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Questions tagged [measurement]

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

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How does measuring a density matrix give Kraus operators?

I am trying to complete this exercise regarding noisy channels. I need to measure a density matrix to get the Kraus operators. However, if I measure, I only get scalars. Can someone please explain how ...
researcher101's user avatar
0 votes
1 answer
24 views

How to find the $+1$ eigenvectors of the stabilizers for the Shor code

I am currently working through chapter $3$ of "Stabilizer Codes and Quantum Error Correction" (Daniel Gottesman's thesis). I would like to know the general method for finding the $+1$ ...
am567's user avatar
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1 vote
2 answers
86 views

Can Bell states be reexpressed with respect to arbitrary local bases?

Suppose I take the Bell state $\Phi^+ = \vert 00\rangle + \vert 11\rangle$. Is it true that I can choose any basis with basis vectors $\vert b_0\rangle$ and $\vert b_1\rangle$ and reexpress the same ...
Joey's user avatar
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1 vote
1 answer
18 views

Moving pauli product rotations past measurements

I'm trying to understand how the clifford + T compiler works in "A Game of Surface codes". How do I move a pauli product rotation block past a pauli product measurement block? More ...
Palash Goiporia's user avatar
2 votes
1 answer
41 views

Measuring stabilizers for qutrit stabilizer code

For stabilizer codes we do many things like extracting error syndromes and preparing states and stuff like that by measuring the stabilizer generators. For qubit stabilizer codes measuring the ...
Ian Gershon Teixeira's user avatar
3 votes
3 answers
241 views

How to mathematically describe the action of CNOT on the control qubit alone?

Basically the title. From what I know, starting from the $|{+0}\rangle$ state where the reduced density matrix of the first qubit $|+\rangle$ is $\frac{1}{2}\begin{bmatrix} 1 & 1 \\ 1 & 1 \end{...
Jack Nathan's user avatar
3 votes
1 answer
74 views

How does the surface code satisfy constraints of relativity?

Consider a surface code in the shape of a rectangle that has very very long horizontal edges and very short vertical edges. I initialize the surface code into the logical state $\vert 0\rangle$. Let's ...
user1936752's user avatar
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1 vote
1 answer
69 views

Does measuring the operator $XX$ preserve superpositions in a given two-qubit state?

Suppose I have a state $$\vert\psi\rangle = a\left(\frac{1}{\sqrt{2}}\vert\Phi^+\rangle + \frac{1}{\sqrt{2}}\vert\Phi^-\rangle\right) + b\left(\frac{1}{\sqrt{2}}\vert\Psi^+\rangle + \frac{1}{\sqrt{2}}\...
Vladimir's user avatar
2 votes
3 answers
89 views

Is an unobserved measurement represented by a mixed state?

If I take a $\vert +\rangle$ state and measure it in the $Z$ basis but do not look at the measurement outcome, how should I describe the state? Is it just a mixed state $$\frac{1}{2}\vert 0\rangle\...
Vladimir's user avatar
0 votes
1 answer
39 views

stim: enhancing performance measuring Pauli strings without keeping the outcome

I have the following question. If I perform projective measurements of a given (multi-qubit) Pauli string in my TableauSimulator I implicitly perform some Gaussian-...
archxrk's user avatar
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1 answer
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Partial standard basis measurement of a three element system

I'm trying to solve a textbook problem. There are three elements in the system. The system is in the state $$\psi=\frac{1}{\sqrt3}\big(|0\rangle|+\rangle|-\rangle + |1\rangle|0\rangle|0\rangle - |1\...
danas.zuokas's user avatar
0 votes
0 answers
8 views

What the stern-gerlach experiment would look like for tensor-product observable?

The experiment says, that having the $Z$ observable and a qubit, we can have outcomes $+1$ and $-1$. Suppose we have more than one qubit, and build an observable like $O = 3Z_1 + 5Z_3 + 2Z_4$. It also ...
HaraldRudobrody's user avatar
6 votes
2 answers
2k views

If Alice measures a qubit and doesn't tell Bob the result, what's Alice's state from Bob's perspective?

