تقرير
Simultaneous Measurements of Noncommuting Observables. Positive Transformations and Instrumental Lie Groups
| العنوان: | Simultaneous Measurements of Noncommuting Observables. Positive Transformations and Instrumental Lie Groups |
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| المؤلفون: | Jackson, Christopher S., Caves, Carlton M. |
| المصدر: | Entropy, Vol. 25, Article No. 1254, 2023 |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics Mathematical Physics Quantum Physics |
| مصطلحات موضوعية: | Quantum Physics, Mathematical Physics |
| الوصف: | We formulate a general program for [...] analyzing continuous, differential weak, simultaneous measurements of noncommuting observables, which focuses on describing the measuring instrument autonomously, without states. The Kraus operators of such measuring processes are time-ordered products of fundamental differential positive transformations, which generate nonunitary transformation groups that we call instrumental Lie groups. The temporal evolution of the instrument is equivalent to the diffusion of a Kraus-operator distribution function defined relative to the invariant measure of the instrumental Lie group [...]. This way of considering instrument evolution we call the Instrument Manifold Program. We relate the Instrument Manifold Program to state-based stochastic master equations. We then explain how the Instrument Manifold Program can be used to describe instrument evolution in terms of a universal cover[,] the universal instrumental Lie group, which is independent [...] of Hilbert space. The universal instrument is generically infinite dimensional, in which situation the instrument's evolution is chaotic. Special simultaneous measurements have a finite-dimensional universal instrument, in which case the instrument is considered to be principal and can be analyzed within the [...] universal instrumental Lie group. Principal instruments belong at the foundation of quantum mechanics. We consider the three most fundamental examples: measurement of a single observable, of position and momentum, and of the three components of angular momentum. These measurements limit to strong simultaneous measurements. For a single observable, this gives the standard decay of coherence between inequivalent irreps; for the latter two, it gives a collapse within each irrep onto the canonical or spherical phase space, locating phase space at the boundary of these instrumental Lie groups. Comment: 47 pages, 1 figure |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.3390/e25091254 |
| URL الوصول: | http://arxiv.org/abs/2306.06167 |
| رقم الأكسشن: | edsarx.2306.06167 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.3390/e25091254 |
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