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
2
votes
2answers
86 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
57 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-...
1
vote
1answer
77 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
58 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\...
0
votes
0answers
46 views

Probability resulting from uncertainty when the measuring device exactly clicks? [migrated]

Background Let's say I have $2$ set of eigenkets of observables of a system $|x_i \rangle $ and $|p_j \rangle$ (which do not commute). Let's say I have a non-ideal detector in the sense the ...
4
votes
1answer
54 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
53 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
23 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
45 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
41 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-...
0
votes
1answer
55 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 ...
0
votes
1answer
32 views

In what sense are Pauli matrices measurement operators?

Neilson and Chuang's textbook shows a nice example of measuring in the $Z$ basis on page 89 in section 2.2.5. The Hermitians for measuring in the $Z$ basis, $|0\rangle\langle 0|$ and $|1\rangle\langle ...
0
votes
0answers
49 views

Qiskit equivalent of get_expectation_value() in ProjectQ

Is there a corresponding function that has the same function as function get_expectation_value() in Project Q? Get the expectation value of qubit_operator w.r.t. the current wave function ...
1
vote
0answers
46 views

Calculating probability that two entangled qubits are the same when measured in different bases

Given the entangled state \begin{equation} |\Phi^+\rangle = \frac{1}{\sqrt 2} |00\rangle + \frac{1}{\sqrt 2} |11\rangle \end{equation} I am trying to calculate the probability that the two qubits end ...
2
votes
3answers
78 views

Do sequences of operations (including measurements) applied to different halves of an entangled pair always commute?

Let us say $A$ has one half of an entangled qubit pair, and $B$ has the other half. $A$ may be able to perform any type of operation on their half of the pair, such as unitary operations, entangling ...
3
votes
1answer
81 views

Why is $\langle \psi| \sigma_z |\psi \rangle=\cos(\phi_1)\cos(\phi_2)$ for $|\psi\rangle=R_y(\phi_2)R_x(\phi_1)|0\rangle$?

I'm trying some example with the rotation gates and stuck here: $$\langle \psi| \sigma_z |\psi \rangle = \langle 0 | R_x(\phi_1)^\dagger R_y(\phi_2)^\dagger \sigma_z R_y(\phi_2) R_x(\phi_1) | 0 \...
5
votes
1answer
89 views

Distinguishing $\frac{| 0 \rangle + e^{i\theta} |1 \rangle}{\sqrt{2}} $ from $| 0 \rangle/|1 \rangle$ with probability $1/2 + \epsilon$

I am given one copy of one of two quantum states - $\frac{| 0 \rangle + e^{i\theta} | 1 \rangle}{\sqrt{2}} $, for some unknown fixed $\theta$. One of $| 0 \rangle/|1 \rangle$ - don't know which one, ...
1
vote
1answer
115 views

How to get measurement result on Qiskit

I want to get measurement result from my circuit output, like '00', '01', '10', or '11' because want to process it further classically. Any suggestion? We can see the highest probability '01'. How I ...
2
votes
1answer
65 views

What are the possible initial states that can be prepared in a lab for use in a quantum computation?

So here's something that's been bothering me. Given the time evolution of the wavefunction can only be unitary or discontinuous as a process of the measurement. So let the observables for our ...
2
votes
1answer
51 views

Computing $H(Z|B)$ in a bipartite density matrix $\rho_{AB}$

Let's say Bob prepares a bipartite quantum state $\rho_{AB}$ to be shared between him and Alice. Bob sends Alice's part to her lab. Alice measures her subsystem $A$ in the computational basis $\...
1
vote
2answers
70 views

Inconsistent result trying to simulate measurement of a 2 qubit system

Consider a 2 qubit system in the initial state: $$ \begin{pmatrix} 0 \\ \frac{\sqrt{2}}{2} \\ -\frac{\sqrt{2}}{2} \\ 0 \end{pmatrix} $$ the so-called Bell-pair. Now let's measure the spin of the first ...
2
votes
1answer
49 views

What is the observable to measure spin along some direction for a 2 qubit system?

Let $M$ be the $2 \times 2$ matrix corresponding to the observable to measure spin along some arbitrary axis $\vec{v}$. This matrix is given by following formula: \begin{equation} M = v_x X + v_y Y +...
2
votes
0answers
44 views

How to improve embedding process in D-Wave?

I am quite new to the quantum computing field. Currently, I am trying to solve a combinatorial optimization problem on a D-Wave system, which I successfully translated into QUBO form. I also managed ...
2
votes
1answer
46 views

How to get probability when the coefficient in wave function is a matrix?

Following this circuit: With $\mathcal{G}, A$ being unitary matrices and $|\psi\rangle$ the initial state. First, the system is: $\frac{1}{\sqrt{2}}(|0\rangle+|1\rangle)\;\otimes|\psi\rangle$ Next: $\...
5
votes
2answers
224 views

How do local quantum gates affect an entangled state?

