Questions tagged [measurement]

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

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Parameterized swap test and perfect swap test

Suppose one has parameterized a swap test by using an ansatz $U(\theta) = \exp(-i\theta \text{ CSWAP})$, and one tries to find an angle $\theta$ such that one can distinguish given two quantum states ...
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41 views

The meaning of non-destructive measurements in QEC

I am starting to study quantum error correction and it's the first time that I see the operators (usually Pauli) as projective measurements which seem to just identify a syndrome but do not destroy ...
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170 views

Can joint measurement be achieved in two labs far apart?

Consider the following scenario: Alice and Bob are in two labs far apart, and they each have one qubit. Can joint measurement (for bipartite projective measurement, they are measurements that cannot ...
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39 views

Retrieve image from Histogram data of Qiskit

I am trying to understand the quantum image processing. Please refer the link- https://qiskit.org/textbook/ch-applications/image-processing-frqi-neqr.html. I am not able to understand how to process ...
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37 views

How do we define qubit measurements in a plane?

When does $\vec{a} \cdot \vec{\sigma}$ define a measurement in x-y, y-z, and x-z planes?
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44 views

Measurement of the second quantum register in the Shor's algorithm [duplicate]

I've read that the measurement of the ancilla qubits is not fundamental for Shor's algorithm, but I don't understand how the algorithm works if I remove it. Without those measurements, do I have $r$ ...
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49 views

Error with IBM's Quantum Composer Qiskit Histogram when Resets are involved?

I am having trouble understanding what IBM's histogram is doing. I have independently verified, in agreement with the statevector given from IBM, that after all these steps the statevector should be ...
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1answer
25 views

What is a histogram of a job a plot of, if not the squared amplitudes of the final state-vector?

The histogram of a circuit is the result of running the circuit (with measurement) many times, right? Does this correspond to the squared amplitudes of the final state-vector? If not, why?
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31 views

What happens to the elements of the simulated state vector when we set a qubit to $|0\rangle$?

In IBM's Qiskit online simulator, we have the (non-reversible) ability to set a specific qubit to $| 0\rangle$. This is convenient but I'm left confused as to what happens to the elements of the ...
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62 views

Density matrix after measuring Bell state in CHSH game

In these notes, the author says the following about the CHSH game Does Alice and Bob’s ability to succeed more than 75% of the time mean that they are communicating? Well, we know it’s not possible ...
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54 views

Partial measurement can be replaced with constant overhead

While reading the chapter on Quantum Computation (starting on page 401) of the draft version of the Arora & Barak book I came across exercise §4 on page 431 that reads as: Suppose that $f$ is ...
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167 views

Does one measurement affect the following measurement errors in mid-circuit measurement?

Suppose I have a quantum circuit with a few measurements (say $N$) on a single qubit. Before all the measurements, I generated calibration circuits and the 2 by 2 calibration matrix for that qubit of ...
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34 views

Mathematics of Measurement then Partial Trace

Say we have the following quantum state: $$ |\psi\rangle = \frac{1}{\sqrt{2}}(|00\rangle +|10\rangle)$$ To measure the first qubit and then further trace out the first qubit, my notes have the ...
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How to find $\langle Z_1...Z_{N-1} \rangle$ knowing $\langle Z_1...Z_{N} \rangle$ and $\langle Z_i \rangle$

I have a quantum circuit with $N$ qubits represented by the unitary $U$. The initial state is $| 00...0\rangle$ and $\psi=U|00...0\rangle$. Given $\langle\psi| Z_1...Z_{N} |\psi\rangle$ and $\langle \...
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108 views

How to distingush between two very similar pure quantum states?

I'm trying to prove the claim that Given two pure states: $|\psi_i\rangle$ and $|\phi_i\rangle$ such that $|\,|\psi_i\rangle - |\phi_i\rangle\,|\le \delta$ then no measurement can distinguish ...
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41 views

Individual processing of quantum circuit measurment results

When superconducting transmon qubits are measured with a readout pulse, the raw readout signal is demodulated, and results appear as clouds on the IQ plane, with one point in the cloud representing ...
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1answer
44 views

Expectation value of an observable containing a single projector vs Born rule for the projector

Suppose I have a state $|\psi\rangle$ and I want to estimate the probability of obtaining a computational basis state $|x\rangle$. Then by Born rule: $$ p(x) = |\langle x|\psi\rangle|^2 = Tr[|x\rangle ...
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147 views

Is the measurement of the second register in Simon's algorithm superfluous?

