Questions tagged [measurement]

For questions related to measurement and its effects as relevant to quantum computation and quantum information.

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2
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1answer
51 views

How to find the POVM the optimally distinguishes two given states?

A quantum state preparation machine emits a state $\rho_0$ with probability $2/3$ and emits the state $\rho_1$ with probability $1/3$. We aim to make the best guess which one is it using a set of two ...
2
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1answer
63 views

Measurement probability of a state from three hilbert spaces

I'm curious how to find the probability measurement of a state when one qubit is measured. For example this state: $|\gamma\rangle = \frac{1}{\sqrt{2}}(| 010 \rangle + | 101 \rangle )$ Assuming these ...
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1answer
45 views

Why does $\sum_n \langle n|M_m\rho M_m^\dagger|n\rangle$ simplify to $\langle \psi|M_m^\dagger M_m|\psi\rangle$?

I was trying to derive the formula for $p(m)$ in exercise 8.2 on page 357 in Nielsen & Chuang. But I am wondering what rule I can apply to simplify this $$\mathrm{tr}(\mathcal{E}_m(\rho) )= \...
3
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1answer
59 views

What does the identity operator represent when computing $\langle\varphi|I\otimes Z|\varphi\rangle$?

Consider a single qubit state $|\varphi\rangle$ and a hamiltonian $H = Z$. Evaluating $\langle \varphi | H | \varphi \rangle$ corresponds to a measurement of $|\varphi\rangle$ in the computational ...
3
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0answers
44 views

Is there some notion of work associated with performing a measurement?

Let a measurement be described by POVM elements $M_i$ such that probability $p(i) = Tr[\rho M_i]$ for some state $\rho$. I want to know whether there is some notion of work associated with such ...
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0answers
21 views

How do we find out the measurement operators $M_{m}$ which gives us the desired measurement results?

From one of the postulates we know we can represent any system with a state space. I am considering, that if I do this I will sensibly assign different vectors to different entities of my system. But ...
2
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0answers
35 views

Do the Heisenberg uncertainty principle and quantum decoherence relate in some way?

Up until now I assumed (in simple words) that a qubit collapses because of the heisenberg uncertainty principle, meaning that we can not measure a qubit without changing it state. But now I've read ...
4
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1answer
87 views

SWAP Test as a Projective Measurement [closed]

In a much cited paper by Lloyd et al Quantum Algorithm for Supervised and Unsupervised Machine Learning, they proposed a rather cute quantum algorithm to evaluate the distance between an input feature ...
3
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1answer
48 views

Probability of measuring one qubit from the state of two qubits

I am new to quantum information and I am trying to work on some problems but I have confused myself over a qubit problem. I have the state of two qubits $|\psi\rangle_{AB}=a_{00}|00\rangle+a_{01}|01\...
3
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1answer
45 views

Circuit that measures PVM

How can I construct a circuit that measures PVM $\{|\psi\rangle\langle\psi|\},|\psi^\perp\rangle\langle\psi^\perp| \}$ where $|\psi\rangle=\cos\frac{\theta}{2}+e^{i\phi}\sin\frac{\theta}{2}|1\rangle$ ...
3
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1answer
62 views

Why do the controlled unitary operations in quantum phase estimation have $2^n$ in their exponents?

Why do the unitary gates on the measurement qubits have $2^n$? Why do we need to apply the unitary gates for any power at all? What would happen if we applied the controlled-$U$ only once, for ...
3
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1answer
73 views

How do I calculate Logarithmic Negativity for the given bipartite state?

How can I calculate Logarithmic Negativity for the given state? $\rho = \frac{1}{2} |0\rangle \langle0| \otimes |+\rangle \langle+| +\frac{1}{2} |+\rangle \langle+| \otimes |1\rangle \langle1| $
7
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3answers
439 views

What do the off-diagonal elements of a density matrix physically represent?

For simplicity, let's take a density matrix for a single qubit, written in the $\{|0\rangle,|1\rangle\}$ basis: $$ \rho = \begin{pmatrix} \rho_{00} & \rho_{01} \\ \rho_{10}^* & 1-\rho_{00} \...
3
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2answers
66 views

Is a projective measurements over a superposition of eigenstates possible?

All observables admit a spectral decomposition in terms of projectors $P_m$ into the eigenspace corresponding to the eigenvalue $m$. So given for example a collection of kets $|0\rangle, |1\rangle,...,...
4
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2answers
211 views

If the eigenvalues of $Z$ are $\pm1$, why are the computational basis states labeled with “$0$” and “$1$”?

