Questions tagged [quantum-measurements]
The quantum-measurements tag has no usage guidance.
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Measurement values affects probabilities in QM?
Consider a non-degenerate operator $\Omega$ with discrete eigenvalues $\omega_i$, where $i=1,2,3,...$. We can write $\Omega = \sum_i \omega_i~|\omega_i\rangle \langle \omega_i|$, where $|\omega_i\...
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Is there a general construction for three-outcome qutrit POVMs?
For qubits, I can consider the General POVM elements: $M_{\pm} = \frac{1}{2}(I \pm \hat{n}\cdot\overline{\sigma})$ where $\sigma $ is a vector containing the Pauli matrices and $\hat{n}$ a vector with ...
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"Jump" operators from Lindblad equation where the external system is measurements
How do we derive the "jump operators" for the Lindblad equation if the external system is measurements? For example in this article for the Bose Hubbard system the Lindblad operators ...
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Why are expectation values of an observable important in QM?
I've been reading that expectation values of an observable is all what we can get and are the key quantities of the theory, but performing the same experiment many times would generate a distribution ...
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Superposition of energy levels
When thinking about a "random" atom in space (say a Hydrogen atom), should I assume that the electron is in a ground state (or any particular excited eigenstate) or is it in a superposition ...
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What happens if we throw the observer in a black hole?
Sorry if this sounds like a silly question, but what would happen if a scientist observes Schrodinger's cat alive, but is then thrown into a black hole before he has leaked any information to the ...
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Josephson supercurrent measurement in a lab
This may be a very trivial question but I am a theoretician and can't find the answer to this question for the life of me. Is it possible to actually measure the Josephson supercurrent flowing through ...
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Quantum time evolution after position measurement
Consider a free particle with hamiltonian $\hat{H}=\frac{\hat{p}^2}{2m}$ and propagator $\hat{U}(t) = e^{-\frac{i}{\hbar}\hat{H}t}$:
we can compute the time evolution of a position wavefunction as:
$$
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How to know what eigenvalue corresponds to measurements of individual qubits in a multiqubit system?
I'm working through the book "Introduction to the Theory of Quantum Information Processing" by Bergou and Hillary, and I've encountered a scenario that I'm not sure how to approach. In ...
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Is there any way to measure a photon and allowing it to continue on its path?
In the context of the double slit experiment and variants thereof, although it doesn't have to be this context, my question is more generic:
Is there any way to measure the position or momentum of a ...
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Value of Measurement in Quantum Mechanics
Consider a Hamiltonian $H$ with discrete eigenvalues $\{E_n\}_{n=1}^\infty$ and eigenstates $\{\psi_n\}_{n=1}^\infty$.
Suppose I prepare a state $\psi=c_1\psi_1+c_2\psi_2$ (normalized) and make a ...
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How is the bomb represented mathematically in the Elitzur-Vaidman bomb tester?
... or more generally, how can one represent mathematically an obstacle in interaction-free measurements? Would it be reasonable to represent it as an "absorption" that transforms $\mid 1\...
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Can you project on an orthogonal basis for a multipartite quantum system using only local operations and classical communication?
Say Alice possesses one qubit, and Bob two, and that the joint state is $|\psi_{A, B_1, B_2}\rangle = \alpha|n_1\rangle + \beta |n_2\rangle$, where $|n_1\rangle$ and $|n_2\rangle$ are orthonormal ...
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Can the collapse of the wave function be modelled as a quantum system on its own?
Imagine I have an observer $\mathcal O$, a quantum system $\mathcal S$ with Hilbert space $V_{\mathcal S}$, a Hamiltonian $H$, a self-adjoint operator $A$ acting on $V_{\mathcal S}$. The system is in ...
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Measurement of Position in Bohmian Mechanics
In many formulations of Bohmian mechanics, researchers seem to claim that 1) measurements of observables such as spin are just measurements of the position of a pointer variable, such as the Stern-...
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Measurement problem and precise mathematical calculation
The infamous measurement problem is a problem in the foundations of quantum mechanics: different people have different views how to understand this problem: some people even deny that there is any ...
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How do we prove that POVMs are the most general measurements?
It is often claimed that POVMs represent the most general measurement statistics possible. But what is the justification for this claim? Textbooks and university courses generally try to build up to ...
