Questions tagged [measurement]
For questions related to measurement and its effects as relevant to quantum computation and quantum information.
631
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Measuring one qubit in an entangled pair in another basis?
Qubits are usually measured in the computational basis, but we can change the basis by a unitary $U$ to measure in the basis formed by the columns of $U$.
For example, if $| \psi \rangle = | 0 \rangle$...
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Finding the "dual" basis of an overcomplete basis for Quantum State Tomography
This question is related to this stack exchange post: What does the POVM corresponding to single-qubit state tomography look like?
From what I understand, when we are interested in reconstructing a ...
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What is the relation between number of measurements and additive error, when estimating the expectation value of an observable?
Given an unknown state $\rho$ I would like to measure it using an observable $O$. I would perform measurements using the orthogonal basis of $O$ on multiple copies of $\rho$ and my answer would ...
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How does this measurement in the Hadamard basis look like?
I am reading this paper by Mahadev. In going from (19) to (20) the author does a Hadamard measurement on two registers. I don't understand what exactly the Hadamard measurement does.
The (simplified) ...
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Can Noise in measurements lead to non-zero probability of a state that was not originally in the state vector?
Consider the following state vector
$$\frac12 (|000\rangle + |011\rangle + |101\rangle + |110\rangle)$$
Can noise in measurements lead to a non-zero possibility of measuring the state $|111\rangle$ ...
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Adding measurement circuits to the singlet state circuit and want to create single circuit
I am trying to add the measurement of Alice and bob's circuit to the singlet circuit. Actually, I am trying to build the e91 protocol. But it is giving me an error like this.
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Can transformations of qubits in quantum computing be carried out instead by transformations of the measurement instrument?
As far as I understand, transforming and maintaining states of qubit devices in quantum computers is associated with all sort of problems such as transformation errors and decoherence. At the same ...
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Double Slit Experiment
Does anyone know if is possible to run one instance of this experiment with two groups of people. One group who is able to observe while the other group is somehow not and still get the expected ...
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Possible post - measurement states for Bell state $\frac{1}{\sqrt{2}}[|00\rangle + |11\rangle]$
This is in reference to page 241 of Introduction to classical and quantum computing by Thomas.G Wong.
The author starts off with a Bell state $\frac{1}{\sqrt{2}}[|00\rangle + |11\rangle]$.
In trying ...
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How to know what eigenvalue corresponds to measurements of individual qubits in a multiqubit system?
I'm working through the book "Introduction to the Theory of Quantum Information Processing" by Bergou and Hillary, and I've encountered a scenario that I'm not sure how to approach. In ...
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What does the outcome $i$ mean when we measuring a quantum system?
The POVM element $E_{i}$ is associated with the measurement outcome $i$, such that the probability of obtaining it when making a measurement on the quantum state
$\rho$ is given by: $p(i)=tr(\rho E_i)...
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How can I simplify tensor product expressions quickly?
Suppose I have a 2-qubit system in the first Bell state, $\left| \beta_{00} \right>$. I want to make the measurement in the computational/$Z$-basis on the first qubit, say qubit $A$. That means I ...
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Isn't measurement-free quantum error correction uneconomic, i.e. requires too much overhead?
For certain quantum computing systems, measurement is an operation that takes up >90% of the total quantum error correction time. Measurement-free quantum error correction has been proposed, where ...
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What we get when measure $|0\rangle$ under computational basis?
It is said if we have been given the state $|0\rangle$, the measurement will yield $0$ with probability $1$ in Nielsen's book.
So here, the measurement will yield $0$ refers to we will get state $|0\...
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Single-shot error correction for the surface code with measurement errors
I am trying to implement a single-shot error correction for the surface code with data + measurement errors (both with prob. p), using the (build-in) BP+OSD decoder. I am mostly following these papers:...
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Trace and change of basis for measurement
Let $|\psi\rangle$ be a state vector for a quantum state that is a linear combination of $|0\rangle, |1\rangle$.
In density matrix, the state vector can be described by $\rho = |\psi\rangle\langle \...
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Does the quantum state fidelity satisfy $F(\rho ,\sigma) \le F(\mathcal{A}(\rho), \mathcal{A}(\sigma))$ if ${\cal A}$ is a process involving ancillae?
It is a well known fact that the fidelity is preserved by unitary evolution, i.e.
$$
F(\rho ,\sigma) = F(U\rho U^\dagger, U\sigma U^\dagger),
$$
for any unitary operator $U$.
