Questions tagged [measurement]

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

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58 views

Reading or Unloading quantum data to classical data

I had a very basic question : Say I perform some set of operations on say N qubits (like QFT, QFT addition etc) finally I have an N qubit final state. If each qubit has something that I want to read ...
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1answer
46 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
67 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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632 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
39 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
16 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
25 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
71 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
55 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
111 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
63 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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43 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
99 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
54 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
69 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
64 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
31 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
68 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
71 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 ...
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1answer
51 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
67 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
64 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
36 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' \...
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1answer
88 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 ...
2
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1answer
113 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
121 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
143 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 ...
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1answer
54 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
130 views

POVM number of measurement

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
53 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
51 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
99 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 ...
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1answer
46 views

Existing measurement error mitigation

Does IBM compute a measurement error mitigation calibration matrix that can be accessed from its device properties or somewhere else? Or does the user have to do that every time?
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2answers
95 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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1answer
46 views

What's the difference between observing in a given direction and operating in that same direction?

So starting with an up particle: $$ \lvert \uparrow \rangle = \begin{bmatrix} 1 \\ 0 \\ \end{bmatrix} $$ My understanding is that you can measure $\lvert \uparrow \rangle$ in $X$ and have ...
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2answers
103 views

Prove that the partial trace is equivalent to measuring and discarding

I'm trying to solve the following question: "Prove that one way to compute $\mathrm Tr_B$ is to assume that someone has measured system $B$ in any orthonormal basis but does not tell you the ...
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0answers
20 views

Is manual or automated error correction more practically promising in the near term?

I'm curious if there's any consensus on this question among actual practitioners, but please feel free to close it if it's hopelessly opinion-based (since we've only taken baby steps toward the ...
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2answers
66 views

Probability of equal outcomes measuring a Bell state in the directions $\vec{n}_1,\vec{n}_2$

Take the Bell state $$\frac{1}{\sqrt{2}}\left(|00\rangle +|11\rangle\right) $$ and measure the first qubit with respect to some axis $\vec{n}_1$ on the Bloch sphere, i.e. measure the observable $$\vec{...
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2answers
99 views

Physical Interpretation of Pauli Matrices as Polarization Check

We know that the Pauli matrices are: $$\sigma_x = \begin{bmatrix}0 & 1 \\ 1 & 0\end{bmatrix}, \sigma_y = \begin{bmatrix}0 & -i \\ i & 0\end{bmatrix}, \sigma_z = \begin{bmatrix}1 & ...
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1answer
45 views

How to design a measurement that distinguishes the following pair of two-qubit states?

A source constantly produces a stream of photons in one of the following states $$|\varphi_1\rangle=\dfrac{1}{\sqrt2}(a|00\rangle+ b|01\rangle+c|10\rangle+d|11\rangle)$$ $$|\varphi_2\rangle=\dfrac{1}...
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1answer
79 views

Trace of Hermitian Operator and Operator Function

I am having trouble understanding the following step. From: $$\operatorname{trace}\left(\sum_z |z\rangle\langle z| \rho_A |z\rangle\langle z| * \log( \sum_z |z\rangle\langle z| \sum_x |\langle x|z \...
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1answer
61 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 ...
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1answer
52 views

How to decode 2-bit message from 2 entangled qubits?

I'm trying to do exercise 3 of this quantum course. Alice and Bob prepare an EPR pair in the Bell + state. They each take one qubit home. Suddenly, Alice decides she wishes to convey one of 4 ...
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1answer
283 views

Does the Copenhagen interpretation (+ “quasi-classical measuring apparatus”) allow one to bypass a derivation's objection?

Background I previously asked this question, in which I'm trying to better understand this joshphysics's derivation of an interpretation of the time-energy uncertainty principle. And the gist of ...
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1answer
68 views

Help in understanding an exercise on observable / measurement

I'm working through Quantum Computing for Computer Scientists (Yanofsky & Mannucci, 2008), and am getting a little confused about Observables. From what I understand an observable is a question ...
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1answer
33 views

What is the state after entangled qubit transfer?

Suppose Alice has 2 qubit entangled state and wants to send 1st qubit to Bob. q1) Now what is left with Alice? Both 1st and 2nd qubits or only 2nd qubit? q2) Does the overall composite quantum ...