I often see Simon's algorithm with two $n$-ary measurement gates for the two computations (Hadamard in upper part, $f$ in lower part). For example, this image taken from wikipedia. In the same ...
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1answer
56 views

Bias in the results of superposition measurements on IBMQ Backends, qiskit

Dear people on this forum, I was doing some research, and I created this circuit in qiskit Please bear in mind that I am really new to this field, and I do not retain much knowledge yet. Therefore I ...
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71 views

Qubit identities get swapped in IBM Qiskit

Edit: Improved code a bit This is a condensed description of the IBM bug that was a problem here, to make it more clear. The following code compiles to a correct circuit when the measurement is ...
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1answer
88 views

Elitzur-Vaidman bomb

In the original paper (Quanum Mechanical Interaction-Free Measurements - Elitzur, Vaidman, p.991), they make an algebraic substitution for the 'appearance' or 'scattering' of the bomb (green arrow): ...
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57 views

How to simulate the state of a system after partial measurement?

Based on the answers at here and here, I have a quantum simulator which implements the operations described in the classic Teleporting an Unknown Quantum State. Careful comparison of circuits with the ...
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1answer
35 views

Given a three-qubit state, how do you obtain the density matrix for the third qubit

I have a quantum simulator that yields a three-qubit final state. However, I need to measure the first two qubits and apply a one-qubit gate (x,y or z) to the third qubit. How do you reduce a three-...
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1answer
23 views

How to change the probability of observation by some set amount when initial probability is unknown?

If I have some state $|\psi> = \alpha |0> + \beta|1>$, I know that the probability of observing $|0>$ is $p_1 = |\alpha|^2$. Is it possible to change the probability of observing $|0>$ ...
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Defining joint-measurability on ensembles of states

Joint Measurability for a collection of POVMs $\{\Omega_j\}_j$ where $j$ is the index of the POVMs with associated effects $\{\Omega^\omega_j\}_{\omega}$ is defined as $$\Omega^\omega_j = \sum_{\theta}...
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61 views

Transformation matrix for a two-qubit operation where there are more than two qubits

I have an OPENQASM program that performs entanglement swapping. It has five qubits: the data qubit and four link qubits. It works, but I want to see the details of the Bell measurement transformation. ...
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1answer
47 views

What are the measurement operators $F_k$ corresponding to a homodyne measurement?

By definition, a measurement is characterized by a set of positive-semidefinite matrices $\{F_k\}$ satisfying the completeness relation $\sum_k F_k = \textbf{I}$. I am interested in knowing how does ...
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1answer
68 views

Show that the effect of a Controlled Unitary on qubits followed by a measurement is unchanged depending on when measurement is taken

I understand that a Controlled Unitary is just a generalization of a control gate, such as CNOT etc, and that it is given in state representation as $$\hat C_U = |0\rangle\langle0|\otimes\mathbb{I} + |...
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1answer
61 views

How to measure a correlated operator $Z_1Z_2$?

I was reading this articl and I am stuck trying to understand equation $(60)$, which reads $$\langle\psi|\Lambda_{1,2}(X)Z_1\Lambda_{1,2}(X)|\psi\rangle=\langle\psi|Z_1Z_2|\psi\rangle$$ where $\Lambda(...
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1answer
86 views

Does entanglement entropy follow a volume or an area law for 2D cluster states?

Consider a 2D cluster state defined on a rectangular lattice, which is universal for one way quantum computers. For a description of the state, see for example question 2 in this problem set. Now, ...
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53 views

Universal resource for measurement based quantum computation

Consider universal resources for measurement based quantum computation, as defined here: We are now ready to formulate the following definition. A family $\Psi$ is called a universal resource for MQC ...
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1answer
54 views

Why does measurement in computational basis result in classic probability?

I am working on a problem related to finding the limits on the joint probability distributions/correlations of three or more quantum systems who share entangled states, after measurement. I have been ...
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47 views

Cliffords to Transform into Common Eigenbasis

Say I have the following Hamiltonian (given in terms of Pauli operators): \begin{equation} H=aX_1Z_2+bZ_1X_2. \end{equation} Both Pauli terms commute with each other. I want to make a measurement of $\...
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1answer
54 views

Which observable $M$ provides the Absolute Average of a statevector?

My question should be fairly simple, though I did not find an answer to it here or anywhere else. I have been working on an algorithm which, similarly to the HHL algorithm, provides a state $|x\rangle$...
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82 views

Can you measure sums of Paulis in the stabilizer formalism?

