Questions tagged [measurement]

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

Filter by
Sorted by
Tagged with
3
votes
1answer
48 views

Entanglement scaling law for 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, ...
2
votes
1answer
40 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 ...
2
votes
1answer
48 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 ...
2
votes
1answer
33 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 $\...
2
votes
1answer
48 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 $|x\rangle$...
3
votes
1answer
62 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? ...
0
votes
1answer
32 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\...
1
vote
0answers
34 views

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 ...
0
votes
1answer
47 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 <...
0
votes
0answers
23 views

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 ...
2
votes
2answers
63 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{...
2
votes
2answers
57 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 $M_m=U_m\sqrt{E_m}$, ...
0
votes
0answers
32 views

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 ...
2
votes
0answers
78 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 ...
3
votes
2answers
65 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 ...
0
votes
1answer
59 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 ...
4
votes
1answer
318 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 $|0\rangle$, $|1\rangle$, $|+\rangle$, $|−\rangle$ ...
1
vote
1answer
65 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 $\{|k\rangle,k=0,1,...N-1\}$. ...
3
votes
0answers
43 views

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,\...
0
votes
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 ...
2
votes
3answers
410 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 ...
0
votes
1answer
64 views

Measurement of single qubit operator $U$ which is both Hermitian and unitary with eigenvalues $±1$

Suppose we have a single qubit operator $U$ with eigenvalues $±1$, so that $U$ is both Hermitian and unitary, so it can be regarded both as an observable and a quantum gate. Suppose we wish to measure ...
6
votes
1answer
95 views

Are SIC-POVMs optimal for quantum state reconstruction?

Mutually unbiased bases (MUBs) are pairs of orthonormal bases $\{u_j\}_j,\{v_j\}_j\in\mathbb C^N$ such that $$|\langle u_j,v_k\rangle|= \frac{1}{\sqrt N},$$ for all $j,k=1,...,N$. These are useful for ...
2
votes
2answers
231 views

How can we measure a quantum system when the sum of amplitudes-squared does not equal one?

How can we measure a quantum system if the sum of amplitudes-squared does not equal one? For example, if we want to measure $|a\rangle = 0.25|0\rangle + 0.25|1\rangle$, how can we measure it?
1
vote
1answer
37 views

Can someone please explain how the syndrome bit still ends up being 0 in this quantum error correction circuit using repetition code?

I'm not too great at dealing with superpositions and applying the CNOT gate when superpositions are involved. Can you go through it in detail each gate using math/matrices etc. It's based on the ...
6
votes
1answer
115 views

Do entangled measurements across multiple copies help in state distinguishability?

Consider two density matrices $\rho$ and $\sigma$. The task is to distinguish between these two states, given one of them --- you do not know beforehand which one. There is an optimal measurement to ...
1
vote
2answers
207 views

How to analyze the following quantum circuit?

I'm trying to analyze the following quantum circuit The goal here is to analyze the final outputs at q3 & q4. For inputs, at q0 & q1, one of the Bell state $$|\psi\rangle = \frac{|01\rangle + ...
7
votes
1answer
100 views

Are projective measurements the only optimal measurements to discriminate between two states?

Consider two density matrices $\rho$ and $\sigma$. The task is to distinguish between these two states, given one of them --- you do not know beforehand which one. There is an optimal measurement to ...
0
votes
2answers
37 views

Find expectation value of the observable $X_1\otimes Z_2$ for a maximally entangled two-qubit system

In this exercise I need to find the expectation value of the observable $M=X_1 \otimes Z_2$ for two qubit system measured in the state $\dfrac{|00\rangle + |11\rangle}{\sqrt{2}}$. I know that $E[M]=\...
2
votes
1answer
89 views

What happens measuring the first qubit of a $GHZ$ state in the basis $\{|+\rangle, |-\rangle\}$?

This exercise ask me to explain what happens when the first qubit is measured in the diagonal base ($|+\rangle,|-\rangle$), considering this state: $|GHZ\rangle=\dfrac{1}{\sqrt{2}} (|000\rangle+|111\...
1
vote
1answer
101 views

Return only the measurements of a circuit

I have written the following program in jupyter: ...
0
votes
1answer
55 views

Pad get_counts() with zeros for unmeasured states? (Qiskit)

After executing a job on qiskit, the typically procedure to get the measurement data from the quantum computer is to call get_counts() like so... ...
5
votes
3answers
137 views

Intuition for why $\frac{|00\rangle+|11\rangle}{\sqrt{2}}$ can be written as $\frac{|++\rangle+|--\rangle}{\sqrt{2}}$

In analyzing measurement of $\frac{|00\rangle+|11\rangle}{\sqrt{2}}$ in the local $|+\rangle$, $|−\rangle$ basis, through algebra manipulation, the initial state is first written as $\frac{|++\rangle+|...
3
votes
2answers
329 views

What does "measurement destroys information" mean?