However in most quantum ...
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geometric intepretation of Helstrom formula
Let's suppose Alice transmit to Bob either one of the two states:
$$|\psi_{\pm}\rangle = \cos(\theta)|H\rangle \pm \sin(\theta)|V\rangle, \quad \theta \in [-\frac{\pi}{4}, +\frac{\pi}{4}]$$
The ...
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indeterministic knowledge on unknown state using a Kraus operator
Suppose Alice transmits a qubit in either of two states $|\psi\rangle_{1}, |\psi \rangle_{2}$.
Bob has 3 Kraus operators: $\hat{E1}, \hat{E2}, \hat{E3}$ such that the average measurement value of $\...
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Motivation behind POVM and projective measurement
This is in reference to Quantum Computation and Quantum Information by Michael A. Nielsen and Isaac L. Chung [page 90, 92].
Any POVM elements $E_{m}$ are defined as $E_{m} = M_{m}^{\dagger}M_{m}$. A ...
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Can you project on an orthogonal basis for a multipartite system using only local measurements and classical communication?
Say Alice possesses one qubit, and Bob two, and that the joint state is $|\psi_{A, B_1, B_2}\rangle = \alpha|n_1\rangle + \beta |n_2\rangle$, where $|n_1\rangle$ and $|n_2\rangle$ are orthonormal ...
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Is it possible to produce an entangled state by measuring an unentangled state?
Wondering if it's possible to produce an entangled state by measuring an unentangled state. I tried a few examples, but it seems it's not possible.
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Why is 3-Coloring in PQMA(2)?
I'm reading https://arxiv.org/abs/0709.0738 about the complexity of PQMA(2) and its relation to NP. It describes a PQMA(2) protocol (3.1) for 3-coloring which contains the following check:
For both $|...
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How to compute marginal probabilities of Alice's qubit (in density operator language)?
Let $| \psi \rangle = \frac{1}{\sqrt{2}}|00\rangle + \frac{1}{2}|01\rangle + \frac{\sqrt{3}}{4} |10\rangle + \frac{1}{4}|11\rangle$ be a state vector describing a closed quantum mechanical system.
...
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What does the product of two density matrices represent physically?
A quantum state, pure or mixed, can be described by a density matrix that encodes the Bloch vector $\hat{m}$ analog of a quantum state like
$\rho = \frac{1}{2}[\mathbb{I} + \hat{m}.\vec{\sigma}]$.
Let ...
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Optimizing Selection of the Optimal Qubit in a 30-Qubit Quantum Circuit
I am working with a quantum circuit consisting of 30 qubits, and for each qubit, I have allocated a dedicated classical register to record individual measurement results. When I execute this circuit ...
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Half Adder using CNOT Gates
As per this schematic of qubits, how this explanation is correct --"If you look again at the four possible sums, you’ll notice that there is only one case for which this is 1 instead of 0: 1+1=10....
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What is qubit decoherence?
If I have understood correctly, in time a single qubit in superposition will collapse on it's own to the $|0\rangle$ or $|1\rangle$ state, but I thought it only collapsed when measured. How is the ...
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Is there a tight operator frame that is also a POVM?
We define the tight operator frame as a set of operators $\{E_i\}_{i=1}^{n}$ satisfying
\begin{equation}
\sum_{i=1}^n \vert \langle \langle E_i \vert X \rangle \rangle \vert^2 = C \Vert V \Vert_2^2, \...
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Why can we simulate any measurement involving $U=R+iQ$ using $U'=R\otimes I+Q\otimes R_x(2\pi)$ instead?
In a book named "INTRODUCTION TO QUANTUM ALGORITHMS VIA LINEAR ALGEBRA", the authors say:
For any complex $N×N$ matrix $U$, we can uniquely write $$U = R + iQ$$
Assume we have $$ U' = R \...
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How to obtain and print the data that is present in classical register after measuring the data of quantum circuit [closed]
Title: Circuit Diagram for Measurement
Give a quantum circuit diagram illustrating a basic measurement setup.
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On modelling the measurement?
Background
So I had the following heuristic idea to model a measurement. Let's say I have $2$ Hamiltonians. They are $H_{system}$ and $H_{detector}$. Now,
$\hat H = \begin{cases}
\hat H_{system}...
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How to prove the "damage lemma" for gentle measurements?
