16
That isn't really the right question to ask. We never measure wave functions. We measure properties like position, momentum, energy of an electron. Whether the electron is spin up or spin down. The behavior of these properties doesn't match what you would expect from classical physics. Wave functions are a mathematical construct that help predict what ...
14
What is a wave function? It is a mathematical function depending on energy and momentum or space and time,$Ψ(p_x,p_y,p_z)$ or $Ψ(x,y,z,t)$ ( in its simple form). This function is a solution of a wave equation, a second order differential equation.
Mathematical functions are a billion, what is the wave function's connection with measurable physical ...
13
$\def\ket#1{\left|#1\right\rangle}\def\bra#1{\left\langle#1\right|}\def\braket#1#2{\left\langle#1|#2\right\rangle}$In quantum mechanics, the overall phase of the wavefunction is not physical. So $e^{i\phi}\ket{\psi}$ represents one physical state, regardless of the value of $\phi$.
This does not imply that ${1\over\sqrt{2}} (\ket{0} + \ket{1})$ and ${1\over\...
11
There is no way to tell if wavefunction collapse is immediately everywhere (whatever that might mean in a relativistic universe), because wavefunction collapse has no observable consequences.
The Everett Interpretation of quantum mechanics (also misleadingly known as the 'Many Worlds Interpretation') explains all observations without requiring wavefunction ...
8
I realise there are many different pure states that can combine into the same mixed state, so "disassembling" may produce infinitely many solutions.
This is indeed true. The decomposition of a density matrix into a classical distribution is highly ambiguous (as I explained at depth in this previous thread).
However, the loose idea of the "...
5
There are no theories describing wave function collapse. The concept is pure interpretation and in my opinion problematic. Wave functions are fully specified as solutions of a wave equation, such as the Schrödinger or the Dirac equation. These equations do not allow for a collapse.
The ensemble or statistical interpretation is among others does not require ...
5
$\vert 1\rangle$ and $-\vert 1\rangle $ are obviously different as vectors of a vector space. However, one has to keep in mind that mathematical objects are related to physical entities via some postulated correspondence. The claim (that your professor is correctly making) is that they represent the same physical states. In other words, there is no ...
3
I would comment this but i need 50 rep so here it is posted as answer instead:
The exact same question is answered in this post:
Maximum theoretical data density
3
when we measure some measurable value the wave function collapses immediately everywhere.
When I studied physics (30 years ago), this concept stopped me from believing what was taught; because it is clearly wrong. Professors couldn't even answer the question "then what IS a measurement"? At the time it was even thought to have to do with humans ...
3
x,y,z,t are mind variables. They exist as physical variables in the physical system of our mind.
Our mind also has memory. We measure x,y,z,t of a particle to some precision and then summarize our memory or the memory of the photographic plate or instrument.
This measurement procedure is detached from the actual events.
We compare with our expectations. If ...
3
It doesn't "happen immediately everywhere" because it doesn't "happen" at all. It's part of the understanding of the person interpreting QM.
In particular, since you've tagged this question quantum-information, faster-than-light, and causality, "wave function collapse" does not convey any information, so it's not subject to any ...
3
It's pity that none of the answers (though great ones have been given!) mentions an interpretation of quantum mechanics which assumes a physical reality of the wavefunction: the hidden variables interpretation. Louis-Victor-Pierre-Raymond de Broglie initially proposed the pilot wave, which is a physical wave corresponding to the wavefunction, and David Bohm, ...
2
Taking a measurement could be seen as "continuous" process per this article. You can see that the particle measured becomes fixed in a certain eigenstate the more you (weakly) measure it/it gets more entangled/information piles up (note: I kind of guess that a "weaker" measurement corresponds to lessened interactions).
"A deeper ...
2
There is no collapse of the wave function. Most physicists agree on this today. Although it wasn't the same only 20 years ago. There cannot be such a process, if the Schrödinger equation is to represent a universal pattern. And I will, of course, adopt the stance that it does.
The collapse of the wave function is an convention adopted by the so-called ...
2
To understand this, you have to give up your classical intuition and think about quantum entanglement and measurement.
The "collapse of the wavefunction" is just an interpretation and different people think about it differently, and some even say it is not physical and not even real.
Entanglement is just a correlation - one that can potentially ...
2
The authors are neglecting the unobservable global phase, see $[11]$ at the very end of references and mentioned above equation $(15)$
$[11]$ In Eq. $(15)$ we have neglected a physically irrelevant, global phase $e^{i\pi/4}$ originating in that $\det(U_{CNOT}) =−1$ in Eq. $(1)$, i.e. $U_{CNOT}\notin \mathcal{SU}(4)$.
2
So, let's start with the fundamental vagueness of the question. The reason behind this vagueness is the lack of clear unpacking of what is meant by "computation" or "prediction" or "modelling".