Suppose Alice has a qubit $|\phi\rangle=\alpha|0\rangle+\beta|1\rangle$ and measures it. Bob knows the initial state but not the result of her measurement. So after the measurement, Alice knows what ...
mp12853's user avatar
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3 votes
1 answer
52 views

How large does the isometry in Naimark's theorem need to be for a 3-outcome POVM?

I am interested in the POVM example Nielsen and Chuang give in the discussion about indistinguishability. They define the POVM $E_1 = \frac{\sqrt{2}}{1+\sqrt{2}} |1\rangle \langle 1|$, $E_2 = \frac{\...
BenPhys's user avatar
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1 vote
2 answers
283 views

Why is a post-measurement state a valid quantum state?

Postulate 3 of the postulates of quantum mechanics in Nielsen & Chuang states that Quantum measurements are described by a collection ${M_m}$ of measurement operators... and the state of the ...
Josh's user avatar
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1 vote
2 answers
97 views

What is a measurement that always identifies $|0\rangle$ but can misidentify $|1\rangle$?

Consider a measurement of $\sigma_{z}$ that will correctly identify $|0\rangle$ every time however sometimes incorrectly identifies $|1\rangle$ as $|0\rangle$. I would like to model how such a faulty ...
Adrien Amour's user avatar
1 vote
1 answer
90 views

Does measurement at the end of all transformations in quantum computing have a specified time?

The concept of measurement in quantum mechanics is usually discussed without specifying how much time such measurement might take. In principle, one can imagine that the time needed to perform ...
quantum novice's user avatar
0 votes
2 answers
30 views

Does $\frac{I + K}{2}\otimes\frac{I+L}{2} = \frac{I+K\otimes L}{2}$ hold for operators $K,L$ acting on different subsystems?

Let's index $i= 1, 2$ be the index representing different systems. A $Z_i$ projective measurement has projectors $P_i = \{ \frac{I+Z_i}{2}, \frac{I-Z_i}{2} \}$. One can verify that the measurement $...
user1936752's user avatar
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0 votes
1 answer
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Surface code with measurement errors

I am trying to implement error correction to a surface code with circuit-based noise model. In this model, there is a probability $p$ for an error in: initialization, Hadamard, CZ (or CNOT) and ...
David Dentelski's user avatar
4 votes
2 answers
72 views

Generalizing error propagation formula to multi-parameters

For single parameter phase estimation we have the Cramer-Rao bound $$(\Delta \theta)^2 \geq \frac{1}{F_{Q}[\rho, \hat{A}]},$$where $F_{Q}$ is the quantum Fisher information and where instead of an ...
John Doe's user avatar
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1 vote
0 answers
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State tomography in Qiskit on a subset of qubits of real QPU

Could anyone please explain how should I carry out a state tomography on a real device in Qiskit (version 0.43.2)? I have access to devices with 127 qubits, but I want to perform a simulation using ...
Andrea's user avatar
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1 answer
49 views

Connection between a Pauli measurement and the corresponding Pauli gate?

Suppose I have a qubit and the ability to act a Pauli $Z$ gate on it. This is a black box that does the phase flip and I don't know how it works on the inside. Can I use this black box to implement a ...
Brendan's user avatar
3 votes
2 answers
92 views

Are measurements in $X$ and $Z$ bases being equal enough to prove equality of quantum states?

Suppose I have two single qubit states $\rho$ and $\sigma$. In my example, they are pure but I keep it general here. Suppose I know that $$\text{Tr}(\vert +\rangle\langle +\vert\rho) = \text{Tr}(\vert ...
user1936752's user avatar
  • 2,997
2 votes
1 answer
53 views

How is a surface code state measured?

What is the exact operation required to measure the logical state of a surface code? Does one need to measure every data qubit, or only some subset of them to perform the measurement? For simplicity, ...
Whitman's user avatar
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2 votes
2 answers
43 views

How to measure whether register contains a specific state?

In a proof that I am reading through there exists a register $M$ in which a state is initialized. We want to measure whether $M$ contains a specific state $c_1$. In the proof, they measure with a ...
Wouter's user avatar
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1 vote
1 answer
72 views

Does measurement in different bases allow for FTL communication?