I am reading a paper on quantum cryptography. The author used two facts: quantum- information cannot be copied and Furthermore, measurements destroy information... For the first statement, I came ...
4
votes
0answers
32 views

Are almost perfectly distinguishable ensembles almost orthogonal?

Let $\varepsilon>0$ and consider an ensemble of states $\{p_x\rho_x\}_{x\in X}$ and suppose there exists a measurement with POVM representation $\{M_x\}_{x\in X}$ such that $$ \sum_{x\in X} p_x\...
7
votes
2answers
121 views

Why is the complexity of $n$-qubit state tomography not upper bounded as $O(3^n)$?

Consider the task of fully determining an $n$-qubit state $\rho$ which can be written as \begin{equation}\tag{1} \rho = \sum_{p \in \{I, X, Y, Z\}^n} \text{Tr}(\rho P_{p}) P_{p} \end{equation} and ...
4
votes
1answer
226 views

Do I need to use classical bits in measurement?

I wonder if I have to add classical bits while performing measurement for a single-qubit quantum circuit. The difference to initialize the circuit is ...
2
votes
0answers
92 views

Applying projectors with mid-circuit measurements

I am trying to apply a non-unitary projector (see image) to my two-qubit quantum circuit using mid-circuit measurements. $$ \begin{pmatrix} 0 & 0 & 0 & 0 \ 0 & 1 & 0 & 0 \ 0 &...
2
votes
1answer
105 views

Measuring tensor products of Pauli operators

Is there a neat way to derive and efficiently implement a measurement circuit for tensor products of arbitrary Pauli operators like $XZZXZ$ in Qiskit ? I tried using the ...
4
votes
1answer
78 views

Measure $\langle \hat{X}\rangle$ and $\langle \hat{Y}\rangle$ from counts

I'm confused about how I can measure $\langle \hat{X}\rangle$ and $\langle \hat{Y}\rangle$ using counts. Here's my code for X: x-basis: ...
2
votes
2answers
93 views

What are the constraints for the coefficents of the basis states in quantum computing?

$\newcommand{\ket}[1]{\left|#1\right>}$ It's known that the Kolmogorov axioms characterise a probability distribution: Probability of an event is a non-negative real number. The sum of all ...
6
votes
0answers
72 views

How does the extremality of a POVM reflect on its Naimark dilation isometry?

Let $\mu:\Sigma\to\mathrm{Pos}(\mathcal X)$ be some POVM, with $\Sigma$ the finite set of possible outcomes, and $\mathrm{Pos}(\mathcal X)$ the set of positive semidefinite operators on a finite-...
2
votes
1answer
103 views

How to normalise when the probability of measurement is zero?

In one of the answers to this question on measuring one qubit it is explained that given a general two-qubit state $$ |\psi\rangle = \begin{bmatrix} \alpha_{00} \\ \alpha_{01} \\ \alpha_{10} \\ \...
0
votes
1answer
66 views

Doing $|0\rangle$ then Hadamard gate then measurement

I am starting to use quantum experience and following exactly first example from lecture. After initializing the qubit to $|0\rangle$, then applying a Hadamard gate, the probability for measuring $|1\...
4
votes
1answer
67 views

What are the conditions under which an unknown quantum state is learnable with arbitrary precision?

Assume that we have an unknown quantum state and we need to learn that unknown state with arbitrary precision. Under what conditions can we learn the unknown state with arbitrary precision? One ...
0
votes
1answer
60 views

Finding the measurement basis for single qubit with given probability of outcome $0$

I have the general state of a single qubit $|\psi \rangle = \alpha|0\rangle + \beta|1\rangle $. Assume I am given a probability $p$ such that $0 < p <1$. Now I need to find the basis in which ...
1
vote
1answer
29 views

What is the correct notation to denote operations conditional on a measurement outcome?

What is the correct mathematical notation to describe the following setup? I have classical state in register $A$ which I can think of as $\sum_i p_i \vert i\rangle\langle i \vert_A$. I measure this ...
2
votes
2answers
48 views

How does a quantum circuit calculating the inverse of a non-injective function act?

Lets say I have a non-injective function $f()$, adding image for reference. Now lets say I build a quantum circuit to calculate $f^{-1}()$. If the input register has the value $i$, does the output ...
0
votes
1answer
53 views

Manual measurement error mitigation returning a negative number of counts

I have a simple 2 qubit circuit which I am trying to protect from errors using the measurement error mitigation technique laid out here: https://qiskit.org/textbook/ch-quantum-hardware/measurement-...
1
vote
1answer
84 views

Get the inverse of a Hermitian operator for measurement in qiskit

I am using qiksit to measure the Hamiltonian H, which isbasically sum of Pauli strings, say something like 2*X^X+0.5*Z^Y. For ...

1
2 3 4 5
8