Questions tagged [measurement]

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

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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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24 views

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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2answers
175 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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30 views

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
28 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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2answers
96 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
68 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
50 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
63 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
105 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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0answers
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 ...
3
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1answer
43 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
32 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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1answer
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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2answers
83 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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1answer
49 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
77 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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4answers
674 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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2answers
49 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. ...
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0answers
21 views

Teleportation and non-orthogonal measurement operators

Consider the simple state teleportation gadget below. Measuring the entangled state after the CZ gate in the $X$ eigenbasis (equivalent to first applying $H$ and then measuring in computational basis) ...
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2answers
30 views

The behaviour of ebits in Entanglement-assisted Quantum Error Correction Codes?

I am reading about Entanglement-assisted Quantum Error Correction Codes from Quantum Information Processing and Quantum Error Correction: An Engineering Approach (Chapter 9) . It is a scheme that ...
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1answer
76 views

ZX-calculus : measurement and output probabilities

I'm discovering ZX-Calculus, and it seems to be much easier to do computations on circuit that would take much more time with the usual formalism. However, I can't find a nice way to represent ...
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1answer
56 views

Quantum state discrimination and lower bound for conditional von Neumann entropy

Consider two quantum states $\rho_A$ and $\sigma_A$, and define the classical-quantum state over a classical binary system $B$ and $A$, $$\omega_{AB}^\epsilon :=\epsilon \vert 0 \rangle \langle 0 \...
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3answers
131 views

Unentangling a qubit from a system: can we convert $\alpha|000\rangle+\beta|111\rangle$ into $\alpha|00\rangle+\beta|11\rangle$?

Let's say I start with the following arbitrary qubits: $$ \color{red}{\vert Q_1 \rangle = \alpha_1 \vert 0 \rangle + \beta_1 \vert 1 \rangle}\\ \color{green}{\vert Q_2 \rangle = \alpha_2 \vert 0 \...
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1answer
77 views

How to compute the probability of finding a given state in the $|+\rangle$ state?

Consider the state $$ \left| \varphi \right>=\frac{i}{\sqrt{3}} \left| 0 \right> + \sqrt{\frac{2}{3}} \left| 1\right>. $$ What is the probability of qubit system when measured in the state $\...
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0answers
46 views

How to know if any two arbitrary qubits are entangled? [duplicate]

Suppose there are two quits called q1 and q2. They are in two different superposition states. If we represent their states on ...
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2answers
112 views

What is the property of any entangled pair of qubits?

We know that any of the Bell states has the special property that the second qubit will be found in a state which is predictable based on measuring one of the qubits. But assuming any other pair of ...
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1answer
56 views

Is it possible to get the $\alpha$ and $\beta$ (amplitudes) of a qubit in Qiskit?

Is it possible to get the $\alpha$ and $\beta$ (amplitudes) of a qubit in Qiskit, i.e. not only probabilities after measurement but complete quantum state?
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2answers
76 views

Problem involving entanglement swapping

I'm trying to solve a problem. I have my own approach to it, as the one in the textbook seems overly complicated. I tried using my own approach, but I'm not sure if what I found was a coincidence or ...
3
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1answer
68 views

Why are POVMs useful? Are they just an axiomatic way to define measurement?

I know the definition of projective measurement, generalized measurement, POVM. I understand the usage of generalized measurement for the reason that it can model experiments "easier" (for example ...
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2answers
33 views

Generalized measurement interpreted as entanglement unitary + measurement. Why is it indeed a unitary?

A generalized measurement can be defined as follow: It is a set of operators $\{M_m \}$ such that, given an initial quantum state $|\psi\rangle$, we have the state after measurement being: $$|\psi\...
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1answer
74 views

Qubit measurement of the state $\frac{1}{\sqrt2}|00\rangle+\frac{i}{2}|01\rangle-\frac{1}{2}|11\rangle$

If we measure the first qubit and obtain $|0\rangle$, what does the second qubit collapses to? $$ \left| \varphi \right>=\frac{1}{\sqrt{2}} \left| 00 \right> + {\frac{i}{2}} \left| 01\right> ...
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1answer
47 views

Does the energy of a qubit change when it undergoes a collapse?

