What is Quantum measurement: Definition and 58 Discussions
In quantum physics, a measurement is the testing or manipulation of a physical system in order to yield a numerical result. The predictions that quantum physics makes are in general probabilistic. The mathematical tools for making predictions about what measurement outcomes may occur were developed during the 20th century and make use of linear algebra and functional analysis.
Quantum physics has proven to be an empirical success and to have wide-ranging applicability. However, on a more philosophical level, debates continue about the meaning of the measurement concept.
Im trying to learn QM on my own and I just want to clear some things up. I feel dumb writing some out but Id rather clear my confusion than believe im interpreting what I read correctly.
From what I've read, every measurement of a system gives us values that are the eigenvalues of a certain...
At the heart of the theory of open quantum systems is the idea that the measurement statistics of many-body systems can be expressed in terms of a reduced density matrix, obtained by tracing over degrees of freedom that are irrelevant to the system of interest.
In general, given a pure state...
For the background of the discussion see my Insight artice ''Quantum Physics via Quantum Tomography'' and the posts #405 and later of the thread ''Nature Physics on quantum foundations''.
Trying to translate your statements into precise formulas, and using ##\Pi## in place of ##E## (which to me...
Hi Pfs
I read this answer in
https://quantumcomputing.stackexchange.com/questions/136/if-all-quantum-gates-must-be-unitary-what-about-measurement
Quantum measurements are special cases of quantum channels (CPTP cards). Stinespring dilation states that any quantum channel is realized by...
I tried to code spinoperators who act like $S_x^iS_x^j$ (y and z too) and to apply them to the states, which works fine. I am not sure about how to code the expectation value in the product Space. Has anyone pseudo Code to demonstrate that?
How do we map experimental measurements of quantum fields, such as those seen in accelerators, to the theory's mathematical formalism? When we see images of particle tracks produced in accelerators such as the LHC, I think it's safe to say a measurement (or series of measurements) has been...
Hi, I'm happy to change ideas in Physics Forums, especially in my interesting fields, include quantum fisher information, and quantum entanglement detection and quantum metrology!
The link is https://www.su.se/english/research/scientists-film-a-quantum-measurement-1.487234
How do they arrive at this distribution over time? It does not appear to be saying that this is the prediction (in it were, then why the "filming"?), and measurement of a single atom's superposition is...
For the sake of this question, I am primarily concerned with the position wave function. So, from my understanding, the wave function seems to 'collapse' to a few states apon measurement. We know this because, if the same particle is measured again shortly after this, it will generally remain in...
Hi Pf
I am looking at the figure in wiki about quantum teleportation.
https://en.wikipedia.org/wiki/File:Quantum_teleportation_diagram.PNG
A wants to send a qubit to B . She receives another qubit from a spdc.
so she has to make a Bell measurement on them. Has these qbits to be close in space...
I am trying to solve the following exercise.
In a H atom the electron is in the state described by the wave function in spherical coordinates:
\psi (r, \theta, \phi) = e^{i \phi}e^{-(r/a)^2(1- \mu\ cos^2\ \theta)}
With a and \mu positive real parameters. Tell what are the possible values...
When a quantum measurement occurs under the Schrodinger picture, the wave function collapses to one of the eigenvectors of the operator-observable and the value measured is the corresponding eigenvalue of that eigenvector. What happens during a quantum measurement under the Heisenberg picture...
I want to know between which two quantities of energy, momentum, and mass there is an uncertainty principle going on. Can I measure any two of those at the same time? If yes, which ones?
Thank you in advance
I cannot post the science alert article where I saw this. Apologies, this put the study in layman's.
@PeterDonis @vanhees71 et al will not need that.
Is this significant?
Could the wave function not instantaneously collapse?
I'm looking for a book about the theory of measurement in quantum mechanics.
A book that goes deep into understanding different kinds and ways.
thank you
Hi,
I'm reading Demystifier's article about an interpretation of quantum mechanics. One concept that seems important for this interpretation is that of what is perceptible by us human beings compared to what is not (non-perceptible).
Demystifier says: A perception by a naked eye is direct, a...
Take 2 people P1 and P2. P1 claims that a Stern-Gerlach device collapsed an electron’s spin to + or - (mixed state if P1 doesn’t know which) while P2 may say it did not collapse, but instead remains in a pure, entangled state. If we continue this sort of thinking (2 people applying different...
I state the following study and then expose my doubt at the end.
MY SYSTEM
A free particle (absence of forces) on one-dimensional space (X axis).
INITIAL STATE
At t=0 the wave function is a Gaussian wave packet NOT normalizet centered in ##x_{0}## and with standard deviation ##\sigma##...
I was wondering how to measure the first or even the second qubit in a quantum computing system after for example a Hadamard Gate is applied to the system of these qubits: A|00>+B|01>+C|10>+D|11>?
A mathematical and intuitive explanation would be nice, I am a undergraduate sophomore student...
A quantum system goes from an uncertain to a certain state upon measurement.This indicates a decrease of entropy--is there a corresponding increase of entropy elsewhere(environment/observer)?Is there any work done on the system in the act of measurement?
Reversible computation is a somewhat well-known topic. (Quantum computers, for instance, must use reversible gates).
Apparently, though, quantum measurements can be reversible too. This also means you could recover the original state by “unmeasuring” the system. Imagine being able to “see” a...
The Fundamental Theorem of Quantum Measurement is stated as follows:
Every set of operators ##\{ A_n \}## ##n =1,...,N## that satisfies ##\sum_n A_n^{\dagger}A_n = I## describes a possible measurement on a quantum system, where the measurement has ##n## possible outcomes labeled by ##n##. If...
Homework Statement
(c is a constant)
The attempt at a solution
-In the first measure we got a1, so the state of the system would be psi1.
