A “garden of forking paths” – The quantum mechanics of histories of events

Indirect Measurements of a Harmonic Oscillator

“…of (2.27) in the context of (5. 15), yet foregoing scaling for the time being. Specifically, we are going to construct a functional calculus associated to the family of commuting operators (M t ) 0≤t<∞ .…”

“…Merkli et al [13,14] rigorously exhibited decoherence for more general, not explicitly solvable examples. Fröhlich [15] and coworkers give a notion of events that forgoes decoherence. From a more applied perspective, Makhlin [31] et al discuss the limitations to an accurate readout of superconducting qubits.…”

Indirect Acquisition of Information in Quantum Mechanics

“…There are numerous, partly contradictory proposals of how to set up a quantum theory of direct measurements or observations. In this paper we follow the so-called "ETH approach" to quantum theory, as sketched in [10], [7] and [9]. Here we briefly summarize those ingredients of this approach that will be needed later.…”

“…We will formulate our insights and results within the so-called "ETH approach" to quantum mechanics, and "ET H" is an abbreviation for " Events, Trees and Histories". (This approach has been introduced in [9], [7], [10]. The work presented in the following sections is a continuation of efforts described in these papers and in [1].…”

“…Next, we sketch the main objectives of this paper. We take for granted the theory of repeated direct measurements in quantum mechanics, as described in [12], [7], and references given there. This theory provides a theoretical underpinning for a formula, originally proposed by Lüders, Schwinger and Wigner (the "LSW formula"), enabling one to assign a probability to every (finite) "history" of direct measurement outcomes.…”