Questions tagged [measurement]

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

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Representing a Bell measurement on non adjacent qubits

I have a state $${|\psi\rangle} = s {\Bigl(|1\rangle_1|1\rangle_2-|0\rangle_1|0\rangle_2\Bigr)}\otimes{\Bigl(|0\rangle_3|1\rangle_4-|1\rangle_3|0\rangle_4\Bigr)}\otimes{\Bigl(|0\rangle_5|1\rangle_6-|1\...
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1answer
18 views

Performing a measurement in the standard computational basis of a three qubit system on two qubits

I often see written "and then we perform measurement in the standard computational basis" but I'm a little fuzzy on what this means as it's never stated what type of measurement we're supposed to take....
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36 views

Confusion about the relation between POVMs and projective measurements

I'm a little confused about the terminology of measurement. So say that we have the single qubit state $|\phi \rangle=c_0|0\rangle+c_1|1\rangle$. If we perform the projective measurement $P_0=|0\...
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26 views

The correct set of measurement operators on a mutiple qubit system

I was wondering if the complete set of measurement operators for a state : $|\phi \rangle=c_{00}|00\rangle+c_{01}|01\rangle+c_{10}|10\rangle+c_{11}|11\rangle$ Would be given by : $P_0\otimes I=|00\...
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1answer
26 views

Implementation of filter operation

If I want to implement the measurement operation corresponding to filtering, i.e. $$ M_1=\left(\begin{array}{cc}1 & 0 \\ 0 & \alpha \end{array}\right)\qquad M_2=\left(\begin{array}{cc}0 & ...
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2answers
119 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 ...
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58 views

Measurements in Qiskit

What is the difference between 2 types of measurements depicted below? At the end of unitary evolution, qubits are in superposition of states, and after measurement I get a set of probabilites ...
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1answer
55 views

What's the probability of measuring outcomes give measurement observable $M$ and state $\rho$ when $\mathrm{Tr}\!\:(\!\!\;M\rho)$ is a complex value?

I'm studying the measurement in quantum computation. It's known that the trace is related to the expectation value and the probability of getting certain outcomes. However, when the trace is a complex ...
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1answer
111 views

given an EPR pair, how do I calculate expectation value?

given A and B share EPR pairs $ (|00⟩+|11⟩)/√2$ both are free to measure their own qubit with the following measurement settings A measures with $[ |0⟩, |1⟩ ]$ B measures with $[ sin(3π/8)|0⟩ + cos(...
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2answers
47 views

Projecting $\lvert ++ \rangle$ on Bell Basis

I understand that, projecting $\lvert 00\rangle$ on the Bell states would produce $\lvert\Phi^+\rangle$. Because, $$ CNOT(H\lvert0\rangle \otimes \lvert0\rangle) = \frac{1}{\sqrt{2}}(\lvert00\rangle +...
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46 views

$n$ qubit vs. a $d=2^n$ qudit states and measurements

The pure states of a qudit inhabit the $\mathbb{CP}(d-1)$ manifold. Is it true that the pure states of $n$ qubits live on the $\mathbb{CP}(2^n-1)$ manifold? If the answer to the first question is yes,...
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39 views

GHZ - measuring particles

I'm referring to an earlier question. It involves secret sharing based on the different measurement directions 3 people i.e Alice Bob and Charlie do. Now there is a block in the referred paper which ...
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93 views

Quantum channel representation of projective measurement

Let $P$ be a projector and $Q = I-P$ be its complement. How to find probability $p$ and unitaries $U_1, U_2$ such that for any $\rho$, $P\rho P + Q\rho Q = p U_1\rho U_1^\dagger + (1-p)U_2\rho U_2^\...
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97 views

Quantum secret Sharing using GHZ state paper

I am reading a paper on Quantum Secret Sharing Quantum Secret Sharing using GHZ states I have doubts regarding the initial phase of the paper, which are: Let me state what things I read and ...
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1answer
41 views

Measuring first qubit of Bell state

Let's consider the following Bell state: $$\lvert \Phi^+\rangle = \frac{1}{\sqrt{2}} (\lvert00\rangle + \lvert11\rangle)$$ What would happen if I measure the first qubit in the standard basis and ...
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242 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 ...
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3answers
325 views

Why is the application of an oracle function not a measurement?