(1) Assume we have the Bell State $$ \frac{\lvert 0_{A}0_{B}\rangle + \lvert 1_{A}1_{B}\rangle}{\sqrt{2}} $$ where A and B stand for Alice and Bob. Now say Bob applies the X gate to his qubit. I think ...
2
votes
0answers
19 views

What are the most popular QND measurement implementations used in photonic quantum computers?

What components are used in order to perform QND measurement in photonic quantum computers?
3
votes
2answers
91 views

How is the additivity of accessible information, $\frac{1}{n} I_{\rm acc}(\rho^{\otimes n})=I_{\rm acc}(\rho)$, proved?

Let $\rho^{XA}$ be a classical-quantum state of the form $$ \rho^{XA} = \sum_{x\in X} p_x |x\rangle\langle x|\otimes \rho_x^A, $$ and let the accessible information be given by $$ I_{acc}(\rho^{XA}) = ...
-1
votes
3answers
99 views

Measure a state in Hadamard basis [closed]

I can't understand how a state measure on the Hadmard basis collapses to $$ |+\rangle =\dfrac{|0\rangle+|1\rangle}{\sqrt{2}} $$ or $$ |-\rangle =\dfrac{|0\rangle-|1\rangle}{\sqrt{2}} $$ as they dont ...
3
votes
1answer
61 views

For a bipartite operator $M\in L(H_{AB})$, suppose $0\leq M\leq \mathbb{I}$. Prove $M^{AB}\leq M^A\otimes \mathbb{I}$

As stated in the title, let $M$ be a linear operator on a finite bipartite Hilbert space. Suppose $0\leq M^{AB}\leq \mathbb{I}$ and $0\leq M^A,M^B\leq\mathbb{I}$, where $M^A=\mathrm{Tr}_B\left(M^{AB}\...
1
vote
2answers
47 views

Measurement interpretation - do individual operators get applied?

The description of measurement operators in Nielsen and Chuang is as follows: Quantum measurements are described by a collection $\{M_m\}$ of measurement operators. These are operators acting on the ...
2
votes
0answers
87 views

Does the von Neumann entropy equal the smallest accessible Shannon entropy?

I've been reading about the von Neumann entropy of a state, as defined via $S(\rho)=-\operatorname{tr}(\rho\ln \rho)$. This equals the Shannon entropy of the probability distribution corresponding to ...
2
votes
0answers
51 views

translating between measurement based and circuit based quantum computation

I think I understand circuit based QC (CBQC) well enough; I know very little about MBQC. From what I read it seems that they are somehow "equivalent". I'd like to check this with a concrete ...
2
votes
1answer
48 views

Why are the probabilities $|\alpha|^2$ and $|\beta|^2$ when measuring in the computational basis?

In measurement in the computational basis, I was being told that it is a way to extract information from a qubit, and it outputs a classical bit. For the quantum state $\alpha |0\rangle + \beta |1\...
3
votes
1answer
55 views

How is measurement performed on a stream of polarized photons?

Is it possible to use a simple laser to measure qubits in optical quantum computers, or is a single-photon emitter absolutely necessary? If you can do it with a simple laser, how would you go about ...
2
votes
0answers
15 views

Measurement on a specific basis and proof of circuit output

I am trying to understand a proof from Practical optimization for hybrid quantum-classical algorithms. In particular, I need clarifications on how do you perform the measurement on a different basis ...
2
votes
1answer
51 views

Umambiguous discrimination using POVM with highest discriminate probability

I was studying Nielsen&Chuang's textbook (about page 92), and come up with a question that I cannot solve it. Given one of the two state $|\psi_1\rangle=|0\rangle$ and $|\psi_2\rangle=\frac{1}{\...
1
vote
1answer
55 views

Moving between $\sum_{I}E_{i}=I$ and $\sum_{i}M^{\dagger}M=I$ for non-hermitian $M$

If $\sum_{i}E_{i}=I$ is a set of POVM's and $\sum_{i}M^{\dagger}M=I$ is a set of general measurement operators, I have always been confused on how to move from one to the other, in regards to the ...
1
vote
0answers
66 views

Expectation value of a quantum circuit [closed]

The expectation value of an operator $A$ is defined by this equation $\langle A \rangle_\psi = \sum_j a_j |\langle \psi | \phi_j \rangle|^2 $. My first question is does it mean that the expectation ...
4
votes
2answers
50 views

How does measuring in the $|\pm\rangle$ basis works in experiments?

I don't get how measuring in different bases works in experiments. From an experimental point of view, what do we do to measure in $|\pm \rangle$ basis? If I'm getting it right measuring in the ...
1
vote
2answers
89 views

Show when $a_k$ and $b_k$ are correlated when measuring in different bases, in the BB84 protocol

I'm trying to answer the following question about the BB84 protocol from Nielsen and Chuang's Introduction to Quantum Information. As I understand it, the string $b$ is determining whether we are ...
6
votes
1answer
186 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
57 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 ...
3
votes
0answers
52 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 ...
3
votes
1answer
46 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
votes
1answer
70 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
vote
0answers
43 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
votes
0answers
27 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
vote
2answers
110 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? ...
1
vote
0answers
54 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
vote
1answer
32 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, ...

1
2 3 4 5
8