Questions tagged [quantum-measurements]

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What is the impact of the time-independent Hamiltonian operator on the observation probabilities?

If you assume that $H$ is a time-independent Hamiltonian, by the Schrodinger equation, the state evolution $|\Psi(t)\rangle$ is given by $ \left( \sum e^{\frac{-i \lambda_j}{\hslash} t} |{ v_j }\...
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Position of the wavefunction's collapse

When a wave function is said to "collapse" to a single point during a measurement, is there uncertainty about the point's position or is it known infinitely precisely?
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How is it that a particle's wave function is not a real thing, yet we can still observe it?

In the double slit experiment, scientists could see an interference pattern on the back panel. However, if the wave function is purely a mathematical object, how can it be the case that some physical ...
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If measurement fixes the state of a quantum system, how do we know that superposition exists?

My very limited understanding of quantum mechanics cannot make sense of the superposition phenomena. It would seem to me like if a measurement makes the wave function of a quantum system collapse, ...
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It is usually said that a Quantum field is a superposition of fields. How do we (in principle) acquire the probabilities for a certain configuration?

I read This paper by Baker, which talks about the interpretation of QFT. Essentially, the author looks for ontological "beings" that one can identify in QFT. The author argues that a fock ...
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1answer
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Is any “measurably independent” bipartite state separable?

Is it true that any bipartite state that is "measurably independent" is separable? I am defining a state $|\psi \rangle \in A \otimes B$ to be "measurably independent" if: The ...
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1answer
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Are there instances where the density matrix is singular?

Are there instances where the density matrix is singular? Can there be cases where a measurement projection onto the density matrix gives a singular matrix?
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3answers
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How is superdeterminism a loophole to Bell's theorem?

I read wiki about superdeterminism and Bell's theorem and the lecture on free will, and I struggle to understand what free will has to do with the Bell's theorem. From my understanding, for Bell's ...
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2answers
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Are observables in QFT actually observable?

Consider some interacting QFT on a lattice (just to avoid infinitely large momentums). The size of the lattice is assumed to be much smaller than the size of the emergent particles (like in our world)....
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0answers
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Can a wave function be measured to arbitrary precision?

Suppose we want to measure a modulus square of a wave function $\psi(\vec{r},t)$ for a single particle. It is important that the wave function depends on time. Are there any fundamental limitations ...
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1answer
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States of a quantum system immediately after a measurement

Consider an observable with a spectrum that has both a discrete and continuous part. If a measurement is made for this observable while the system is in some state, if the measurement outcome was one ...
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Sequential Stern-Gerlach experiments without an intermediate measurement

What happens if we pass a particle through several Stern-Gerlach devices (say, oriented along x- and z-axes) without measuring the state of the system between them? My initial assumption has been that ...
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Why are “weak measurements” defined via a second-order approximation of the dynamics?

Consider an initial (separable, pure) bipartite state $|\Psi\rangle=|\psi\rangle\otimes|\phi\rangle$, evolving with an interaction Hamiltonian $H\equiv A\otimes B$. At a time $t$, the evolves state is ...
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Expected value in usual quantum mechanics vs quantum information

In standard Quantum Mechanics, one computes the expected value of an operator $A$ (arbitrary state $|\Psi\rangle$) as $$ \langle\Psi|A|\Psi\rangle. $$ This has the virtue that we can compute for ...
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1answer
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Interaction of quantum particles

I am still a student, so if the question is stupid, I apologize. If quantum particles interact with each other constantly and continuously (described by a single wave function in quantum mechanics or ...
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1answer
35 views

Simultaneous measurement of multiple observables

Commutation relations tell us which observables are compatible and which ones are not. How is that extended to more than two observables being measured at the same time (or successively)? If $\hat A$, ...
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1answer
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Does any uncertainty relation exist for interfering measurements (ie. for 2 subsequent measurements of 2 incompatible observables on the same system)?

To test the usual Robertson-Schrodinger uncertainty bound, we follow the methods delineated in the answer here by Timaeus. This method talks about non-interfering measurements. For two incompatible (...
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1answer
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Why isn't the variance of a quantum observable depend on how gently or roughly the measurement is carried out?

