Questions tagged [measurement]

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

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7
votes
1answer
151 views

What are examples of extremal non-projective POVMs?

Fix some finite-dimensional space $\mathcal X$. Define a POVM as a collection of positive operators summing to the identity: $\mu\equiv \{\mu(a):a\in\Sigma\}\subset{\rm Pos}(\mathcal X)$ such that $\...
3
votes
1answer
46 views

Why are 3, rather than 2 gates used in quantum variational circuits?

In the hello many worlds tensorflow tutorial and in the lockwood paper (2020) I have seen that often in QVC the following combination of gates is used: $R_z(\theta), R_y(\theta), R_x(\theta)$ I am ...
2
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0answers
49 views

Is there a list of known quantum measurements?

Quantum Measurement can be divided into General Measurements, Projective measurements and general POVMs. And there are also some special kinds of quantum measurements that have their own name, such as ...
2
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1answer
41 views

Measuring second excited state |2> using “calibrations” not Open Pulse

I am tying to measure the second excited state in a system that does not support Open Pulse. Instead I am using calibrations. The method detailed here does not work. I get the error ...
2
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1answer
55 views

How to perform a projective measurement on one component of a composite system?

For simplicity, let $|\phi\rangle|\psi\rangle\in\Bbb C^2\otimes\Bbb C^2$. I know how to compute the projective measurement $\{P_m\}_m$ of $|\phi\rangle|\psi\rangle$ on $\Bbb C^2\otimes\Bbb C^2$, but I ...
1
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0answers
27 views

How to transform fermionic operators in qiskit

I encountered some problems when using the qiskit pakage to define the 2-electron reduced density matrix (2-RDM), which is a 4-index tensor, $\langle a_i^\dagger a_j^\dagger a_k a_l\rangle$. I need to ...
0
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0answers
26 views

Source code for Hamiltonian measurement in qiskit [duplicate]

In variational quantum eigensolver, it is common to transform the Hamiltonian to a qubit form by Jordan-Wigner transformation, for example. After that, the algorithm needs to measure the qubit ...
1
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2answers
75 views

How to measure a qubit Hamiltonian in qiskit

I am using qiskit to get some measurement results of observables similar to the Hamiltonian. Can someone provide the way how qiskit measures the Hamiltonian (Jordan-Wigner transformed) when using VQE? ...
-4
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0answers
48 views

What is a qubit's impulse response?

As far as I know, qubits are primarily measured in the frequency domain, sending a relatively long, spectrually pure pulse to interrogate the qubit's state. In general, what would happen if you sent a ...
1
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0answers
53 views

Born rule as the sudden approximation applied twice?

Background I haven't seen this done before as tempting as it seems and was wondering if there was some way to disprove the below? In short can one think of the measurement as the sudden approximation (...
1
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1answer
30 views

Does Toffoli AND conjugate affect superposition if used in Shor's algorithm?

I have come across several papers that use Toffoli AND conjugate to minimize the T-depth. But since it contains a measurement, does it affect Shor's algorithm (in terms of interference, entanglement, ...
4
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1answer
99 views

Qiskit - Circuit drawing esthatics - can i force the measurements in my circuit show at the end?

I'm studying an introduction course to quantum computation at my uni and we got homework to draw a certain circuit using qiskit. I managed to understand how to do what is asked from me, and this is ...
2
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2answers
129 views

Measuring the product is the same as first measuring with one matrix then with the other

I want to show that if one measures $M_1$ on $|\psi\rangle$ then measures $M_2$ on the resulting state and then the associated probability space will be the same as the one for measuring the product $...
4
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1answer
36 views

What does it mean to make a simultaneous measurement?

In Quantum Computing quantum measurements are described by a collection of measurement operators $\{M_n\}$ such that the probability of the outcome $m$ is given by $p(m)=\langle\psi|M_m^\dagger M_m|\...
1
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1answer
59 views

What is the “quantum mean value problem”?

What is the "Quantum mean value problem"? A definition I found was that it is "estimating the expected value of the tensor product observable on the output state of a quantum circuit&...
1
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1answer
35 views

Operation conditioned on measurement result

I have a 2 qubit circuit where I wish to measure the first qubit and the measurement outcome determines what operation to implement on qubit 2. The whole process can be simulated using the following ...
3
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2answers
135 views

What does the POVM corresponding to single-qubit state tomography look like?

Let $\rho$ be a single-qubit state. A standard way to characterise $\rho$ is to measure the expectation values of the Pauli matrices, that is, to perform projective measurements in the three mutually ...
5
votes
1answer
116 views

What is the relation between POVMs and observables (as Hermitian operators)?

Let $\renewcommand{\calH}{{\mathcal{H}}}\calH$ be a finite-dimensional Hilbert space. An observable $A$ is here a Hermitian operator, $A\in\mathrm{Herm}(\calH)$. A POVM is here a collection of ...
2
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0answers
19 views

Approximating an ensemble with an orthogonal ensemble

Consider an arbitrary ensemble $\{p_x\rho_x\}_{x\in X}$ and define the state $$ \rho = \sum_{x\in X} \vert x \rangle\langle x \vert \otimes p_x\rho_x. $$ I am interested in understanding the quantity $...
3
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1answer
60 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
votes
1answer
68 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 ...
2
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1answer
51 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
66 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
45 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 ...
0
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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
37 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
votes
1answer
104 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
votes
1answer
56 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
votes
1answer
47 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
votes
1answer
77 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
votes
1answer
77 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
votes
3answers
543 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
votes
2answers
71 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
votes
2answers
213 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
138 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: ...
1
vote
1answer
50 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
votes
4answers
114 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
votes
1answer
447 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
votes
5answers
926 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
65 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
votes
2answers
95 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 $...
8
votes
1answer
248 views

How to distinguish between collapsed and uncertain qubits 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 ...
6
votes
1answer
186 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
vote
1answer
74 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
votes
0answers
30 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
votes
1answer
80 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 ...
1
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2answers
78 views
1
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1answer
53 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
votes
1answer
69 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
votes
1answer
63 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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