Consider a simple quantum eraser setup using polarizers: An incident beam polarized at 45º is sent towards a double slit. After slit A there is a horizontal polarizer and after slit B there is a vertical polarizer. At the back screen, if we run this experiment, we will see a particle pattern and...
Hi there, have a wonderful next year!
I'm here because I have a doubt. I was trying to generalize the Einstein Field Equation for Von Neumann W* Algebra, which is related with non-integer, non always positive degrees of freedom. In particular, with the sum of positive and negative fractal...
In his paper "Theory of self-reproducing automata", Von Neumann asserted that it is in principle possible to set up a self-reproducing automaton that consists of the following automata:
A scanner - given an object X returns a description of X
B builder - given a description of X...
Today the inexact differential is usually denoted with δ, but in a text by a Russian author I found a dyet (D-with stroke, crossed-D) instead:
In response to my question to the author about this deviation from normal usage, he stated that this was a suggestion from von Neumann. (Which of course...
I'm not sure about my proof. So please check my step. I used log as a natural log(ln).
Specially, I'm not sure about "d/dt=dρ/dt d/dρ=i/ħ [ρ, H] d/dρ" in the second line. and matrix can differentiate the other matrix? (d/dρ (dρ lnρ))
The von Neumann entropy for an observable can be written ##s=-\sum\lambda\log\lambda##, where the ##\lambda##'s are its eigenvalues. So suppose you have two different pvm observables, say ##A## and ##B##, that both represent the same resolution of the identity, but simply have different...
Nobel laureate Hans Bethe was a friend of mathematician-physicist John von Neumann, and he once said:
"I have sometimes wondered whether a brain like von Neumann's does not indicate a species superior to that of man"
and
"[von Neumann's] brain indicated a new species, an evolution beyond man"...
In the Many Worlds Interpretation's wikipedia article (https://en.wikipedia.org/wiki/Many-worlds_interpretation), it says, at the "Reception" part:
"(...) On the other hand, the same derogatory qualification "many words" is often applied to MWI by its critics, who see it as a word game which...
I do not know exactly where to ask this. I do not even know if I can. I chose the General Discussion forum since it seems to me the best place to ask this within this site.
Having said this, Did John von Neumann ever go to Oslo or any other part of Norway?
It is known that he traveled at least...
I was trying to show how to get Schrödinger’s equation from the von Neumann equation and I’m not quite confident enough in my grasp of the functional analysis formalism to believe my own explanation. Starting from
$$i\hbar\frac{\partial}{\partial t}\rho=[H,\rho]$$
We have...
I'm looking for work published discussing the relationship between von Neumann entropy as well as entanglement with regard to chemical reactivity in the ultracold temperature scales. An article published under the title "Ultracold chemistry and its reaction kinematics" discussed this...
Definition 1 The von Neumann entropy of a density matrix is given by $$S(\rho) := - Tr[\rho ln \rho] = H[\lambda (\rho)] $$ where ##H[\lambda (\rho)]## is the Shannon entropy of the set of probabilities ##\lambda (\rho)## (which are eigenvalues of the density operator ##\rho##).
Definition 2 If...
Hi All
Read a thread that about Von-Neumann observations that was closed because it was a bit too vague, but I sort of got a sense of what the poster was on about - and it also is interesting anyway for anyone that doesn't know it so I thought I would do a post about it.
Since Von-Neumann's...
I've been studying the von Neumann measurement scheme (and understanding the math part) where the system and apparatus are quantum in contrast to the orthodox where the apparatus is classical. I'd like to know the following.
1. Is the von Neumann measurement scheme 100% orthodox and believed by...
In holographic entanglement entropy notes like here, they let alpha go to one in (2.41) and get (2.42). But (2.41) goes towards infinity, when doing that! Can someone explain how alpha --> 1 will make (2.41) into (2.42)? Thank you!
I have been studying about computers and found that they evolved from the basic mechanical devices with limited functions to the amazing machines we have today. Its all very new and interesting to me.
I believe that programming is the act of writing an algorithm in a higher or lower level...
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...
Homework Statement
I have a financial intermediation model with delegated monitoring to a venture capitalist. At the moment all participants are risk neutral and i want to introduce risk aversion to the model. Therefore i need a utility function under the von neumann morgenstern criteria, ie...
Homework Statement
Prove that the maximum value of the Von Neumann entropy for a completely random ensemble is ##ln(N)## for some population ##N##
Homework Equations
##S = -Tr(ρ~lnρ)##
##<A> = Tr(ρA)##
The Attempt at a Solution
Using Lagrange multipliers and extremizing S
Let ##~S =...
Bohm's deterministic theory was designed to be equivalent to standard QM, but what I'm not sure about is whether that includes Von Neumann's rules.
Von Neumann's rules for the evolution of the wave function are roughly described by:
Between measurements, the wave function evolves according to...
How should I prove this?
From John Preskill's quantum computation & quantum information lecture notes(chapter 5)
If a pure state is drawn randomly from the ensemble{|φx〉,px}, so that the density matrix is ρ = ∑px|φx〉<φx|
Then, H(X)≥S(ρ)
where H stands for Shannon entropy of probability {px}...
I'm trying to refresh some numerical science stuff. Von Neumann analysis, if I take a slimmed down equation, convection. \frac{∂u}{∂t}+a ∇ u =0 If I'm using Euler forward, \frac{u^{n+1}-u^n}{\Delta t}+\frac{a}{2h} \left( u_{j+1}^n -u_{j-1}^n \right) =0 For \hat{u}^n = G^n\hat{u}^0 a growth...