Imagine for a moment that we could distinguish between arbitrary quantum states. We’ll show that this implies the ability to communicate faster than light, using entan- glement. Suppose Alice and Bob ...
Nir Sharma's user avatar
2 votes
1 answer
50 views

Existence of a two-outcome measurement $M$ such that the induced distributions differs between different density matrices

Let $\rho \neq \sigma$ be density matrices. I want to show that there exists a two-outcome measurement $M$ such that the induced distributions $M(\rho)$ and $M(\sigma)$ differ. From what I learned, ...
Gabi G's user avatar
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2 votes
1 answer
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How to compute the measurement probability in the Hadamard test?

In the Hadamard test (e.g., page 40 of these lecture notes) we have: But if you look at standard textbook reference, like Nielsen and Chuang, there's an example for how to compute the measurement ...
Count Ably's user avatar
3 votes
1 answer
65 views

Fault-tolerant correlated measurement on logical qubits

So I have an encoded Bell pair $(|\overline{0}\overline{0}\rangle+|\overline{1}\overline{1}\rangle)$ in CSS code(e.g. Steane code) and I hope to perform stabilizer measurement of $\overline{XX}$ non-...
AndyLiuin's user avatar
  • 325
1 vote
0 answers
25 views

What happens after the ancilla is measured in a parity measurement?

Measurement of qubits results in collapsing the wavefunction/state in $|0\rangle$ or $|1\rangle$. I have a doubt about Parity Measurement (Source). We entangle physical qubits with ancilla qubits by $\...
Akash Yadav's user avatar
1 vote
0 answers
32 views

How to obtain this measurment result for arbitrary qubits in $X$ basis?

I have seen the following claim. Suppose one has two qubits $\vert\psi\rangle = a\vert 0\rangle + b\vert 1\rangle$ and $\vert\phi\rangle =a'\vert 0\rangle + b'\vert 1\rangle$ and both are measured in ...
Lorraine's user avatar
0 votes
0 answers
53 views

Where is my mistake in using a measurement operator instead of Born’s rule to calculate the probability of detecting photons at an arbitrary angle?

As I asked in this question: How can I calculate the measuring probabilities of a two qubit state along a certain axis? From here I know how to calculate the probability of measuring a general state ...
Alex1111's user avatar
0 votes
0 answers
24 views

How can I find the probabilities corresponding to measurement results of an observable of the GHZ states?

I'm working on a problem involving the calculation of probabilities for outcomes of a measurement on a quantum state perturbed by an error. The state in question is a GHZ state $|\text{GHZ}\rangle = \...
Alex1111's user avatar
2 votes
1 answer
51 views

Quantum Information Retrieval from Bipartite Mixed States under LOCC: Maximizing Individual State Knowledge

In the context of Local Operations and Classical Communication (LOCC), given a bipartite mixed state represented as $\rho=\frac{1}{n}\sum_{i=1}^n|\psi_i\rangle\langle\psi_i|$, where $|\psi_i\rangle$ ...
Pratapaditya Bej's user avatar
0 votes
0 answers
59 views

How to Correctly Measure All Qubits in a Quantum Circuit?

Description: I'm currently working on a project that involves running quantum circuits as a hybrid job on the aws tensor network simulator 'tn1'. Error on the Cloudwatch logs:...
Neel's user avatar
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1 vote
1 answer
51 views

How can I calculate the measuring probabilities of a two qubit state along a certain axis?

If I have an arbitrary two-qubit state (in this example given from spins), and I want to measure the state of the first spin along a direction $\vec{n}$. This vector n has an angle theta with respect ...
Alex1111's user avatar
4 votes
1 answer
103 views

Can post-measurement states have entropy larger than the original state?

Given a set of measurement operators $\{M_i\}$ that sum to unity, consider the post-measurement states on some $\rho$ as $\rho_i:=(\sqrt{M_i}\rho\sqrt{M_i})/p_i$ and $p_i:=\mathrm{Tr}(M_i\rho)$. It's ...
Shadumu's user avatar
  • 321
3 votes
2 answers
60 views

How to calculate pseudo-threshold of the [[5,1,3]] code analytically to match simulation?