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What are the conditions for Peres' rank-1 POVM construction to actually be implementable?
I am trying to understand the implementation of POVMs on a Hilbert space by using unitary operations and projective measurements in a larger Hilbert space. In A. Peres' Quantum Theory: Concepts and ...
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Doubt regarding measurement of spin in quantum mechanics as per 1st chapter of Quantum Mechanics, A Theoretical Minimum by Leonard Susskind
Susskind starts with an experiment in which he measures the spin of a particle , which can either take a value of $+1$ or $-1$ along any particular axis. He takes a measuring device $\mathcal A$ which ...
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Commuting operators and their physical interpretation in QM
I'm studying Quantum Mechanics for the first time at the moment and I have a few questions in mind.
So recently, I saw a proof on that if two operators share the same eigenstates is equivalent to the ...
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Uncertainty principle, maybe it doesn't forbid simultaneous measurements of position and momentum?
Consider the single-hole diffraction of an electron. We can make the hole as small as we like and determine the electron's position with arbitrary accuracy. When it is in the hole, we can hit it with ...
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Heisenberg uncertainty principle during measurement
I am currently studying quantum mechanics and again came across the uncertainty principle, and I seem to lack any intuition about what it means. I full understand how it can be derived using ...
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What is the Hamiltonian of a Measurement?
In quantum mechanics, any kind of measurement causes the quantum state to change to something we'll call "definite", but sometimes it's actually not definite, just a very small variance.
But ...
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Explicit demonstration of a quantum measurement interaction
$$\newcommand{\bra}[1]{\left \langle #1 \right \rvert}
\newcommand{\ket}[1]{\left \rvert #1 \right \rangle}
\newcommand{\braxket}[3]{\left \langle #1 \middle \rvert #2 \middle \rvert #3 \right \rangle}...
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$SU(2)$ vs. $SO(3)$ transformation, spinor rotation and measurement
Is it possible to measure the effects of $SU(2)$ rotations acting on spinor wave functions $\psi$ in the fundamental representation? That means, is it possible to extract information that ...
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Can a POVM with repeated elements be considered a PVM?
A positive-operator valued measure (POVM) is a set $\{F_i\}$ whose elements are each Hermitian and positive semidefinite ($F_i^\dagger=F_i$; $F_i\succeq 0$) and which together sum to unity ($\sum_i ...
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POVMs for which measurement cannot be written as a probabilistic sum of measurements
Consider POVM given by the operators:
$π ̂_0=\frac{2}{3} |0⟩⟨0|$
$π ̂_1=\frac{2}{3} (\frac{-1}{2} |0⟩+\frac{√3}{2}|1⟩)(\frac{-1}{2}⟨0|+\frac{√3}{2}⟨1|)$
$π ̂_2=\frac{2}{3} (-\frac{1}{2} |0⟩-\frac{√3}{...
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Are there any other nondeterministic processes than measurement in quantum theory?
Nondeterministic refers to a system or process that does not have a single predictable outcome. In other words, when a system is nondeterministic, it means that multiple outcomes are possible for a ...
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Intuition for Relative Phase of Energy-State Qubits
Consider a general qubit $|\Psi \rangle = \alpha |0 \rangle + \beta |1\rangle$.
My understanding is as follows:
If such a qubit is implemented using electron spin, for example, the computational basis ...
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Quantum Measurement and the law of thermodynamics
When discussing the conceptual issues of quantum mechanics, concepts like Bell's inequality, non-locality, and the Kochen-Specker theorem are often brought up. Many physicists have dedicated time to ...
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How do I have to understand the Response measurement of optomechanical coupling with a network analyzer
I have a optomechanical device like a beam which couples to a membrane. My procedure is to lock my laser frequency near the optical resonance. Why should always the steepest point be chosen? I now ...
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Can an electron move in a well-defined path? [closed]
Considering the probabilistic relationship between the momentum and position of an electron, are the pictures that show the interaction between electrons and positrons an accurate description of ...
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Accuracy of finding electron's magnetic moment
In the little book QED, Feynman says:
"experiments have Dirac’s number at 1.00115965221 (with an uncertainty of about 4 in the last digit); the theory puts it at 1.00115965246 (with an ...
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What happens when a projection observable produces a zero vector?
I'm new to quantum mechanics, but not quite as new to linear algebra and operator theory, and trying to understand the nature of observations from a mathematical perspective.