I know how to get Von Neumann entropy from a density matrix. I want to get a real number from measurements that give real numbers as outcomes. (there are complex numbers in a density matrix).
So suppose Charlie sends 1000 pairs of particles in the same state to Bob and Alice. They agree to...
Hi
I have discovered that the Von Neumann bias correction method only works when the bias is 100% stable, for example tossing the same loaded coin again and again.
Does anyone know of a bias correction method which can correct an unstable bias? Is this impossible?
Edit: Let's say I have a...
According to John von Neumann’s interpretation of QM, consciousness is why the wave function collapses. Copenhagen is on the same general idea, but does not mention it that categorically.
Multiverse interpretation of QM says there is no wave function collapse, therefore the observer or...
I'm trying to get to the bottom of things concerning the shaping of an optical pulse(change of state) with linear optics. Using linear optical apparatus we can shape the pulse of a photon in such methods as cavity dumping. You feed an optical cavity with near monochromatic(short bandwidth)...
***EDIT: This is nonsensical. I'm new to density matrices, and I had a sign error that led to some confusion. In addition... this just doesn't make sense, reading it over. I apologize for the post. I'd appreciate it if a moderator removed this, please.
I'm reading about the von Neumann entropy...
Is anyone thoroughly familiar what von Neumann was trying to say in his von Neumann Chain concept where one can locate anywhere the observer and the observed? I've been reading the original and analyzing it for hours and can't seem to completely get the context in light of present day concept...
Density matrix and von Neumann entropy -- why does basis matter?
I'm very confused by why I'm unable to correctly compute the von Neumann entropy
S = - \mathrm{Tr}(\rho \log_2{\rho})
for the pure state
| \psi \rangle = \left(|0\rangle + |1\rangle\right)/ \sqrt 2
Now, clearly the simplest...
Can anyone help me out with von Neumann entropy please??
I've been wondering if I could be able to calculate the entropy of a system which is part of a bigger system.
For example, let's say that there's a cavity and two atoms(atoms are two-level system).
The hamiltonian of the system would...
Von Neumann wrote in a major physics book decades ago that consciousness was what collapse the wave function.. how could he stated this bizaare statement and the facts remain up to this day?
Is the interpretation been refuted already by the latest discovery of Decoherence? I can't find...
The Von Neumann entropy is \mathcal{S}(|\psi\rangle) = -Tr[\rho_a ln \rho a] . The linear entropy S_L = \frac{l}{l-1}(1 - Tr[\rho_a^2]) For l =2 the linear entropy is written 4Det(\rho_A) which is also called the tangle \tau. I understand this just fine, I can show that. Now it says the Von...
(a) Let α and β be two von Neumann ordinals. Show that α ⊂ β if and only if α ∈ β.
(b) Show that the Axiom of Foundation implies that a transitive set which is linearly ordered by ∈ is an ordinal
I can't seem to follow through this properly, any help?
I am confused by the definition of the Von Neumann entropy. In Nielson and Chung's book page 510, the Von Neumann entropy is defined as
S (\rho) = - tr(\rho \log \rho)
where \rho is the density matrix. What is the definition of the logrithm of a matrix? Is it some series expansion of a...
Dear all,
I am a new member of this forum. I saw it many and I found it very interesting.
I am solving a 2d transport equation. I discretized it in space with an upwind scheme and in time with Backward Euler difference. Hence, if I want to solve the problem I have to solve a linear system of...
I just wanted to run this working by some of you.
Simplest Greenberger-Horne-Zeilinger state (entagled) state is:
\mid GHZ \rangle = \frac{1}{\sqrt{2}}\left(\mid 0 \rangle_{A}\mid 0 \rangle_{B}\mid 0 \rangle_{C}+\mid 1 \rangle_{A}\mid 1 \rangle_{B}\mid 1 \rangle_{C}\right)
density matrix is...
We have a hyperbolic pde (in fact the 1d wave equation) with indep vars X, T
We use the central difference approximations for the second derivatives wrt X, T to get
[phi(Xn, Tj+1) -2phi(Xn, Tj) + phi(Xn, Tj+1)]/(dT^2) = [c^2][phi(Xn-1, Tj) -2phi(Xn, Tj) + phi(Xn=1, Tj)]/(dX^2)
where dX...
What's the difference between thermodynamic entropy and von Neumann entropy? In particular, how is temperature related to the von Neumann entropy?
Also, what has information got to do with these two entropies?
Let P be a density matrix. Then the von neumann entropy is defined as
S(P) = -tr(P*log(P))
But how is log(P) defined ?
--edit--
found the answer. the trace is independent of representation so that if P is diagonalized with eigenvalues {k} then S(P) = H({k}) where H is the shannon entropy.
Could somebody please explain or give me a link to an explanation of the idea about measerument that von neumann put forward. That is that a system interacts with a pointer state associated with the measurering device with the hamiltonian
H:=c * d(t) * A (X) * P
where d(t) is diracs delta...
I wonder If someone could state the mean ergodic theorem von neumann without using meassure spaces ? I have studied normed spaces, banach spaces and hilbert spaces, that is complete normed inner product spaces.
Could someone state and explain the theorem for me? :smile: