Questions tagged [quantum-measurements]
The quantum-measurements tag has no usage guidance.
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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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The problem of measurements in quantum mechanics [closed]
Is it true that in the standard Copenhagen interpretation, which is shared by most physicists, the collapse is caused by the measuring instrument? And also the fact that according to it, Schrödinger’s ...
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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 ...
user375600
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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(\...
user317042
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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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Using the Correlation of Measurement Results as Entanglement Quantifier for Pure State Bipartite Systems (Quantum Mutual Information for Pure States)
Piece of Information 1:
This text states that since correlation and entanglement are equivalent for pure states, one could use a quantum-correlation measure as a quantifier of entanglement. For ...
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Observing a Superposition in the Double-Slit Experiment
Consider a standard double-slit experiment using light, where $|\Psi\rangle = \frac{1}{\sqrt{2}}(|L\rangle +|R\rangle)$ may represent the superposition state of a single photon passing through 'both ...
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How do we detect disturbance on a system when we make a measurement?
Summary
I am taking an intro. to quantum mechanics course and was taught that superposition exists until we measure the system which makes the wave function of a quantum system collapse. I have a ...
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Measurement of total angular momentum in quantum mechanics
Consider a system composed of two spin-1/2 particles. The total spin operator is defined as
$$
\mathbf{S} = \mathbf{S_1} + \mathbf{S_2}
$$
We can write a common eigenbasis of the operators $\mathbf{S^...
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On "no backaction on the system" in the Ideal (non demolition, Von Neumann) quantum measurement
Some context:
An ideal quantum measurement (in Von Neumann's sense) is described by the following situation:
There is a hilbert space $\mathcal{H_S}$ with basis $|\sigma_i\rangle_{1\leq i \leq n}$ ...
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Schrödinger evolution after a position measurement, without collapse
Consider the following physical situation. Two position detectors are located next to each other, each one carries only YES/NO information on whether the particle hit that detector. A particle, let's ...
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Quantum measurement in a strong magnetic field
I have a thought experiment that has been puzzling me regarding a spin-$\frac12$ particle placed in an extremely powerful magnetic field (say 1000 T for the sake of hyperbole) directed along the ...
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Ideal quantum measurement
Schlosshauer (in Decoherence and the Quantum-to-Classical Transition) defines ideal quantum measurement as a von-Neumann measurement in which
(1) the apparatus states correspond 1-to-1 to given system ...
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How to measure an unknown state produced by a source of qubits?
What kind of experiment can allow me to measure an unknown state produced by a source of qubits? For example: the state of photon polarization. But it can be another one.
I have no information about ...
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Measurements on macroscopic objects [duplicate]
I know that macroscopic objects undergo measurements continuously from the environment in which they are placed.
I also know that in a quantum computer one can make a measurement of only a few qubits.
...
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Can a state be both classical-quantum and quantum-classical, but still not be classical-classical?
Given a bipartite quantum system $ \mathcal{H}_A \otimes \mathcal{H}_B $, we define a quantum-classical (q-c) state to be any state that may be written in the form:
$$ \rho = \sum_j q_j \rho_j^A \...
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