# Questions tagged [measurement]

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

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### What is the Helstrom measurement?

I have been reading the paper Belief propagation decoding of quantum channels by passing quantum messages by Joseph Renes for decoding Classical-Quantum channels and I have crossed with the concept of ...
794 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 ...
819 views

### How to perform quantum state tomography on two qubits?

I would like to do a quantum tomography on two qubit states. Recently, I successfully did so for one qubit based on Nielsen-Chuang. They advise to use this formula for one qubit density operator ...
401 views

### What is the result of measuring $\sigma_x$ on the state $|01\rangle+|10\rangle$?

I confused about how to calculate the probabilities and getting a certain result of measuring Bell's states with Pauli matrices as the operator. When you measure something, the state involved would be ...
5k views

### How can I build a circuit to generate an equal superposition of 3 outcomes for 2 qubits?

Given a $2$ qubit-system and thus $4$ possible measurements results in the basis $\{|00\rangle$, $|01\rangle$, $|10\rangle$, $|11\rangle\}$, how can I prepare the state, where: only $3$ of these $4$ ...
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### Are true Projective Measurements possible experimentally?

I have heard various talks at my institution from experimentalists (who all happened to be working on superconducting qubits) that the textbook idea of true "Projective" measurement is not what ...
429 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 ...
296 views

### How is it possible to guess what state the qubit was in by measuring it?

Let's say that the qubit is in the state $\psi = \alpha|0\rangle+\beta|1\rangle$. We want to find out the values $\alpha$ and $\beta$. If we measure it in, say, the standard basis, then the outcome we ...
324 views

### Are there any algorithms that take measurements in an intermediate step?

As a beginner in quantum computation, I noticed that all quantum algorithms take various gates followed by measuring the qubits in the last step. Is it always the case? Are there any algorithms that ...
474 views

### How is measurement modelled when using the density operator?

I've just learned about the density operator, and it seems like a fantastic way to represent the branching nature of measurement as simple algebraic manipulation. Unfortunately, I can't quite figure ...
432 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 ...
3k views

### Measuring in standard basis meaning

What does it mean to measure a qubit (or multiple qubits) in standard basis?
183 views

### Problem with quantum tomography on two qubits

With reference to question on how to do quantum tomography on two qubits, I would like to ask you for help again. I tried to do the tomography on state \psi=\frac{1}{2}\begin{pmatrix}...
431 views

### Why does a controlled gate not constitute a measurement?

I have recently listened to a talk on quantum computing and was fascinated to learn about IBM Q Experience. Between the explanations in the User Guide and in Nielsen's book, I came to the following ...
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I recently found out about shadowgraphy and was wondering if a technique like this could be used to: Visually show entanglement Suffice as a measure (e.g. continous partial trace) Most useful ...
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### 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? ...
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### Bit Flip, Seperable state and Several Question about Cirq

1)I want to use noise model for my state and bit_flip is not defined on cirq. ...
231 views

### Trouble understanding the EPR Experiment

I fail to understand the EPR experiment. From Wikipedia: Alice now measures the spin along the z-axis. She can obtain one of two possible outcomes: +z or −z. Suppose she gets +z. Informally speaking, ...
4k views

### How to calculate an Expected Value of some operator acting on qubits?

I'm trying to implement the Variational Quantum Eigensolver in Qiskit. Suppose, I have an operator $A = \sigma_1^z\sigma_2^z$ acting on some two-qubit state $|\psi\rangle$. After a measurement I get ...
205 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 ...
2k 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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### Measuring ancillas in Shor's algorithm

When considering Shor's algorithm, we use ancilla qubits to effectively obtain the state $$\sum_x \left|x,f(x)\right>$$ for the function $f(x) = a^x \mod N$. As I have learned it, we then measure ...
855 views

### Understanding a quantum algorithm to estimate inner products

While reading the paper "Compiling basic linear algebra subroutines for quantum computers", here, in the Appendix, the author/s have included a section on quantum inner product estimation. Consider ...
942 views

### Why isn't the circuit performing a measurement in the Bell basis?

Nielsen and Chuang (on page 188 exercise 4.33) says that the circuit including CNOT and Hadamard is performing a measurement in the Bell basis. But I can't see how. The matrix representing the ...
151 views

### How can measuring a particle in a GHZ state leave behind a maximally entangled pair?

I am trying to understand the section on the Wikipedia page for GHZ states entitled "Pairwise entanglement". In this section, it is claimed that measuring the third particle in a GHZ state ...
291 views

### How to show whether two states are indistinguishable or not by measuring in a different basis?

I'm struggling with understanding a bit of basic quantum mechanics math that I was hoping someone could clarify. If I have two states such as these: $$\frac{1}{\sqrt{2}}(|0\rangle+|1\rangle)$$ and ...
102 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 ...
275 views

### What does the POVM corresponding to single-qubit state tomography look like?

Let $\rho$ be a single-qubit state. A standard way to characterise $\rho$ is to measure the expectation values of the Pauli matrices, that is, to perform projective measurements in the three mutually ...
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### Measurement of a qubit and storage of the information on a bit

Suppose we have the quantum circuit below with a quantum register of 2 qubits and a classical register of 2 bits. The Hadamard gates and CNOT gate are not important for the question. When we measure a ...