-In the second measure, there's no information about what eigenvalue we got. Would the state of the system still be psi1? Psi1 is written in terms of B...
The following, regarding quantum measurement, is stated in the paper "Limitation on the amount of accessible information in a quantum channel" :
"Our discussion of measurement will be based on a specific physical model of measurement, to which we now turn. Suppose we have a quantum system ##Q##...
The following is a somewhat mathematical question, but I am interested in using the idea to define a set of quantum measurement operators defined as described in the answer to this post.
Question:
The Poisson Distribution ##Pr(M|\lambda)## is given by $$Pr(M|\lambda) =...
In page 9 of http://www.theory.caltech.edu/people/preskill/ph229/notes/chap4.pdf we can find simple form of Bell inequalities for three binary variables:
$$ P(A=B) + P(A=C) + P(B=C) \geq 1 $$
which is kind of obvious: "This is satisfied by any probability distribution for the three coins because...
Hi to all who might respond,
Consider the 'peculiar' double-slit setup below.
There is a double-slit configuration such that the two slits are never open at the same time. That is: whenever the top slit is open for a certain interval, Ts, the bottom slit is closed for the same interval and vice...
I'm well aware of the common adage and quantum fact that, until a particle is measured by some sort of instrument, it exists in a state of superposition, can interfere with itself, etc. My questions pertains to the definition of "measurement".
In order for something to qualify as a measurement...
If we consider a measurement of a two level quantum system made by using a probe system followed then by a von Neumann measurement on the probe, how could we determine the unitary operator that must be applied to this system (and probe) to accomplish the given measurement operators.
I've recently been wondering about the notion of measurement in quantum mechanics. While I'm aware that understanding and precisely defining the concept of a quantum mechanical measurement is at the heart of interpreting the subject, I would like some feedback on some aspects of this topic I...
Quantum mechanical foundations are usually phrased in terms of measurement. I believe this is the main cause why these foundations remain shaky after almost 100 years of a good mathematical basis. Classical mechanics never had any reference to measurement in its foundations, and hence it was...
Good day,
May anyone help me to confirm the formula use for three tangle using concurrence.
From my reading,
three tangle,
$$\tau=\tau_{A(BC)}-\tau_{AB}-\tau_{AC}$$
and it can be related to concurrence
$$\tau=C^2_{A(BC)}-C^2_{AB}-C^2_{AC}$$
and I used formula for C is...
It's often claimed that in Mathematical Foundations of Quantum Mechanics Von Neumann concluded that it's the observer's consciousness that collapses the wavefunction (Process 1).
But I am reading Chapter 6 of the book (both original and translation) word by word, and I don't find this...
Good day,
From my reading according to negativity for tripartite state, it is given as below;
$$N_{ABC}(\rho)=(N_{A-BC}N_{B-AC}N_{C-AB})^{1/3}$$
with
$$N_{I-JK}=-2\Sigma_i\sigma_i(\rho^{TI})$$
where
$$\sigma_i(\rho^{TI})$$
being the negative eigenvalues of
$$\rho^{TI}$$,
the partial...
Hi,
I just completed my second year of my physics undergraduate degree. And recently did a course on Quantum Mechanics. I have a few questions regarding the basic theory and postulates, probably, because due to lack of full clarity.
So,
Consider a wave function ψ(x,o), which is well behaved and...
A measurement of an observable that does not commute with energy will generally cause a change in the expectation value of the energy. Is there a clear formalism to describe how energy is conserved overall?
Let suppose I have an observable ##A## with associated projection-valued measure ##\mu_A##
$$A = \int_{a \in \mathbb{R}} a \cdot \textrm{d}\mu_A(a)$$
for a system in the (possibly mixed) state ##\rho##. Let ##S \subset \mathbb{R}## be a measurable subset and let ##Z = \mu_A(S)## be the...
I am taking a course in quantum information theory. In this theory, the state of a system is given by a density matrix, while a measurement is completely positive, trace preserving map of the form:
Λ = ∑il i >< i l ⊗ Λi
, where Λi is completely positive.
Can anyone tell me how this is...
So I have not been able to find too much information about this. Specifically in the context of the double slit experiment. I've seen just about the only video on Youtube that tries to explain this, but I did not understand-- I felt like somethings were not explained. I am acquainted with why a...
The objective of this post is to: (i) generate a discussion of whether results of the double-slit experiment address solely the nature of matter, or do the results also address the nature of probability; and (ii) to determine if there have been any comparably structured experiments outside of...
Do you believe that "conscious" observation has anything to do with "collapsing" superimposed quantum states, or do you simply believe that interaction with a macroscopic, or sufficiently large system, is what causes superimposed quantum states to collapse? Why?
Suppose it is known that a photon has diagonal polarisation (e.g. it has just passed through a diagonal slit), then Alice comes along and measures the photon using a horizontal/vertical polarisation basis. So, I believe there is a 50% chance she will get a horizontal result and 50% chance she...
Homework Statement
For a particle in an isolated system,
the Hamiltonian operator has normalised eigenstates and eigenvalues u_{n}(x) and E_{n}, respectively.
The operator of another variable Q has normalised eigenstates and eigenvalues \phi_{n} and q_{n}, respectively.
The lowest two Q...
I would like to know, does anyone know of specific examples of quantum measurement of energy? The reason I am asking is that anything that is observed is ultimately in a position space as opposed to momentum space (for example, it might be specific position of the errow of a measurement device)...
Hello, another graduate school advising situation.
Well, like everyone else (almost), i am interested in possibility of TOK and the like;
however, since I am more of a humian empiricist I typically become bitterly skeptical of String-theory and Branes and such. Since in my opinion those...