Questions tagged [measurement]

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

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Randomness using simple parallel Hadamard circuit

I've recently tried to build a Random generator using 5 hadamard gates (shown as U2 below) measured to 5 classical bits in parallel as shown in the circuit image. I've executed this circuit for 8192 ...
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1answer
28 views

What is the representative matrix for a measurement in the Bell-state basis?

I have a few questions about measurement in Bell-state basis. In particular, if $Z = \begin{bmatrix} 1 & 0\\ 0 & -1 \end{bmatrix}$ is for a measurement on the computational basis, then what ...
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38 views

Question About How Qiskit Reset Gate Affects Other Entangled Qubits

I am trying to understand how the reset gate in Qiskit affects qubits its entangled with. Consider the following circuit with qubits $q_0$ and $q_1$: Where circuit240 takes $|0\rangle$ to $a|0\rangle ...
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72 views

How to measure the sign of quantum amplitudes

I have a quantum state on $ n $ qubits ($ 2^n $ amplitudes) for which I know the amplitudes are real numbers. I want to take the state out as a vector. I can estimate the magnitude of the amplitudes ...
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1answer
66 views

Bra-Ket Notation and Proof of a Ket Equation in Two-Party Shared-Entanglement Setting

Disclaimer: I had posted this question previously on the physics StackExchange, but received no response there. My question is two-part. First, imagine a bipartite quantum state $|\Phi \rangle_{AB}$, ...
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125 views

Are separable, orthogonal states LOCC distinguishable?

Consider two states $\sigma_0,\sigma_1\in\text{L}(\mathcal{H}_{AB})$, and suppose $\sigma_0,\sigma_1$ are separable and orthogonal. Is it possible to distinguish between $\sigma_0,\sigma_1$ through ...
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Many-photon limit of dispersive shift Hamiltionian

In the context of superconducting quantum computing measuments, consider the dispersive shift Hamiltonian: $$ H/\hbar = \omega_R a^\dagger a + \frac{1}{2} (\omega_Q + \frac{2g^2}{\Delta} a^\dagger a)\...
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33 views

Books about the measurement for Hamiltonian Energy

I am searching for articles/books about the measurement energy of Hamiltonians in adiabatic quantum computing. Do you know of any good resources?
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Can Shor's 9 Qubit Code Correct for a measurement on the first qubit?

Start with Shor's codeword for $|0 \rangle$: $|\psi\rangle = \frac{1}{\sqrt{8}}(|000\rangle + |111\rangle)\otimes(|000\rangle + |111\rangle)\otimes(|000\rangle + |111\rangle)$. Now, assume that ...
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1answer
88 views

How many samples are required to estimate the probabilities of a state?

Suppose that we have a quantum state of the form: $$|\psi\rangle = \sqrt{p}|0\rangle + \sqrt{1-p}|1\rangle$$ In order to get an estimate of the probability of reading $|0\rangle$ or $|1\rangle$, we ...
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1answer
27 views

Efficient diagonalisation of low-rank observables

Let $n$ be the number of qubits we're using, and let $$\mathrm H=\sum_{i=1}^T\alpha_i\mathrm U_i|0\rangle\langle0|\mathrm U_i^\dagger$$ be an $n$-qubit hermitian observable where $T=O(\mathrm{poly}(n))...
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Computing variance under the action of a unitary operator

I wish to calculate the expectation and variance for an observable on a particular qubit of a multi qubit quantum state. I'm using a quantum computing simulation library which allows me to apply ...
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120 views

Projective vs general measurements - a missing piece

This may be a very basic and common question (also discussed a lot), but strikingly enough I couldn't find the answer in the books or elsewhere. The projective measurement is given by the PVM on the ...
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35 views

Confusion about the state of a system after a measurement

I'm confused about the state of a system after a measurement. Say we have a particle $v$ in the state: $ |\psi\rangle= \sqrt{1/4} \ |0\rangle + \sqrt{3/4} \ |1\rangle $. From my understanding, if one ...
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42 views

Which entangled qubit is measured in this example?

