not guarantee that a system remains unchanged. Its method distinguishes changes within a system, changes in observational access, and changes produced by participation or measurement. The paper also addresses competing explanations, explicit identity criteria, and the difference between a state being new to an observer and being new under a stated system criterion. The guiding principle is: “A boundary in observation is not, by itself, a boundary in continuity.” Version 1.0 presents a philosophical framework for interpretation under limited access. It does not propose a physical mechanism, explain quantum interference, or claim to provide a complete solution to identity persistence.

Oct 7, 20260 citations

d

, of outcomes. While direct measurement indeed confirms their manifestly discrete character, here we employ a salient feature of quantum physics known as mutual unbiasedness to show that such coarse-grained observables are in a sense neither continuous nor discrete. Depending on

d

, the observables can reproduce either the discrete or the continuous behavior, or neither. To illustrate these results, we present an example for the construction of such measurements and employ it in an optical experiment confirming the existence of four mutually unbiased measurements with

d=3

outcomes in a continuous variable system, surpassing the number of mutually unbiased continuous variable observables.