Why is the application of an oracle function not a measurement, causing the collapse of the system? How can you know the state of the system (the input of the oracle function) without measurement?
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41 views

How to determine the minimum number of experiments needed to compute m-many k-local Pauli expectations?

Say I have an algorithm over N qubits and I want to find the expectation value of an operator $O$ composed of a sum of mterms, each of which is the tensor product of some number of single-qubit Pauli ...
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50 views

Does the dilation in Naimark's theorem produce a state?

A POVM, as defined for example in (Peres and Wooters 1991), is defined by a set of positive operators $\mu(a)$ satisfying $\sum_a \mu(a)=\mathbb 1$. We do not require the $\mu(a)$ to be projectors, ...
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80 views

Shor 9 qubit code — how are the observables measured and eigenvalues obtained during syndrome measurement?

Say we have the Shor 9 qubit code $$|\psi_L\rangle=\tfrac{1}{\sqrt{2^3}}((|000\rangle+|111\rangle)^{\otimes3}+(|000\rangle-|111\rangle)^{\otimes3}),$$ and we have a bit flip error. My lecture notes ...
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52 views

Deutsch-Jozsa algorithm as a generalization of Bernstein-Vazirani

It is known that both algorithms use the same gates: $H^{\oplus n}U_fH^{\oplus n}$. After the circuit, the qubits are in the state $\sum_y \left( \sum_x (-1)^{f(x)+xy} \right) |y\rangle $. In DJ's ...
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86 views

How to measure a Bell inequality violation in IBM Q?

Note: Cross-posted on Physics SE. I made some circuit to prepare a 2 qubit state, but I am having trouble understanding how to measure Bell's inequality. I know the inequality is of the form $$|E(a,...
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1answer
42 views

Interpreting results from IBM's processor vs. simulator

I am working with a circuit where I use 4 cables, and perform measurements in all of them. Nevertheless, I am only interested in the results from two cables since the other two are ancillas. When I ...
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1answer
114 views

Grover's algorithm returns skewed probability distribution

I wrote an implementation of Grover's algorithm that looks like this: ...
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1answer
68 views

Correct way of expressing a measurement in a different computational basis

Sometimes we find that the result we want from a quantum algorithm is expressed in terms of a basis that is different from the usual computational basis, which I will call $$ B_C = \left\{ \lvert 0 \...
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1answer
149 views

What is an example of a measurement that is LOCC but not separable?

Could you give me an example of a measurement which is separable but not LOCC (Local Operations Classical Communication)? Given an ensable of states $\rho^{N}$, a separable measurement on it is a POVM ...
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36 views

Measuring Ising anyons: What is a fusion measurement?

I have several doubts about measuring Ising anyons. Measurement is crucial for quantum computation and even more so for magic state distillation which is necessary to make Ising anyons universal. ...
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2answers
195 views

Why can't a quantum computer strongly simulate itself?

We can strongly simulate a quantum circuit if we can estimate the probability of measuring $|0^n\rangle$, say, at the end to within some fixed relative error. Now, by measurement, a quantum ...
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36 views

Application of improved compatibility

Note: Cross-posted on Physics SE. It's a standard piece of quantum information theory that noise can be helpful in augmenting compatibility of quantum observables. For example given a qubit state $\...
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1answer
227 views

How to complete this teleportation circuit? How to create a copy of $|\psi〉$?

This is a quantum circuit. M represents the act of making a measurement on the first two qubits. The circuit is supposed to transfer the state $|\psi\rangle = a |0\rangle + b |1\rangle$ ($a, b \in \...
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1answer
49 views

How does the actual measurement collapsing an error to an orthogonal basis look like?

An error can be written as a linear combination of $\Bbb I$, $X$, $Z$, $XZ$ Pauli matrices. So when measuring an errand state we aim at collapsing the error into one of these four possibilities. How ...
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56 views

What does it mean to perform a measurement in correspondence with different projections?