Sorry, I am a newbie to quantum computing. I am reading an overview paper (released just a week ago) titled Advances in Quantum Deep Learning: An Overview (Garg & Ramakrishnan, 2020). I am stuck ...
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1answer
34 views

What are the two measurements per box being done in the Bell Tests in the IBM Quantum Experience “Entanglement and Bell tests” Section

I am confused as to what is being measured in the boxes in the example drawings shown on the Entanglement and Bell Tests section in the IBM Q Experience: https://quantum-computing.ibm.com/docs/guide/...
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73 views

Nielsen & Chuang Exercise 4.34 “Measuring an operator”

I need help with the exercise 4.34 from Nielsen & Chuang Book. I am supposed to get a matrix corresponding to the circuit. Thanks
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1answer
94 views

Measuring Probability of Mixed States

I am a little stuck on understanding the measurement probabilities of a 3 qubit system (QCQI q 4.41). 1)H gates are applied to both $q_1$ and $q_2$ 2) $C^{(1,2)}_3(X)$, a Toffoli, controlled by $q_1$...
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94 views

Increasing the von Neumann entropy despite the measurment?

Background Assume we have a density matrix $\rho$ of a sub-ensemble. However, we have an imperfect measuring instrument. While it does perform a measurement, we do not know exactly when it performs ...
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73 views

What is the best strategy to get an upper bound to measure $|00\cdots 0\rangle$?

You are given a quantum state$\newcommand{\bra}[1]{\left<#1\right|}\newcommand{\ket}[1]{\left|#1\right>}\newcommand{\bk}[2]{\left<#1\middle|#2\right>}\newcommand{\bke}[3]{\left<#1\...
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2answers
107 views

Why can I apply $HS^\dagger$ and then measure in the computational basis to measure $Y$?

I come from a CS background I was reading Neven and Farhi's paper ("Classification with Quantum Neural Networks on near Term Processors"), and I am trying to implement the subset parity problem using ...
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How does Teleportation based Error Correction (TEC) detect and correct loss/erasure errors?

I'm looking at papers like Demonstration of teleportation-based error correction in the IBM quantum computer (page) 10 and Role of syndrome information on a one-way quantum repeater using ...
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1answer
51 views

Showing measurement of a Hermitian Unitary operator gives final states as eigenvectors

This is related to exercise 4.34, The operation described can be written as $(H \otimes I)C^1(U)(H \otimes I)(|0\rangle \otimes |\psi\rangle)$ I can get to the point where the state of the system is ...
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13 views

Computation and measurement of readout error in IBM quantum experience

If p(1|0) (p(0|1)) is the probability that a detector registers 1 given that the actual state is 0 (registers 0 given that the actual state is 1), I guess that the readout error should be computed as ...
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2answers
60 views

Readout error in IBM quantum experience processor

Is there a section on the IBM website that shows information about the readout error for the devices of quantum experience? I have only seen the errors for single-qubit (U2) and CNOT gates but nothing ...
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68 views

Result of Grover on Qiskit simulator

I have executed this circuit and I don't understand why the result is $|11\rangle$ ? [q[0], q[1]] : solution register [q[2]] : ...
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1answer
40 views

Results of SAT on the Qiskit simulator

I computed SAT formula with the Grover search algorithm on the Qiskit simulator with default parameters, but I don't understand why the incorrect solutions don't have a probability of 0? The SAT ...
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3answers
37 views

What's the interpretation of the eigenvalues of qubit's projective operators?

Usually, while conducting a measurement on a qubit we are using two projectors, namely $P_0 = |0\rangle \langle 0|$ and $P_1 = |1\rangle \langle 1 |$. For the case of $P_0$ we have two possible ...
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1answer
23 views

Help in understanding the usage of eigenvalues in the definition of the projective measurement

Recently I was reading about the projective measurement in "Quantum Computation and Quantum Information" by Nielsen & Chuang, where they describe the projective measurement as follows: ...
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1answer
52 views

Fidelity With Bell State Calculation

Let's say I have the following state: $$ |\psi\rangle = \sqrt{\frac{2}{3}} |0000\rangle_{a_1b_1a_2b_2} + \sqrt{\frac{1}{6}} \big( |0011\rangle_{a_1b_1a_2b_2} + |1100\rangle_{a_1b_1a_2b_2} \big). $$ I ...
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59 views

What is $\vert 0 \rangle \otimes \vert + \rangle$?

A simple question that I cannot seem to figure-out why I cannot achieve the correct result. When I evaluate $$\vert 0 \rangle \otimes \vert + \rangle,$$ I end up with $$\begin{bmatrix}1\\0\end{bmatrix}...
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207 views

Qiskit - Z expectation value from counts?

For a given state $|\psi\rangle$, how would I work out $\langle\psi|Z|\psi\rangle$ ? If I run a quantum circuit and get the counts dictionary on qiskit, I get observables in the Z basis. For n=1 ...
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Why Alice and Bob don't get the same result when they measure in the same basis?