The computational basis is also known as the $Z$-basis as the kets $|0\rangle,|1\rangle$ are chosen as the eigenstates of the Pauli gate \begin{equation} Z=\begin{pmatrix}1 & 0 \\ 0 & -1\end{...
4
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2answers
116 views

Computing expectation value of product of observables in PennyLane

In PennyLane, the following circuit returns the expectation value of the PauliZ observable on qubit (wire) 1: ...
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1answer
49 views

How can I understand these two equations about the indirect measurement?

I'm reading an article about environmental monitoring and information transfer. Suppose $S$ represents a quantum system and $E$ is the environment. Assume at time $t=0$ there are no correlations ...
5
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4answers
107 views

Derivation of the identity $\sum_j p_j \langle \psi_j|M|\psi_j \rangle = \sum_j p_j \operatorname{tr}\left(|\psi_j \rangle \langle \psi_j|M\right)$

For measurement, we know $$\langle M \rangle = \sum_j p_j \langle \psi_j|M|\psi_j \rangle = \sum_j p_j \operatorname{tr}\left(|\psi_j \rangle \langle \psi_j|M\right).$$ My question is, how can we go ...
7
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1answer
413 views

Does the no-hiding theorem suggest that quantum information is never destroyed?

According to Wikipedia: The no-hiding theorem proves that if information is lost from a system via decoherence, then it moves to the subspace of the environment and it cannot remain in the ...
8
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5answers
914 views

If quantum computing always return random measurement (or uncertain measurement), why do we still need it?

I am very new to quantum computing and currently studying quantum computing on my own through various resources (Youtube Qiskit, Qiskit website, book). As my mindset is still "locked" with ...
2
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1answer
62 views

Cirq: Result of rotating qubit measurements never come [0 1] or [1 0 ], always come as [0,0] or [1,1]

I am creating a 2 qubit entangled state: ...
2
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2answers
66 views

What is the relation between observables (as defined in the measure-theoretic framework) and POVMs?

A POVM is typically defined as a collection of operators $\{\mu(a)\}_{a\in\Sigma}$ with $\mu(a)\in\mathrm{Pos}(\mathcal X)$ positive operators such that $\sum_{a\in\Sigma}\mu(a)=I$, where I take here $...
6
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1answer
216 views

Distinguishing collapsed and uncertain qubit in a quantum circuit

I have been through the Young's double slit experiment. It's a direct proof or instance of showing that a wave is collapsed via observation or measurement, and shows no interference patterns. I want ...
5
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1answer
177 views

What does $M_m |\psi_i\rangle$ mean in the equation $p(m|i)=\langle\psi_i|M_m^\dagger M_m|\psi_i\rangle$?

I have trouble understanding two equations in the Nielsen & Chuang textbook. Suppose we perform a measurement described by the operator $M_m$. If the initial state is $|\psi_i\rangle$, then the ...
1
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1answer
55 views

Probability on measuring bell state in x-basis with pauli operator sigma x [duplicate]

I am confused about how to calculate the probabilities of getting a certain result when measuring a Pauli observable on a Bell state. When you measure an observable the state is projected onto an ...
2
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0answers
27 views

Expectation value of the coherent term

I am trying to and understand a statement of a paper I am reading URL. Figure 3c shows the circuit. $\newcommand{\bra}[1]{\langle #1\rvert}\newcommand{\braket}[2]{\langle #1\rvert #2\rangle}\...
2
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1answer
78 views

Quantum teleportaion seems to occuring without entanglement in circuit (what's wrong)

Please, pardon the caption. No intention of making new theories. I am a bit confused about the quantum teleportation. I missed a hadamard gate before CNOT gate for creating the EPR pair. But the ...
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2answers
77 views
1
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1answer
50 views

What are the matrices in the POVM for measuring the first $m$ qubits?

Suppose you have a quantum state $|w\rangle$ consisting of $m + n$ qubits, and you set up a measurement that measures the first $m$ qubits in the standard basis. What are the matrices in the ...
3
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1answer
52 views

How can measuring a particle in a GHZ state leave behind a maximally entangled pair?

I am trying to understand the section on the Wikipedia page for GHZ states entitled "Pairwise entanglement". In this section, it is claimed that measuring the third particle in a GHZ state ...
3
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1answer
57 views

Why do the eigenvectors of a spin observable not align with the direction of the spin?

The italicized section below is referring to chapter 3 of "Quantum Mechanics: The Theoretical Minimum" by Leonard Susskind and Art Friedman. It is written that the operator that corresponds ...
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1answer
81 views

Trouble understanding the EPR Experiment

I fail to understand the EPR experiment. From Wikipedia: Alice now measures the spin along the z-axis. She can obtain one of two possible outcomes: +z or −z. Suppose she gets +z. Informally speaking, ...
5
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1answer
68 views

Are there any algorithms that take measurements in an intermediate step?