Suppose we wanted to measure the observable $Z_{1} + Z_{2} + \cdots + Z_{N}$ in a stabilizer state. Is it possible to do this using only Clifford operations, and possibly adding some auxiliary qubits? ...
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33 views

Find the Probability for a "+" outcome when making a Pauli-x Measurement

So, we apply Equation 3.28 (above) to our initial vector state, following the equation below, to get $|\psi(t)\rangle$. What I obtained was the basically the same equation, except now we have a $|up\...
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What are useful abstraction levels for external quantum input/output of quantum computers?

Section "2.2.3 Quantum measurement" in Nielsen&Chuang uses very general measurement axioms: Postulate 3: Quantum measurements are described by a collection $\{M_m\}$ of measurement ...
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66 views

Calculating measurement probabilities from a quantum circuit

Currently I'm trying to calculate the circuits I'm building and show that they work as intended. Somehow, my measurments do not, at all, represent my calculated expectancies. This is my circuit in <...
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Measuring in qiskit collapses onto the Z-Plane. Why do any rotations other than Y matter?

We have the situation where a 50/50 split between $|1\rangle$ and $|0\rangle$. This was done using a $H$-Gate. Now, when measuring in qiskit, if my understanding is ...
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2answers
71 views

How does measurement change the effective transformation matrix?

I have simulated three cases in Qiskit and tried doing some manual calculations to verify the simulated results. Case 1: The initial state is $\psi_i = |00\rangle = \begin{Bmatrix}1 \\0 \\ 0 \\ 0\end{...
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65 views

Show that there are unitaries $U_m$ such that $M_m=U_m \sqrt{E_m}$, for any measurement $M_m$ and associated POVM $E_m$

Nielsen and Chuang's QCQI, section 2.2.6, page 92, asks Suppose a measurement is described by measurement operators $M_m$. Show that there exist unitary operators $U_m$ such that $M_m=U_m\sqrt{E_m}$, ...
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How to choose $\beta$ in Gaussian derivative component of DRAG pulse?

From definition of the DRAG pulse it is: $$f(x)=Gaussian+1j*\beta*(-(x-duration/2)/\sigma^2)Gaussian,$$ where $Gaussian(x, amp, \sigma)=amp*e^{-(1/2)*(x-duration/2)^2/\sigma^2}$. If I try it in ...
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80 views

Schur transform and the outcome probabilities for a particular type of state

I was reading about the Schur transform and its applications in knowing about an unknown quantum state. Consider $\rho^{\otimes k}$, which means $k$ copies of an unknown $n$ qubit quantum density ...
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70 views

Do we need ancillary qubits to implement orthogonal measurements?

Consider an $n$ qubit state $|\psi\rangle$. Let's say I want to implement an $m$ outcome orthogonal measurement on $|\psi\rangle$, where $m \neq n$. Denote the set of $m$ orthogonal measurement ...
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61 views

How is transformation for measurement in an arbitrary basis derived?

I started with Qiskit today and find it very exciting. As a first question I want to understand how to measure an arbitrary state $|\Psi\rangle$ not in the basis of ...
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322 views

Why does quantum distinguishability ensure no faster-than-light communication?

On page 56-57 in Nielsen and Chuang, for a proposed scenario, it's said that: if Bob had access to a device that could distinguish the four states $|0\rangle$, $|1\rangle$, $|+\rangle$, $|−\rangle$ ...
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67 views

How to compute the measurement probabilities of $|\phi\rangle=\sum_k c_k |k\rangle$ in a rotated basis $V|k\rangle$?

I came across the following question and have some conceptual questions. Consider a general quantum state $|\phi\rangle$ of dimension $N$ spanned by some standard basis $\{|k\rangle,k=0,1,...N-1\}$. ...
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What does the $I$ mean when measuring ${\rm Tr}(\rho (I\otimes\sigma\otimes\cdots))$ in quantum tomography?

In Nielsen and Chuang's QCQI, I learned that the quantum tomography for n qubit can be described easily in math as we need to measure $Tr(\rho W_k),\forall k$ where $W_k\in\{I,\sigma_x,\sigma_y,\...
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1answer
24 views

As regards measurement how would a quantum-full-adder perform multiple additions simultaneously?

Here in this video from 15:14 Arvin Ash demonstrates a quantum-full-adder circuit, he goes on further to illustrate how it can perform multiple operations ...
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417 views

Is there any simple mathematical proof that measurement destroys entanglement?

Is there a simple mathematical way to prove that measurement destroys entanglement? I can see that this is indeed true if I just take a specific measurement on an entangled state. What I am looking ...

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