Can the state of a qubit affect its energy? Please elaborate on your answer
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1answer
46 views

How are states of a qubit measured in a quantum computer? [closed]

How is a state of a qubit measured physically on a quantum computer?
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2answers
78 views

Matrix representation of a measurement

It is well known that any operation on a quantum computer is described with a unitary matrix (a quantum gate) because quantum computing is reversible. Only non-reversible operation is a measurement ...
3
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1answer
67 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 \begin{equation}\psi=\frac{1}{2}\begin{pmatrix}...
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2answers
68 views

How do qubits use the “superposition” to make many trials instead of just some?

Ok, I understand the difference between quantum bits and classical bits. But, unfortunately, all explanations on the Internet stop at this point. This is what I understand that happens: A particle ...
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3answers
79 views

Measuring in an arbitrary basis

I'm new to quantum computing, so apologize if my question seems obvious. Say we have a state $|\Psi>$ and we want to measure it in the computational basis. From what I've been able to understand ...
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2answers
354 views

Why does measuring one qubit after the other in this entangled system alter the result?

Suppose I have the following circuit where q0 and q1 are measured one after the other. The simulation results state that the state 00 occurs 75% of the time, and the state 11 occurs 25% of the time. ...
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1answer
37 views

Minimum number of ancilla qubits to unitarily simulate a measurement?

Let's say I have a ket which is a momentum eigenket $| p \rangle$ and then I measure the position and obtain $|x' \rangle$. $$ | p \rangle = \int | x \rangle \langle x | p \rangle dx \to | x' \...
3
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1answer
132 views

Quantum tomography on two qubits

I would like to do a quantum tomography on two q-bit state. Recently, I successfully did so for one q-bit based on Nielsen-Chuang. They advise to use this formula for one q-bit density operator ...
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1answer
122 views

How to measure one of the qubits in a two-qubit register?

How do I measure the first qubit of an entangled vector, say \begin{pmatrix} 1 \\ -1 \\ 0 \\ 0 \\ \end{pmatrix} is what I get on the end of Deutsch's algorithm. If I get it right, I should now ...
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2answers
132 views

Give an explicit example of a $d = 4$ SIC-POVM

For $q=e^{2 \pi i/3}$, the set of $d^2$ vectors ($d=3$) \begin{equation} \left( \begin{array}{ccc} 0 & 1 & -1 \\ 0 & 1 & -q \\ 0 & 1 & -q^2 \\ -1 & 0 & 1 \\ -q &...
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1answer
167 views

Probability of measuring the first qubit in the state $\frac{1}{\sqrt 2}(|0⟩+|1⟩)$ in a two-qubit state

If I consider $a|00\rangle + b|01\rangle +c|10\rangle +d|11\rangle$ as a valid two-qubit system, what is the probability of measuring the first qubit in state $\frac{1}{\sqrt 2}(|0⟩+|1⟩)$? I know ...
2
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1answer
58 views

Difference between unitary transformations and measurement

Say I have some qubit $|q\rangle = \alpha |0\rangle + \beta |1\rangle$. If I apply some unitary $U$, I get $U |q\rangle$; great. I can also think of $U$ as a change-of-basis matrix that maps the $|0\...
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2answers
159 views

Are three POVM measurements on a single qubit physically realizable?

In Nielsen and Chuang Quantum Computation and Quantum Information book section 2.2.6, a POVM of three elements are used to measure a single qubit in order to know for sure whether the state is $|0\...
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2answers
56 views

What does “measuring a state” mean?

I have been reading about secret sharing schemes, and they regularly come up with a line that says 'that a person upon receiving a state measures the state in one of the basis say the computational ...
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2answers
60 views

How to distinguish two states with same density matrix using a quantum state tomography?

I tried to measure quantum state with a quantum state tomography. However, I encountered a situation when two different quantum states had the same density matrix. In particular, these states were $\...
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0answers
22 views

Tensored vs ordinary measurement mitigation runtime

My experiments show that the runtime of actually applying the measurement filter matrices to circuit execution results is much slower for tensored mitigation than ordinary mitigation. Tensored ...
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0answers
112 views

Problem with measurement error mitigation using VQE

I am attempting to mitigate measurement error while running on one of IBM's real devices and am doing so by passing CompleteMeasFitter into ...