As a beginner in quantum computation, I noticed that all quantum algorithms take various gates followed by measuring the qubits in the last step. Is it always the case? Are there any algorithms that ...
2
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1answer
74 views

EPR Experiment: What does it mean for Alice to measure $\vec{v} \cdot \vec{\sigma}$ on her qubit?

I am trying to understand Box 2.7 on page 113 of Quantum Computation and Quantum Information book by Nielsen and Chuang. They start out with following wave function: \begin{equation} \psi = \frac{|01\...
2
votes
1answer
61 views

How changing the basis of measurement produces a state which is not in the possible system states?

Consider we have a quantum system which has two possible states (as double-slit experiment): the photon could be pass through the first slit the photon could be pass through the second slit And we ...
2
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1answer
97 views

How does the outcome of measurement of a qubit change when we use different basis despite the system hasn't changed? [closed]

Let's assume that the quantum state of the system is written in a standard basis {$|0\rangle, |1\rangle$} and when we performed a measurement we got $|0\rangle$ as an outcome of measurement so we ...
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0answers
60 views

Time accuracy required to reconstruct the density matrix?

So usually when you talk to physicists who accept the multi-world interpretation of quantum mechanics they claim that the measurement is reversible if you take into account the worlds we don't observe....
0
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1answer
48 views

Why is it important to be in the basis in which measurements will be performed?

This might seem obvious to some but I would like to know what is exactly the purpose of this? And if there is a change of basis...it's just simply taking the new basis and writing it in terms of the ...
3
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0answers
61 views

How can I measure a qubit on a generic axis on Qiskit?

I'm trying to prove Bell's inequality by following the one made by Wigner, that is: $P(+_a,+_b) \le P(+_a,+_c) + P(+_c,+_b)$ And that this proof is NOT satisfied for angles between the various axes $\...
6
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1answer
167 views

Trying to understand this measurement of a simple quantum circuit

It's a newbie question, I know. But I was just wondering if someone could help me understand why this simple circuit results with the measurement shown. I've just didn't get the last step. It's not ...
2
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2answers
87 views

IBM quantum experience: Why are intermediate measurements ignored?

Why am I getting here a measurement outcome of $00$? I measure after the first $X$ gate in a separate output bit c[1] which should result in a $1$ and I measure ...
8
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2answers
520 views

What does it mean to “measure an operator”?

I was reading a book and then I found this statement. I will put the text as well as a screenshot of the text. The expectation value of an operator is the mean or average value of that operator with ...
3
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1answer
47 views

Measuring in the computational basis in the single qubit gate QFT implementation

I've come across this paper about a single-qubit-gate-only QFT implementation. In the paper it is claimed that measuring a qubit after applying the Hadamard gate (it isn't called Hadamard gate in the ...
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2answers
66 views

Why is the Measurement Result Always 1? (expected to find uniformly random measurement)

I created a $|0\rangle$ state then applied $H$ gate to get $\frac{1}{\sqrt{2}}(|0\rangle+|1\rangle)$ and then I meausred my state. But I always found 1. I expected to find 0 and 1 uniformly random ...
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1answer
33 views

Mechanism of measurement in IBM quantum devices

I am trying to find out about the mechanism of measurement in IBM Q devices. To be specific, if I apply two Hadamard gates on the first qubit and identity on the second then is it possible to ...
3
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0answers
56 views

Can we characterise how correlated the expectation values associated with a pair of observables are?

Consider a state $\rho$ and two observables $P$ and $Q$. Is there a good way to characterise how correlated the associated expectation values are? Be it in terms of mutual information or something ...
2
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1answer
78 views

Question about quantum error correction and density matrixs

I am now studying QEC and feel confused. If I have a density matrix before the correction: The circuit is: $\rho = p^0(1-p)^3|\varphi\rangle \langle\varphi|+p^1(1-p)^2\sum_{i=1}^3X_i|\varphi\rangle \...
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1answer
48 views
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1answer
64 views

What is the meaning of measuring a Bell state with Pauli operators?

There will be a certain value of getting the probability when measuring any Bell's state with Pauli operators such as observable X, Y, or Z. What is the meaning behind all this measurement? the result ...
2
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2answers
99 views

What are the possible results of measuring $X$ and $Z$ on the state $|01\rangle+|10\rangle$?

When calculating the probability of getting +1 on X-basis on the first qubit of Bell's state $|01\rangle+|10\rangle$, the result is 1/2 with the state after measurement |++⟩ while the probability of ...

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