Identifying weak values with intrinsic dynamical properties in Modal theories

Abstract

The so-called eigenvalue-eigenstate link states that no property can be associated to a quantum system unless it is in an eigenstate of the corresponding operator. This precludes the assignation of properties to unmeasured quantum systems in general. This arbitrary limitation of Orthodox quantum mechanics generates many puzzling situations such as for example the impossibility to uniquely define a work distribution, an essential building block of quantum thermodynamics. Alternatively, Modal theories (e.g., Bohmian mechanics) provide an ontology that always allows to define intrinsic properties, i.e., properties of quantum systems that are detached from any possible measuring context. We prove here that Aharonov, Albert and Vaidman's notion of weak value can always be identified with an intrinsic dynamical property of a quantum system defined in a certain Modal theory. Furthermore, the fact that weak values are experimentally accessible (as an ensemble average of weak measurements which are post-selected by a strong measurement) strengthens the idea that understanding the intrinsic (unperturbed) dynamics of quantum systems is possible and useful in a given Modal theory. As examples of the physical soundness of these intrinsic properties, we discuss three intrinsic Bohmian properties, viz., the dwell time, the work distribution and the quantum noise at high frequencies.

References in corpus (23)

• Experimental joint weak measurement on a photon pair as a probe of Hardy's Paradox
• Complex weak values in quantum measurement
• A strong no-go theorem on the Wigner's friend paradox
• Work measurement as a generalized quantum measurement
• Grounding Bohmian Mechanics in Weak Values and Bayesianism
• Non-equilibrium quantum fluctuations of work
• Applied Bohmian Mechanics
• Failure of the work-Hamiltonian connection for free energy calculations
• Concepts of work in autonomous quantum heat engines
• Measuring work and heat in ultracold quantum gases
• Weak values and quantum properties
• Comment on: How the result of a single coin toss can turn out to be 100 heads
• Experimental nonlocal steering of Bohmian trajectories
• On the Weak Measurement of Velocity in Bohmian Mechanics
• Observing momentum disturbance in double-slit "which-way" measurements
• Time-dependent exchange and tunneling: detection at the same place of two electrons emitted simultaneously from different sources
• Quantum dissipation with conditional wave functions: Application to the realistic simulation of nanoscale electron devices
• Experimental simultaneous read out of the real and imaginary parts of the weak value
• Quantum Trajectories based on the Weak Value
• Stochastic Schrödinger equations and conditional states: a general Non-Markovian quantum electron transport simulator for THz electronics
• Experimental Comparison of Bohm-like Theories with Different Ontologies
• Interpreting weak value amplification with a toy realist model
• Proposal for a clumsiness-free test of macroscopic realism

Cited by in corpus (6)

• Resonant tunneling diodes in semiconductor microcavities: modeling polaritonic features in the THz displacement current
• Assessing Quantum Thermalization in Physical and Configuration Spaces via Many-Body Weak Values
• Comment on "Association between quantum paradoxes based on weak values and a realistic interpretation of quantum measurements"
• Kinetic energy equipartition: a tool to characterize quantum thermalization
• Time Derivatives of Weak Values
• Bohmian Mechanics as a Practical Tool