In this answer there is a simple method given to compute the "worst case pseudo-threshold" of the Shor code. I want to apply this to the $[[5,1,3]]$ perfect code. Namely, given a ...
Eric Kubischta's user avatar
1 vote
0 answers
15 views

Action of below circuit using heisenberg representation

Can someone please explain how the above gate affects logical operators? My understanding is that the circle indicates that we are measuring the second qubit? My initial guess is that it is equivalent ...
am567's user avatar
  • 585
2 votes
0 answers
72 views

What does it mean to take the maximum over all POVMs?

What does it mean to take the maximum over all POVMs (in the definition of accessible information for example) ? The set of POVMs is infinite, how can we be sure that the maximum is attained by one of ...
yosh's user avatar
  • 127
1 vote
1 answer
34 views

What is the explicit action of the following circuit?

Would somebody please be able to explain the action of this circuit to me? (Taken from Arthur Pesah's blog post "Computing with Quantum Codes using Transversal Gates") I understand overall ...
am567's user avatar
  • 585
3 votes
2 answers
81 views

What does it mean that the elements of a generalized measurement are operators?

I have a very simple question on Generalized measurements. The definition I was given is the one below: A set of operator $\left \{ M_{\alpha} \right \}$ is called generalized measurements for an ...
OffHakhol's user avatar
  • 155
0 votes
2 answers
73 views

Performing a projective measurement, is the resulting expectation value $\langle \Psi|M|\Psi\rangle$ bounded between $+1$ and $-1$?

Suppose we have a quantum state $|\Psi\rangle = \alpha|0\rangle + \beta|1\rangle$.According to a measurement operator M, the projective measurement of $|\Psi\rangle$ is given by $\langle\Psi|M|\Psi\...
aghin's user avatar
  • 129
2 votes
1 answer
48 views

Measuring one register of the state $\frac{1}{2^{m}} \sum_{x}\sum_{k} (-1) ^ {x\cdot k} |k\rangle |f(x)\rangle$

I'm reading the article which contains lemma 1. Its proof contains the statement, that probability of getting $|0\rangle$ (denote it as $\text{Pr}\left[|0\rangle\right]$) after measuring the first ...
Georgy Firsov's user avatar
0 votes
1 answer
78 views

Why does measuring a GHZ state in the computational basis destroy the entanglement?

Measuring in a basis other than the computational (Z) basis will generally destroy any entanglement present in the GHZ state, as the entanglement is defined with respect to specific basis states. Why? ...
Rayhan Kabir's user avatar
1 vote
1 answer
42 views

Getting a numeric result from the variational quantum eigensolver

I am confused about how the VQE is able to print out a decimal number for the ground state energy of a molecule. For example, for $\text{LiH}$, the ground state energy I get for an interatomic ...
Angel Martinez's user avatar
1 vote
0 answers
40 views

Why divide $\theta$ by 2 when doing the Bell's Inequality Experiment?

I understood the CHSH game correlations by watching Prof. Vazirani's video. I also understood that the correlation between two measures taken from different basis are related by the cosine of the ...
Gustavo Mirapalheta's user avatar
2 votes
0 answers
125 views

Solution Nielsen and Chuang exercize 10.71

Exercise 10.71: Verify that when $M = e^{−iπ/4}SX$ the procedure we have described gives a fault-tolerant method for measuring $M$. The book describes a procedure to perform the measurement. Instead ...
Maria 's user avatar
  • 21
2 votes
1 answer
101 views

Niemark's theorem - simulating POVMs with PVMs

I am having trouble understanding Niemark's theorem from books (e.g watrous). The wikipedia page is clearer but most calculations are not justified. I want to contruct the PVM associated with the ...
yosh's user avatar
  • 127
2 votes
1 answer
124 views

How can one derive the POVM to unambiguously discriminate between $|0\rangle$ and $|+\rangle$?

Page 92 of Nielsen and Chuang describes a POVM that can determine if a given state is either $|0\rangle$ or $|+\rangle$ with no error, but with some chance of an inconclusive result. The POVM is: $$...
shashvat's user avatar
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