Let $\rho$ be a mixed state. For all $i \in [m]$, let $S_i$ be quantum operation, which is a two-outcome POVM measurement, and "accept" a state $\sigma$ with probability $tr(S_i(\sigma))$ ...
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How to calculate probability of measuring $|1\rangle$ after application of $R_x$ gate
I was trying to understand how to calculate
the probability of measuring $|1\rangle$ when executing the following circuit in Qiskit:
...
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How to avoid measurement in Quantum Computing?
Using Qiskit, I tried to implement "weak measurement" to avoid measurement but it looks like a hard task for my skills-set. If you have any guidance for that, kindly purpose!
Besides that, I ...
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Performing Binary Operations on Classical Bits
I am trying to prepare the n-qubits GHZ state using LOCC on Qiskit. The implementation uses the result of some mid-circuit measurements for later operations. I am now using something like
...
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How to implement projective measurement from multiple measurements?
In the following paper by Harrow et al.: https://arxiv.org/pdf/1607.03236.pdf, they want to implement a measurement operator that is the average of a set of measurement operators. On page 9, right ...
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Commute partial trace operator and measurement operator
Suppose I have a general measurement $M$ applying on n-qubit registers. So we are able to use the POVM notation, where $\sum_m M_m = I$ and $M_m = E_m^\dagger E_m$.
And I want to know the exact ...
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Unambiguous State Discrimination
I have a collection of possible states that are not necessarily orthogonal to each other -- suppose $A_1, A_2, ... A_N, B_1, B_2... B_N$. I get a new state $C$, and I want to determine whether its in ...
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States for Tight Maassen-Uffink Uncertainty Relation
I was reading this paper titled
"Entropic Uncertainty Relations and their Applications". There,at equation (47) we have the Maassen-Uffink uncertainty relation which states that for a pair ...
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Converting Qubits to +-1/2 Spin System for Expectation Value Calculation
I have a quantum system that consists of spin states with eigenvalues of +-1/2. However, in quantum computing, qubits are typically represented as states |0⟩ and |1⟩. I want to calculate the ...
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Quantum relative entropy between pre- and post-measurement states
The quantum relative entropy between the states $\rho$ and $\sigma$ is defined by
$$D(\rho||\sigma)= \textrm{tr}\Big(\rho \big(\log\rho - \log \sigma \big) \Big)\,,$$
as long as the support of $\rho$ ...
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Two-way quantum computers (like in Ising model) - are they possible? Could solve general NP problems? [closed]
Standard one-way quantum computers (1WQC) allow for e.g. Shor, Grover algorithms, however, general NP problems seem too difficult for them(?) - bringing an open question if they could be somehow ...
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How can Mid-Circuit Measurements be performed in pennylane
I am trying to understand how to do mid circuit measurements in pennylane. As an example here is a simple preperation of a bell state:
...
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How do we show that a measurement is a projective measurement
In order to show that a measurement is a projective measurement, is it sufficient to prove that the measurement operators $\{M_{m}\}$ satisfy the properties:
Hermitian: $M_{m}^{T*} = M_{m}$
...
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What does "${\cal M}_{A,\alpha}$ is a measurement operation" mean?
My question regards this paper: https://arxiv.org/abs/1909.07534
If you look at the sentence below equation 8, it says that
Ma,x is measurement operation post-selected with a measurement outcome $x$.
...
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What would be the outcome if a quantum measurement has macroscopic consequences?
Suppose there are n qubits each in the state $|+\rangle$ with equal probability of measurement as 0 and 1.
Set up a measurement of each qubit such that if we measure 1 it triggers a nuke which blows ...
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The Output of Transversal Bell Measurement in Knill's Method of Fault-Tolerant Error Correction (FTEC)
On page 26 of arXiv:quant-ph/0504218, it is written that in Knill's method of fault-tolerant error correction (FTEC), the output of the transversal bell measurement becomes $(P_m \otimes I) | \Phi_0 \...
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Why can Shor code fix arbitrary errors?
This is taken from Page 434 of Nielsen and Chuang:
To simplify the analysis, suppose noise of an arbitrary type is occurring on the first
qubit only; we’ll come back to what happens when noise is ...
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3
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Why is the error propagation by the CNOT gate considered without taking into account the state?
In the syndrome measurement circuit of a stabilizer code, I think you would consider that Pauli errors propagate through the CNOT gates. I don't understand why one usually considers the propagation of ...
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