Questions tagged [measurement]

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

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2
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1answer
19 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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0answers
16 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
42 views

Measure Bell state: First qubit in $\vec{n}_1$, second in $\vec{n}_2$

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
52 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 & ...
2
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1answer
42 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
64 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 \...
3
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1answer
48 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
39 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
215 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 ...
3
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1answer
54 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
30 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 ...
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1answer
49 views

Is measuring real qubit states in a complex basis such as $|0\rangle\pm i|1\rangle$ possible?

Say I want to measure a photon in state $\dfrac{\sqrt 2}{2}|0\rangle-\dfrac{\sqrt 2}{2}|1\rangle$ in the measurement basis $[|i\rangle,|-i\rangle]$.
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1answer
69 views

In the CHSH inequality, how can I know which term is supposed to have the minus sign?

I try to follow the calculation from IBMQ experience regrading of Entanglement and Bell test which they derive the value of question as \begin{equation} C=\langle A B\rangle-\left\langle A B^{\prime}\...
1
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1answer
57 views

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
20 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....
2
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2answers
46 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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2answers
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\...
4
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1answer
37 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
252 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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1answer
92 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 ...
3
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1answer
56 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
121 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
49 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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1answer
51 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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0answers
42 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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2answers
98 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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1answer
101 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 ...
2
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1answer
49 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 ...
4
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1answer
251 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
330 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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0answers
44 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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1answer
58 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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2answers
90 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 ...
3
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1answer
63 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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0answers
117 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
45 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
122 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
82 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 \...
4
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1answer
158 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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0answers
39 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
202 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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0answers
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
237 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 \...
3
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1answer
52 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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1answer
60 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
170 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
112 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
113 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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2answers
156 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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1answer
98 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 ...