Let's suppose for a second that you actually do have an infinitely powerful computer that is able to simulate the dynamics of any number ...
2
One possible decomposition is given by the eigenvalue decomposition
$$
\rho = \sum p_k \vert\psi_k\rangle\langle\psi_k\vert\ .
$$
Any other decomposition
$$
\rho = \sum q_\ell \vert\phi_\ell\rangle\langle\phi_\ell\vert$$
is related to this one through
$$
\sqrt{q_\ell}\vert\phi_\ell\rangle = \sum v_{\ell k}\sqrt{p_k}\vert\psi_k\rangle\ ,
$$
where $(v_{\ell k})...
2
To add a very simplistic statement to the other very complete and well thought out answers:
Absolute phase is not physical, relative phase is physical.
That's why the two states in your first example are physically the same, whereas the two states in your latter example are not.
2
entanglement between two qubits means that if a measurement is made on
one of them, the other one is decided instantaneously.
This is true, but this does not allow for faster than light communication. If you have one qubit with you and i have one qubit with me and you make a measurement on your qubit, that will mean my qubit is decided . But how does that ...
1
Einstein referred to entanglement as "spooky action at a distance", Erwin Schrodinger came up with Schrodinger's cat as an absurd analogy. But today people and pop science magazines extol the virtues of these absurdities demonstrating the wonderful mysticism entanglement not to mention sophist arguments to play down the obviously faster than ...
1
Let's say we consider a Hilbert space $\mathscr{H} \equiv \mathscr{H}_{\mathrm{A}} \otimes \mathscr{H}_{\mathrm{B}}$.
Here, $\mathscr{H}_{\mathrm{A}}$ and $\mathscr{H}_{\mathrm{B}}$ could be e.g. the Hilbert spaces of distinguishable particles; or if $ \mathscr{H}_{\mathrm{A}} = L^2(\mathbb{R}^3)$ and $ \mathscr{H}_{\mathrm{B}}= \mathbb{C}^2$, then $\mathscr{...
1
In the axiomatic algebraic formalism, say of the Ostwalder-Schrader axioms of nets of local algebras, it turns that the local algebra must all be isomorphic to the unique hyperfinite factor of type $III_1$. Hence specific theories depend upon how these algebras embed within each other.
For more details, see the paper The Role of Type III Facyors in QFT by ...
1
There are several issues here. First there is a question about whether physics is deterministic enough that it can be computed even in principle. The second is how to motivate statistical mechanics.
The first one is somewhat outside the scope of this SE, although the question does show up here from time to time. One can argue that certain quantum events are ...
1
Consider two elements of the set of thermal operations, with unitaries $U$ and $U'$ and Hamiltonians $H_B$ and $H_{B'}$, respectively. Following your convention, I will write $\gamma_\bullet=\frac{e^{-H_\bullet/kT}}{\operatorname{tr}(e^{-H_\bullet/kT})}$.
Then, the concatenation of both thermal operators is the map
$$
\rho\to \mathrm{tr}\big[U_{SB}U'_{SB'}(\...
1
Multimode states are product states
$\vert n_1n_2\ldots,n_{\ell'}\ldots,n_\ell\ldots \rangle =\vert n_1\rangle\otimes\ldots \vert n_{\ell'}\rangle
\otimes \ldots \otimes \vert n_\ell\rangle\otimes \ldots $ and the working assumption is probably that if $\langle n_1\ldots,n_\ell=0,\ldots\vert\psi_i\rangle = 0$ then $\hat \alpha_\ell \vert\psi_i\rangle=0$ so $...
1
Yes, in the simplified model of time-independent Hamiltonian $H$ effecting a quantum gate $U=\exp(-iHt)$ multiplying $H$ by a constant factor $\gamma > 1$ does shorten the gate's duration.
In practice, physics constants, material properties, control electronics etc constrain what Hamiltonians can be engineered on any given hardware platform. For example, ...
1
I am not completely clear what your ‘not’ collapse is, but it still seems to be a collapse of the wave function. Indeed, if there is a ‘not’ observable then the wave function must collapse into an eigenstate of the ‘not’ operator at each time when we measure the ‘not’ observable.
We can never observe an uncollapsed wave function i.e. a wave function that is ...
1
The books on information theory are plenty - you could find lots of them by googling, searching on amazon, or searching in this site (for example, here).
From my personal experience, Elements of information theory by Cover and Thomas is pretty accessible to somebody with physics background. Another excellent source is the Shannon's original paper - it is old,...
1
Einstein referred to entanglement as "spooky action at a distance", Erwin Schrodinger came up with Schrodinger's cat as an absurd analogy. But today people and pop science magazines extol the virtues of these absurdities demonstrating the wonderful mysticism entanglement not to mention sophist arguments to play down the obviously faster than light ...
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