Measurement, information, and disturbance in Hamiltonian mechanics
- URL: http://arxiv.org/abs/2104.02064v1
- Date: Mon, 5 Apr 2021 06:09:28 GMT
- Title: Measurement, information, and disturbance in Hamiltonian mechanics
- Authors: David Theurel
- Abstract summary: Measurement in classical physics is examined as a process involving the joint evolution of object-system and measuring apparatus.
A model of measurement is proposed which lends itself to theoretical analysis using Hamiltonian mechanics and Bayesian probability.
The process of continuous measurement is then examined; yielding a novel pair of Liouville-like master equations.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Measurement in classical physics is examined here as a process involving the
joint evolution of object-system and measuring apparatus. For this, a model of
measurement is proposed which lends itself to theoretical analysis using
Hamiltonian mechanics and Bayesian probability. At odds with a widely-held
intuition, it is found that the ideal measurement capable of extracting finite
information without disturbing the system is ruled out (by the third law of
thermodynamics). And in its place a Heisenberg-like precision-disturbance
relation is found, with the role of $\hbar/2$ played by $k_BT/\Omega$; where
$T$ and $\Omega$ are a certain temperature and frequency characterizing the
ready-state of the apparatus. The proposed model is argued to be maximally
efficient, in that it saturates this Heisenberg-like inequality, while various
modifications of the model fail to saturate it. The process of continuous
measurement is then examined; yielding a novel pair of Liouville-like master
equations -- according to whether the measurement record is read or discarded
-- describing the dynamics of (a rational agent's knowledge of) a system under
continuous measurement. The master equation corresponding to discarded record
doubles as a description of an open thermodynamic system. The fine-grained
Shannon entropy is found to be a Lyapunov function (i.e. $\dot S\geq0$) of the
dynamics when the record is discarded, providing a novel H-theorem suitable for
studying the second law and non-equilibrium statistical physics. These findings
may also be of interest to those working on the foundations of quantum
mechanics, in particular along the lines of attempting to identify and unmix a
possible epistemic component of quantum theory from its ontic content. More
practically, these results may find applications in the fields of precision
measurement, nanoengineering and molecular machines.
Related papers
- Teaching ideal quantum measurement, from dynamics to interpretation [0.0]
Ideal measurements are analyzed as processes of interaction between the tested system S and an apparatus A.
Conservation laws are shown to entail two independent relaxation mechanisms.
Born's rule then arises from the conservation law for the tested observable.
arXiv Detail & Related papers (2024-05-29T22:36:06Z) - Measuring the Loschmidt amplitude for finite-energy properties of the
Fermi-Hubbard model on an ion-trap quantum computer [27.84599956781646]
We study the operation of a quantum-classical time-series algorithm on a present-day quantum computer.
Specifically, we measure the Loschmidt amplitude for the Fermi-Hubbard model on a $16$-site ladder geometry (32 orbitals) on the Quantinuum H2-1 trapped-ion device.
We numerically analyze the influence of noise on the full operation of the quantum-classical algorithm by measuring expectation values of local observables at finite energies.
arXiv Detail & Related papers (2023-09-19T11:59:36Z) - Evolution of many-body systems under ancilla quantum measurements [58.720142291102135]
We study the concept of implementing quantum measurements by coupling a many-body lattice system to an ancillary degree of freedom.
We find evidence of a disentangling-entangling measurement-induced transition as was previously observed in more abstract models.
arXiv Detail & Related papers (2023-03-13T13:06:40Z) - Quantum measurements and equilibration: the emergence of objective
reality via entropy maximisation [0.0]
We formalise the hypothesis that quantum measurements are driven by the natural tendency of closed systems to maximize entropy.
We lay the groundwork for self-contained models of quantum measurement, proposing improvements to our simple scheme.
arXiv Detail & Related papers (2023-02-22T10:06:17Z) - Scalable Spin Squeezing from Finite Temperature Easy-plane Magnetism [26.584014467399378]
We conjecture that any Hamiltonian exhibiting finite temperature, easy-plane ferromagnetism can be used to generate scalable spin squeezing.
Our results provide insights into the landscape of Hamiltonians that can be used to generate metrologically useful quantum states.
arXiv Detail & Related papers (2023-01-23T18:59:59Z) - Probing finite-temperature observables in quantum simulators of spin
systems with short-time dynamics [62.997667081978825]
We show how finite-temperature observables can be obtained with an algorithm motivated from the Jarzynski equality.
We show that a finite temperature phase transition in the long-range transverse field Ising model can be characterized in trapped ion quantum simulators.
arXiv Detail & Related papers (2022-06-03T18:00:02Z) - Finite resolution ancilla-assisted measurements of quantum work
distributions [77.34726150561087]
We consider an ancilla-assisted protocol measuring the work done on a quantum system driven by a time-dependent Hamiltonian.
We consider system Hamiltonians which both commute and do not commute at different times, finding corrections to fluctuation relations like the Jarzynski equality and the Crooks relation.
arXiv Detail & Related papers (2021-11-30T15:08:25Z) - Effects of the free evolution in the Arthurs-Kelly model of simultaneous
measurement and in the retrodictive predictions of the Heisenberg uncertainty
relations [0.0]
We study the effect of the full dynamics on the optimal limits of retrodictive and predictive accuracy of the simultaneous measurement process.
We show that the inclusion of the free Hamiltonian induces a spreading on the probability density of the measurement setting.
arXiv Detail & Related papers (2021-09-01T19:17:39Z) - Effective Theory for the Measurement-Induced Phase Transition of Dirac
Fermions [0.0]
A wave function exposed to measurements undergoes pure state dynamics.
For many-particle systems, the competition of these different elements of dynamics can give rise to a scenario similar to quantum phase transitions.
A key finding is that this field theory decouples into one set of degrees of freedom that heats up indefinitely.
arXiv Detail & Related papers (2021-02-16T19:00:00Z) - Evolution of a Non-Hermitian Quantum Single-Molecule Junction at
Constant Temperature [62.997667081978825]
We present a theory for describing non-Hermitian quantum systems embedded in constant-temperature environments.
We find that the combined action of probability losses and thermal fluctuations assists quantum transport through the molecular junction.
arXiv Detail & Related papers (2021-01-21T14:33:34Z) - Non-destructively probing the thermodynamics of quantum systems with
qumodes [0.6144680854063939]
In quantum systems there is often a destruction of the system itself due to the means of measurement.
One approach to circumventing this is the use of ancillary probes that couple to the system under investigation.
We highlight means by which continuous variable quantum modes (qumodes) can be employed to probe the thermodynamics of quantum systems in and out of equilibrium.
arXiv Detail & Related papers (2017-07-13T17:57:11Z)
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.