Consider an ensemble specified by a state $|\psi\rangle$ on which we decide to make measurements of an observable $A$. If the state $|\psi\rangle$ is not an eigenstate of $A$, there will be a scatter ...
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2answers
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Uncertainty in position measurement in two ensembles. First with same $\psi$ but different $N$, and second with same $\psi,N$ but different apparatus

Imagine an ensemble of $N$ identical and identically prepared quantum systems, all of which are in the state $\psi(x,t)$ at time $t$. Given the state (which could be a Gaussian in position) the ...
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How sharply does the wavefunction collapse upon measuring position? [duplicate]

It cannot be a Dirac delta as this is not a continuous normalisable function. Further to the answer written by John Rennie How does wave function collapse when I measure position? We may assume that ...
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1answer
45 views

Hermitian operator with gaussian eigenfunction [closed]

I'm struggling to find a hermitian operator whose eigenstate is a gaussian function in $|\psi(x)|^2$. How do i do this? Just to be clear, this is in order to realistically model the wavefunction ...
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1answer
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Question about Projective Value Measurements

Nielsen and Chuang define a projective measurement as an observable $M$ which has spectral decomposition $$\sum_m mP_m$$ Where the $m$'s are $M$'s eigenvalues and each $P_m$ is a projection on to $M's$...
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Measurement accuracy in quantum mechanics?

Here's some classical background to this thought experiment. Let us first consider a classical scale ruler (called A) of a continuous classical variable. Rulers must be discretised. Let's compare this ...
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1answer
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Does measuring a photons position violate the uncertainty relation?

The velocity of a photon has an exact value: the speed of light. We don't have to make a measurement of the photon's velocity to know its velocity. So if we measure the photon's position (thereby ...
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Measurement in quantum mechanics?

Question 1: suppose there is a quantum observable superposition of 4 eigenstates $\lambda_1e_1 + \lambda_2e_2 + \lambda_3e_3 + \lambda_4e_4$. Does a 'measurement' have to reduce this wavefunction to a ...
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What state does a system collapse to after measuring a degenerate eigenvalue?

$\newcommand{\ket}[1]{|#1\rangle}$ Let $\hat A$ be some observable, and $\ket n$ and $\ket m$ two degenerate eigenstates with eigenvalue $a$, such that $$\hat A \ket n=a\ket n,$$ $$\hat A \ket m=a\ket ...
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1answer
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Where does the expression $\mathrm{Tr}(K) = \sum_{j=1}^{n}\langle\psi_j|K|\psi_j\rangle$ for the partial trace come from?

During my studies of composite quantum systems I find some expressions that leave me with a little doubt. For example: Let K be a linear operator defined in the Hilbert space H. Where H is given by $H ...
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Why is throwing one part of the EPR state away not the same as measuring it and not looking at the result?

Disclaimer: The amount of sense that the following makes might differ depending on which interpretation of quantum mechanics you are supporting. Suppose that I have the EPR-state \begin{align*} \frac{...
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3answers
84 views

Why does the wavefunction of a particle spread out after a measurement?

Quantum mechanics states that the wave packet of a particle "spreads-out" in position again after a measurement on this particle has been made. Is this spreading or "dispersion" ...
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Measurement of non well-defined magnitudes (position)

Lets consider an hydrogen atom (superposed states) and the measurement of it's angular momentum ($\hat{L_{z}}$, in this case) since at least is defined. I imagine the measurement could be something ...
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Interpretation of measurements and Eigenstates for continuous variables [duplicate]

I find myself (probably like many others) somewhat unclear on the implications of the postulate of quantum mechanics that "measurements of a value leave the system in an eigenstate". The ...
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1answer
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Is uncertainty necessarily nonzero for non-eigenstates?

Is uncertainty necessarily nonzero for an operator acting upon a state which is not one of its eigenfunctions? For instance, if a wave function representing a state is not an eigenfunction of the ...
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1answer
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How precisely can particle position be measured in a laboratory?

If we have any given particle, such as a photon or an electron (it doesn't really matter what for the sake of the question), how precisely can modern physics devices measure their position? ...
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1answer
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Determining the probability of measuring a particular eigenvalue for angular momentum given the angular wave function

Suppose I know the normalised angular wave function of a particle that is defined as $\psi(\theta,\phi)$ How would I use this to determine the probability of measuring a particular observable such as ...
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1answer
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How does Stern-Gerlach experiment lead to conclusion of electron's spin?

As far as I understood in the Stern-Gerlach experiment, silver atoms while passing through an external inhomogeneous magnetic field they split into two groups. My question is how does that separation ...
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4answers
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Stern-Gerlach apparatus measures the magnetic moment. How to measure spin?

Since the Stern-Gerlach apparatus employs a magnetic field, it actually measures the magnetic moment $\mu$. If you assume a certain proportionality constant between $\mu$ and spin, then you can also ...
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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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1answer
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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
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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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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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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
81 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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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
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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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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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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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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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