In error correction, like the bit flip, you perform a measurement which corresponds to different projections so that the outcomes can teach you about the error. What does it mean? How do you actually ...
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2answers
127 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 ...
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1answer
92 views

For CNOT gate with control qubit set to 1, the measured state of the second qubit unexpectedly depends on the measurement

I have the following circuit in qiskit. It is a simple CNOT operation with the control qubit set to 1, by running the control qubit through an X-gate. However, when I measure the 2nd qubit, I get the ...
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2answers
108 views

Why is measurement needed in teleportation?

One of the postulates of QC is, that measurements in every circuit can be postponed or never performed in a circuit while achieving the same functionality of the circuit (at least this the way I ...
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155 views

If a qubit is in $|1\rangle$ state, is it possible to prove that it is in $|1\rangle$ state?

Measuring is clearly not the answer here. Is there some trick to prove it is $|1\rangle$ state?
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97 views

Why does $|P_U − P_V |$ equal $\langle \psi |U^{\dagger} M U|\psi\rangle −\langle \psi |V^{\dagger} M V |\psi\rangle$?

In QC and QI by Chuang and Nielsen, they state that the $P_U$ of operation $U$ acting on $\psi$ can be reached by $\langle \psi |U^{\dagger} M U |\psi\rangle$. Where $P_U$ (or $P_V$) is the ...
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1answer
68 views

Do the probability amplitudes describe the probability of projective measurement?

I don't really know the difference between projective measurement and regular measurement or POVM. Until now, wherever I read about the subject I saw that the amplitude describes the probability of ...
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1answer
82 views

Where does the Xmon simulator from Googles cirq framework its entropy from?

Measurements create entropy as we all know. But computers themselves are deterministic machines. Most devices use processor heat as a source for random number generation as far as I know - which has ...
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35 views

What does simultaneous measurement of a mutually commuting set of observables mean?

If I have a mutually commuting set of observables $\{A, B, C, D,...\}$ and when we talk of simultaneous measurements of these observables, do we mean a single apparatus is required for simultaneous ...
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63 views

Do weak measurements (with/without weak values) have any application in quantum computation?

I have seen their applications in quantum state tomography but not in computation as such.
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785 views

Optimal strategy to a quantum state game

Consider the following game: I flip a fair coin, and depending on the outcome (either heads/tails), I'll give you one of the following states: $$|0\rangle \text{ or } \cos(x)|0\rangle + \sin(x)|1\...
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1answer
113 views

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 ...
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67 views

Is qubit superposition a basis-dependent concept?

The qubit $a\left|0\right>+b\left|1\right>$ is a superposition w.r.t. the basis $\left\lbrace\left|0\right>,\, \left|1\right>\right\rbrace$ because it may collapse to $\left|0\right>$ ...
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110 views

Evaluate the given quantum circuit

The input state on the qubit is $|1\rangle\otimes(2|0\rangle+|1\rangle)$. I am assuming this means that the first qubit has the state $|1\rangle$, and the second qubit has the state $2|0\rangle+|1\...
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92 views

What are some examples of measuring qubits in different basis states?

What are some examples of measuring qubits in different basis states (it's known that preferable choices are the computation basis states $|0\rangle$, $|1\rangle$ and the Bell basis states $|+\...
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1answer
45 views

What is the post measurement state given an input and the outcome measurement?

Given a two-qubit state of equal superposition, what is the post-measurement state (should be the same number of qubits that have changed as a result of the measurement) on one of the two qubits and ...
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1answer
58 views

How is postselection used in quantum tomography?

I refer to this paper but reproduce a simplified version of their argument. Apologies if I have misrepresented the argument of the paper! Alice has a classical description of a quantum state $\rho$. ...
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37 views

Why does state preparation of 'off the shelf' qubits not follow from the Born rule (Mermin)?

In Mermin's Quantum Computer Science, section 1.10 (Measurement gates and state preparation), Mermin writes that: This role of measurement gates in state preparation follows from the Born rule if ...
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323 views

Measuring qubits in QuTiP

How can you measure qubits in QuTiP? As far as I have seen you can define a Hamiltonian and let it evolve in time. It is also possible to define a quantum circuit, however, measuring and running it ...