Questions tagged [quantum-measurement]

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In quantum mechanics, do quantum systems not exist before measurement? [closed]

If a quantum system manifests itself only during measurement, and if the wave function is only our knowledge of a quantum system, maybe it does not physically exist at all before measurement? Maybe a ...
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Study of quantum mechanics [closed]

Is it possible for each of 2 observers (one stationary and the other moving) to calculate the probability of a particle to be 50% in one location and 50% in another location? I have just been ...
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1answer
50 views

How can I understand these two equations about the probability of measurement?

I have trouble understanding these two equations in the nielsen-and-chuang textbook. Suppose we perform a measurement described by the operator $M_m$, if the initial state is $|\psi_i\rangle$, then ...
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1answer
74 views

How could theoretical physics without experimentalists aid distinguish observer effect from Kennard's uncertainty principle?

Regarding this experiment which was carried out in 2012: https://arxiv.org/abs/1208.0034 I'm wondering how could the scientific society be totally convinced(prior to this paper being published) based ...
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1answer
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Can a qubit be collapsed repeatedly?

So I know a qubit collapses after measurement. Now since each eigen state can be represented as a superposition of eigen states in another basis, does that mean measuring a qubit on different eigen ...
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How does quantum contextuality relate to realism?

According to Spekkens contextuality can be defined as follows: Suppose A, B and C are Hermitian operators such that A and B commute, A and C commute, but B and C do not commute. Then the assumption ...
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3answers
151 views

Is quantum randomness just epistemic uncertainty of the microstates of macroscopic systems? [closed]

As far as I can tell, randomness in QM occurs when a classical measurement is made. Classical measurements involve macroscopic systems. We cannot know the detailed microstates of these systems. How ...
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2answers
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Help proving bound on POVM measurement probabilities

I am trying to follow Nielsen and Chuang's 1 proof that the difference in measurement probabilities is bounded by the difference between two unitary operators applied to a given state. Can someone ...
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1answer
45 views

Bell State Measurement Algorithm

I'm relatively new to quantum computation and am taking a course in it. I was wondering if it is possible to code an algorithm which would be able to take an input of a 2 qubit state and perform a ...
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24 views

Subsequent measurement of energy [duplicate]

I am interested in the subsequent measurement of energy, like assume the energy of the electron was measured to be $E_1$ and the wavefunction of the electron is described by a finite superposition of ...
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3answers
127 views

What happens to phase after wavefunction collapse?

Suppose an initial quantum state $\psi = a_1\phi_1 + a_2\phi_2 + ... + a_n\phi_n$, where $\phi_i$ is the eigenfunction with eigenvalue $\lambda_i$ of some measurement operator. Post-measurement, we ...
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42 views

Continuous Valued POVMs

I'm thinking about the mathematical details of continuous variable QM, namely the infinite $|x\rangle$ and $|p\rangle$ bases. Is it possible (and should we) think of these bases and their measurements ...
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How do we measure arbitrary observables in quantum mechanics?

The postulate of quantum mechanics say that The operators corresponding to the dependent variable $\omega(x,p)$ are given Hermitian operators $\Omega(X,P)=\omega(x\rightarrow X,p\rightarrow P)$. Now ...
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2answers
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Is the Copenhagen interpretation still the most widely accepted position?

In my undergraduate Quantum Mechanics textbook (Griffiths), of the Copenhagen interpretation it says "Among physicists it has always been the most widely accepted position". I'm currently ...
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39 views

What are the possible and meaningful measurements on a quantum walk on a graph?

In the contest of quantum walks, the graph is defined as $G=\{V,E\}$ with $V$ the set of vertices and $E$ the set of edges. Thus, the Hilbert space is defined as the $\mathcal{H}=\operatorname{span}\{\...
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Are Bohm's later books worth reading? [closed]

I mostly see Bohm's later books such as Wholeness and the implicate order and The Undivided Universe quoted in discussions of pseudoscience and quantum mysticism. Do they offer any useful insight into ...
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3answers
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Is there a theoretical or technological limit for arbitrary precise measurement of the position of a point particle in QM?

I have read this question: Where pglpm says: So the answer to your question is that in a single measurement instance we actually can (and do!) measure position and momentum simultaneously and with ...
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14answers
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Why is it impossible to measure position and momentum at the same time with arbitrary precision?

