Difference between revisions of "Quantum Measurement"
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* Probability: The probability of obtaining a particular eigenvalue is given by the squared modulus of the inner product of the system's state vector with the corresponding eigenvector. | * Probability: The probability of obtaining a particular eigenvalue is given by the squared modulus of the inner product of the system's state vector with the corresponding eigenvector. | ||
* State After Measurement: After the measurement, the system is left in the eigenstate corresponding to the measured eigenvalue. This is known as the collapse of the wave-function. | * State After Measurement: After the measurement, the system is left in the eigenstate corresponding to the measured eigenvalue. This is known as the collapse of the wave-function. | ||
| − | + | While progress certainly has been made, the understanding of [[Quantum Measurement]] has not changed significantly since David Bohm said this in 1951:<ref>David Bohm, Quantum Theory'' Prentice Hall (1951) Chapter 22 ISBN 978-0486659695</ref><blockquote>The quantum theory as developed thus far provides in principle, a way to calculate the probable results of any measurement that one wishes to carry out. To calculate the average value of any observable A, we simply write ''Ā = ∫ ψ*Aψ dx,'' where ''ψ'' is the wave function of the system under investigation. If the quantum theory is to be able to provide a complete description of everything that can happen in the world, however, it should also be able to describe the process of observation itself in terms of the wave functions of the observing apparatus and those of the system under observation. Furthermore, in principle, it ought to be able to describe the human investigator as he looks at the observing apparatus and learns what the results of the experiment are, this time in terms of the wave functions of the various atoms that make up the investigator, as well as those of the observing apparatus and the system under observation. In other words, the quantum theory could not be regarded as a complete logical system unless it contained within it a prescription in principle for how all of these problems were to be dealt with.</blockquote> | |
==Issues== | ==Issues== | ||
Latest revision as of 14:58, 23 April 2025
Contents
Full Title
Quantum Measurement is the process of obtaining information about a quantum system, such as its position or momentum. This process involves interacting with the system and causing it to collapse from a superposition of states to a single definite state.
Context
- Eigenstates and Eigenvalues: When a measurement is performed, the system collapses to one of the eigenstates of the observable, and the measurement result is the corresponding eigenvalue.
- Probability: The probability of obtaining a particular eigenvalue is given by the squared modulus of the inner product of the system's state vector with the corresponding eigenvector.
- State After Measurement: After the measurement, the system is left in the eigenstate corresponding to the measured eigenvalue. This is known as the collapse of the wave-function.
The quantum theory as developed thus far provides in principle, a way to calculate the probable results of any measurement that one wishes to carry out. To calculate the average value of any observable A, we simply write Ā = ∫ ψ*Aψ dx, where ψ is the wave function of the system under investigation. If the quantum theory is to be able to provide a complete description of everything that can happen in the world, however, it should also be able to describe the process of observation itself in terms of the wave functions of the observing apparatus and those of the system under observation. Furthermore, in principle, it ought to be able to describe the human investigator as he looks at the observing apparatus and learns what the results of the experiment are, this time in terms of the wave functions of the various atoms that make up the investigator, as well as those of the observing apparatus and the system under observation. In other words, the quantum theory could not be regarded as a complete logical system unless it contained within it a prescription in principle for how all of these problems were to be dealt with.
Issues
First kind of quantum measurement
The first kind of quantum measurement, also known as the projective measurement, is a measurement that completely collapses the quantum system into one of its possible states. This type of measurement is irreversible and provides a definite outcome.[2]
Second kind of quantum measurement
Non-demolition measurement is a type of quantum measurement that does not entirely collapse the system, but instead provides information about the system while still preserving its superposition of states. This type of measurement is used in quantum systems that require continuous monitoring without disturbing the system. What is the difference between the first kind and non-demolition measurement? The main difference between the first kind and non-demolition measurement is the effect they have on the quantum system. First kind measurements completely collapse the system, while non-demolition measurements only provide partial information while preserving the superposition of states. Non-demolition measurements are also reversible, while first kind measurements are irreversible.[3]
References
- ↑ David Bohm, Quantum Theory Prentice Hall (1951) Chapter 22 ISBN 978-0486659695
- ↑ Physics Forum, Quantum measurement: first kind vs non-demolition 2012-08-09 https://www.physicsforums.com/threads/quantum-measurement-first-kind-vs-non-demolition.626599/
- ↑ Andreas Reiserer, Stephan Ritter and Gerhard Rempe, Nondestructive Detection of an Optical Photon 2013-11-14 https://www.science.org/doi/10.1126/science.1246164