I'm simulating the BB84 protocol using simulaqron. My problem is that when Alice and Bob measure in the same basis, they don't get the same result. How can I fix this error? . BB84.py ...
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305 views

How to get the relative phase of a qubit?

Question1. If there is a state $|\phi\rangle=\frac{1}{\sqrt{2}}(|0\rangle+e^{i\theta}|1\rangle)$, and I want to know the angle $\theta$. What kind of measurement should I do? Could somebody give me ...
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Constructing and Measuring in an Arbitrary 3-qubit basis

As part of a Quantum Theory project I have "constructed" an arbitrary 3-qubit basis: $\left|B_0\right> =\left|000\right>$ $\left|B_1\right> = \frac{1}{\sqrt{2}}\cos(x)(\left|100\right> +...
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1answer
36 views

Half of Standard Basis Measurement

I know that we can measure a state in standard basis (Z) where the post measurement state is either $|0\rangle$ or $|1\rangle$. But can you do a 'half-Z' basis measurement? I mean, you only measure ...
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118 views

How to implement controlled gate based on measurement (quantum teleportation)?

I am implementing the teleportation algorithm on IBM Q Experience (GUI interface). Certain operations on the third qubit are only performed if the classical measurement result is 1, for example ...
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1answer
167 views

VQE Cirq example

Is my understanding correct that in this example the Hamiltonian measurement is not performed through measuring individual Pauli operators because all its terms are mutually commuting? So, for each ...
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1answer
51 views

CPTP, Kraus representation and classical registers

What is the best mathematical representation of a quantum system that has some classical registers and some quantum registers? I'm asking because I'm considering any "physical" process $\pi()$ that ...
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2answers
96 views

How to measure in the bell basis?

The question is quite straightforward, I have some two qubit state and I want to measure it in the Bell basis. This question answers me partly, but I still have some doubts because, I thought that ...
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2answers
122 views

Viewing two-qubit measurement as a projective measurement

I am following Nielsen and Chuang, section 2.2.5: A projective measurement is described by an observable, $M$, a Hermitian operator on the state space of the system being observed. The ...
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31 views

Do Bell state measurements satisfy the completeness condition from the no-signalling theorem?

Do Bell state measurements satisfy the completeness condition from the no-signalling theorem? In a quantum experiment involving unitary evolution and projective measurements,  do Bell state ...
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1answer
67 views

Exercises on computing by hand quantum circuits

I'm trying to become familiar with manipulation of the Dirac notation. I want to be able to compute quickly the final states obtained in a small circuit. Typically, it should include 2 to 5 qubits, ...
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1answer
40 views

$X$ measurement on graph state leads to edge contraction

I cannot understand the proof of Lemma 5 from the paper "Resources Required for Preparing Graph States". Here it is: (In this paper, $|G:S\rangle$ denotes $Z_S$ applied to the graph state $|G\rangle$,...
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31 views

Getting dot product from two wavefunctions

I'm looking at some examples, but I cannot get the expected result when it comes down to making the measurement on the following state where we measure the first qubit which is the ancilla state. ...
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102 views

Reading or Unloading quantum data to classical data

I have a very basic question: say I perform some set of operations on $N$ qubits (like QFT, QFT addition etc), and thus have a $N$ qubit final state. If each qubit has something that I want to read ...
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52 views

How to find measurement probabilities of a single qbit in a tensored state

Given a tensored state of qbits such as $$ \frac{1}{\sqrt{3}}|0\rangle_1|1\rangle_2 + \sqrt{\frac{2}{3}}|1\rangle_1|0\rangle_2 $$ or $$ \frac{1}{\sqrt{2}}(|0\rangle_1|+\rangle_2 + |+\rangle_1|-\...
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1answer
103 views

When increase the shot, why the result is different?

when I measure the shot = 1024 when I measure the shot = 8192 I want to derive result value 011(=3) However, I know if measure the more shots, increase the accuracy. why this result derive??? why ...
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694 views

What is the opposite of measurement, in a quantum circuit?

My understanding is that at the level of quantum mechanics, almost all operations are reversible in time. Most gates in a quantum circuit clearly obey this rule; they can be reversed by applying some ...
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75 views

Is there a function that gives the ideal probability distribution of a measurement in Qiskit?

I want to compare the theoretical output of a circuit measurement with the actual output from a real quantum computer. I can approximate the ideal output by running the circuit on a simulator. ...