I'm aware of the uncertainty principle that doesn't allow $\Delta x$ and $\Delta p$ to be both arbitrarily close to zero. I understand this by looking at the wave function and seeing that if one is ...
2
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1answer
63 views

Why is measuring $M$ equivalent to measuring $UMU^{-1}$ after applying $U$?

I read a paper talking about Bell basis measurement circuit that simultaneously measures $XX, YY,$ and $ZZ$. It said: after applying a quantum gate $U$, a target measurement of $M$ on the original ...
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1answer
55 views

Doesn't the non-commutivity of $x$ and $p$ complicate the measurement of a quantum system's (e.g.) Energy?

A classical system is parameterized by $x$ and $p$ coordinates, and so any other observable -- such as energy -- is some function $E(x,p)$ of them. I assume, then, that to measure the energy one must ...
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1answer
59 views

Measurements, QFT and Wightman's axiom 3

I think I might have misconceptions about the conceptual core of QFT. Let me explain where I am puzzled. In QM, the measurement process is accounted by the postulate of collapse of the wave function: ...
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3answers
287 views

What happens to spin after measurement, does it evolve and randomise like position evolves after measurement?

When a particle's position is measured, if one considers the wavefunction to collapse then one can assume it collapses into a delta function peaked at the measured position, and then after some finite ...
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1answer
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A thought experiment in Quantum Mechanics

Suppose you have a particle in deep space, and two observers, such that none of these particles interact with the other two unless either observer decide to. Then if one observer makes a measurement ...
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5answers
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Is information conserved in quantum mechanics (after wave function collapse)?

I have heard in popular science that there is a law of "conservation of information." Some times this is described as: for any event that happens, there is enough information to reconstruct ...
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1answer
69 views

What causes quantum entanglement to end?

I seems strange to me that I could not easily find information on "when quantum entanglement ends?", "What causes quantum entanglement to end?". Google search finds explanations of ...
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1answer
104 views

Value of tensor product of projectors

If I have two projectors $\pi_1, \pi_2$ such that for some $|{\phi}\rangle$: $\langle {\phi}| I \otimes \pi_1 |{\phi}\rangle \geq e$ and $\langle {\phi}| \pi_2 \otimes I | {\phi}\rangle \geq e$ What ...
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1answer
51 views

Why does commutativity mean that two observables can be measured together?

BACKGROUND As far as the Heisenberg uncertainty principle is concerned, my understanding of commuting observables $\hat{A}$ and $\hat{B}$ is that the measurement outcome $a_i$ does not perturb (or ...
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3answers
128 views

Can someone explain the measurement problem with little bit of mathematics?

Can someone mathematize the statement of the quantum measurement problem? I am only interested in the statement of the problem (and not its solutions). Thanks. Still confused. Stated in this way (as ...
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1answer
68 views

Does an entangled pair remain entangled after the first measurement?

Consider an entangled pair described by the wavefunction $$\lvert1,0\rangle = \frac{1}{\sqrt{2}}(\lvert\uparrow_1\downarrow_2\rangle-\lvert\downarrow_1\uparrow_2\rangle)$$ in in the $S_z$-basis. If ...
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2answers
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Given a collapsed state, can we derive the prior shape of the wavefunction?

More or less the title. Assume that we have found a box containing a completely isolated system of particles. We do not know for how long this system has been allowed to evolve. We do know what ...
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5answers
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Why do eigenvalues correspond to observable quantities?

It makes sense to me that we can find some operator that gives us eigenfunctions that correspond to definite values for some desired observable. However, I do not see how the eigenvalues happen to ...
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1answer
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Wigner's friend question [closed]

This is probably a dumb question, but does anyone know whether both Wigner and Wigner's friend observe the same result once both have been in the room and measured?
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2answers
75 views

Show completeness of general Gaussian POVM

In Continuous-Variable quantum information, a general Gaussian measurement is described by the POVM elements (say on a single mode for simplicity) $$ \Pi(\alpha) = \frac{1}{\pi} D(\alpha) \Pi^0 D^{\...
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1answer
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Given a POVM $\{F_j\}$ with $F_j=|\psi_j\rangle\!\langle\psi_j|$, what do the quantities $F_j|\phi\rangle$ and $\langle \psi_j|\phi\rangle$ represent?