Consider a two-...
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Implementing a POVM as a Quantum Circuit: Is There a General Method? [duplicate]
I am studying quantum information theory, and I have found an exercise about implementing a POVM as a quantum circuit. Specifically, the POVM is given by $\Pi_1= \lambda |0 \rangle \langle 0 |$ and $\...
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Is there any limit to the utility of quantum measurements in the sense of a Lieb-Robinson bound?
So the Lieb-Robinson bound of 1972 derives an emergent maximum speed $v \ll c$ of the propagation of quantum information under time evolution generated by some local Hamiltonian $H(t)$. Basically, ...
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Non-Orthogonal Measurements in Quantum Systems
If we aim to transmit some information using the polarization of photons, lets suppose horizontally polarized = |0> and vertically polarized = |1>. We can decode this information at the receiver ...
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Why is this a correct explanation for the Uncertainty Principle? [duplicate]
There's this really common explanation for Heisenberg's Uncertainty Principle, but I quote it from Classical Dynamics by Marion and Thornton:
The wave character of the photon precludes an exact ...
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Ideal Von-Neumann measurement scheme - Do the system states need to be orthogonal too?
This question follows up on this question on the ideal Von-Neumann Measurement scheme - also regarding the way Schlosshauer (978-3-540-35773-4) puts it on page 50 f.
In this scheme one has given a ...
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Physicality of post-measurement description of a state based on information of measurement outcomes
Say, we find two exact systems in a pure state. When Alice does von Neumann measurement on it, the state collapse to a pure state because Alice knows the measurement outcomes. In this case, we have $\...
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Confusion regarding working around with the mathematics of operators acting on the whole tensor product state
In 'Quantum Information by Stephen Barnett' (Page 95), we have:
$$
P(m, l)=\left|{ }_a\langle l|\otimes\langle m|\hat{U}| \psi\rangle \otimes| A\rangle_a\right|^2=\left\langle\psi\left|\hat{\pi}_{m l}\...
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Equivalence of two POVMs in continuous variable system
In continuous variable systems, the Gaussian POVM is generally defined as [see e.g. Eq. ($1$) of this article]
\begin{equation}
\Pi_j(\alpha_j) = \frac{1}{\pi} D_{j}(\alpha_j) \Pi_j^0 D_{j}^\dagger(\...
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How do we measure an electron's position by shining light on it?
I saw this post which says:
The way you do it is just a simple logic. Imagine a tennis ball and imagine you can't really see it, just like you can't see an electron. So the only way you can see where ...
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Calculating Optomechanical coupling rate
How do I calculate the optomechanical coupling rate $G$ [Hz/m] through thermal motion? I measured the spectrum with a spectrum analyzer which was connected to a rf-source and the laser detector. I get ...
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Does a measurement violate conservation law? [duplicate]
(Edited according to the discussion with @naturallyInconsistent. The edited part is highlighted in italic.)
We have an experimental bench and we assign a coordinate system $(x,y)$ to it.
We shall call ...
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How do physicist keep entangled particles entangled while moving them/storing them?
Once an entangled particle is measured, it's wave function collapses. From my understanding, any sort of information exchanged to the particles can be considered a mistaken measurement. So how do ...
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How to determine elements of the covariance matrix from homodyne measurements?
Suppose we have a source which can repeatedly create an $n$-mode Gaussian state with covariance matrix $\sigma$. How can I use homodyne measurements to completely determine $\sigma$? If the quadratues ...
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Ensemble interpretation and density matrices - why is it impossible to distinguish two equivalent density matrices?
I read this in a paper : "... we cannot distinguish them by making measurements because they have the same density matrix". The authors are referring to two different decompositions of the ...
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Why does one need a low resolution when trying to tell $|0\rangle^{\otimes n}$ and $|1\rangle^{\otimes n}$ apart in a coarse grained measurement?
I am looking at a certain measure for macroscopic quantum states, namely the one in http://dx.doi.org/10.1103/PhysRevA.89.012116. I use the notation from https://arxiv.org/abs/1706.06173 (p. 15-16, ...
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Can the concept of interaction-free measurement help us build better detection devices?
Interaction-free measurements are based on the idea that even if interaction is not happening the chance that it may happen may change the result of the experience. such as in the Elitzur–Vaidman ...
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