I mainly understand the concept of quantum measurement from an axiomatic viewpoint, and can't seem to find an answer to what I am wondering. If it is addressed somewhere else, pointers and/or ...
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7answers
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Why do we use Eigenvalues to represent Observed Values in Quantum Mechanics?

One of the postulates of quantum mechanics is that for every observable $A$, there corresponds a linear Hermitian operator $\hat A$, and when we measure the observable $A$, we get an eigenvalue of $\...
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1answer
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What is the meaning/significance of the values measured from an observable?

I'm reading Nielsen and Chuang, and I'm trying to understand what we actually mean when we talk about observables and their relationship to measurements. I'm more of a mathematician than a physicist, ...
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38 views

Qubit state probability

Consider the general qubit state $\alpha \begin{pmatrix} 0 \\ 1\end{pmatrix} + \beta \begin{pmatrix} 1 \\ 0\end{pmatrix}$ in a general orthnormal basis with vectors $\begin{pmatrix} \alpha \\ \beta \...
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Measuring momentum in a 2 height well

In a 2 height finite square well we know that qualitatively the position wavefunction will have a lower amplitude in the side of the well with a smaller potential energy (since it will be travelling ...
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1answer
58 views

Settling Copenhagen Interpretation / Measurement in QM & Existence of Quantum Gravity

It is my understanding that there are many interpretations of observation/measurement in Quantum Mechanics (I am only familiar with the Copenhagen one). The Schrodinger's Cat experiment forms a ...
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1answer
48 views

Why are there so few ion-trap experiments studying quantum trajectories?

The quantum trajectory theory describes the behaviour of a quantum system under continuous monitoring. Initially it is theoretically studied in quantum optics and single atom scenario (e.g., ion trap ...
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1answer
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Book recommendation for how classical mechanics emerges from quantum mechanics?

Question So I read this interesting link: The most glaring problem is that the state spaces of classical and quantum mechanics are completely different, so you can’t have a simple limiting procedure ...
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1answer
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What does Schrödinger equation reduce to in the limit of a continuous position measurement?

If we measure position of a quantum particle, we force its wavefunction to collapse into a wavefunction whose probability density is given by a Dirac delta function (all the probability density of ...
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2answers
61 views

Are distributions of position and momentum assumed to be independent in quantum mechanics?

Given a wave-function of a single particle we can calculate probability density for positions. We can also calculate probability density for momenta. Are these probability densities assumed to be ...
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1answer
77 views

Quantum measurement paradox

let's define 'a measurement device' as a system which is highly sensitive to the eigenstate of an observable. The sensitivity is quantified let's say by how irreversible and grand the small changes in ...
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1answer
47 views

Continuous spectra and measurement

Suppose I have a particle whose momentum I measure to be $p$ with uncertainty $\delta p$. Right after the measurement we know that its wave function is given by $\psi(x)=\int g(p)e^{ipx/\hbar}dp$ (...
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1answer
107 views

Pauli matrices Measurements

When performing a measurement On qubits with the Pauli matrices, They all correspond to outcomes +1,-1 because that's their eigenvalues? In my notes it says that the $z$ Pauli matrix can be broken ...
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1answer
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What theories of quantum mechanics can eschew global phase?

Whilst reading the quantum.country essay by Michael Nielsen and Andy Matuschak, they mention (a bit further down from here) that there is formulations of QM that can completely ignore global phase ...
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Identifying Collapse in Wave-function [duplicate]

Is there a machine or instrument which will notify us instantly when the wave-function has collapsed if we have access to only one of the entangled particles? Note that the wave function collapse will ...
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2answers
119 views

Conservation of energy in quantum tunneling

By this question, a particle can tunnel to inside a potential barrier. One aspect of this process that was not addressed in the answers was the conservation of energy. Motivated by this question, I am ...
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Field measurements in QFT

If I understand it correctly, QFT assigns a field operator to every point in space. For a free scalar field: $$ \hat{\phi}(\mathbf{x},t)=\int \frac{d^3p}{(2\pi)^3} \frac{1}{\sqrt{2\omega_{\mathbf{p}}}}...