# Questions tagged [measurement]

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

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### Does entanglement entropy follow a volume or an area law for 2D cluster states?

Consider a 2D cluster state defined on a rectangular lattice, which is universal for one way quantum computers. For a description of the state, see for example question 2 in this problem set. Now, ...
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### Universal resource for measurement based quantum computation

Consider universal resources for measurement based quantum computation, as defined here: We are now ready to formulate the following definition. A family $\Psi$ is called a universal resource for MQC ...
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### Why does measurement in computational basis result in classic probability?

I am working on a problem related to finding the limits on the joint probability distributions/correlations of three or more quantum systems who share entangled states, after measurement. I have been ...
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### What are useful abstraction levels for external quantum input/output of quantum computers?

Section "2.2.3 Quantum measurement" in Nielsen&Chuang uses very general measurement axioms: Postulate 3: Quantum measurements are described by a collection $\{M_m\}$ of measurement ...
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### Calculating measurement probabilities from a quantum circuit

Currently I'm trying to calculate the circuits I'm building and show that they work as intended. Somehow, my measurments do not, at all, represent my calculated expectancies. This is my circuit in <...
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### Measuring in qiskit collapses onto the Z-Plane. Why do any rotations other than Y matter?

We have the situation where a 50/50 split between $|1\rangle$ and $|0\rangle$. This was done using a $H$-Gate. Now, when measuring in qiskit, if my understanding is ...
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### As regards measurement how would a quantum-full-adder perform multiple additions simultaneously?

Here in this video from 15:14 Arvin Ash demonstrates a quantum-full-adder circuit, he goes on further to illustrate how it can perform multiple operations ...
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### Is there any simple mathematical proof that measurement destroys entanglement?

Is there a simple mathematical way to prove that measurement destroys entanglement? I can see that this is indeed true if I just take a specific measurement on an entangled state. What I am looking ...
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### Measurement of single qubit operator $U$ which is both Hermitian and unitary with eigenvalues $±1$

Suppose we have a single qubit operator $U$ with eigenvalues $±1$, so that $U$ is both Hermitian and unitary, so it can be regarded both as an observable and a quantum gate. Suppose we wish to measure ...
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### Are SIC-POVMs optimal for quantum state reconstruction?

Mutually unbiased bases (MUBs) are pairs of orthonormal bases $\{u_j\}_j,\{v_j\}_j\in\mathbb C^N$ such that $$|\langle u_j,v_k\rangle|= \frac{1}{\sqrt N},$$ for all $j,k=1,...,N$. These are useful for ...
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### How can we measure a quantum system when the sum of amplitudes-squared does not equal one?

How can we measure a quantum system if the sum of amplitudes-squared does not equal one? For example, if we want to measure $|a\rangle = 0.25|0\rangle + 0.25|1\rangle$, how can we measure it?
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### Can someone please explain how the syndrome bit still ends up being 0 in this quantum error correction circuit using repetition code?

I'm not too great at dealing with superpositions and applying the CNOT gate when superpositions are involved. Can you go through it in detail each gate using math/matrices etc. It's based on the ...
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### Do entangled measurements across multiple copies help in state distinguishability?

Consider two density matrices $\rho$ and $\sigma$. The task is to distinguish between these two states, given one of them --- you do not know beforehand which one. There is an optimal measurement to ...
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### Why is the complexity of $n$-qubit state tomography not upper bounded as $O(3^n)$?

Consider the task of fully determining an $n$-qubit state $\rho$ which can be written as \begin{equation}\tag{1} \rho = \sum_{p \in \{I, X, Y, Z\}^n} \text{Tr}(\rho P_{p}) P_{p} \end{equation} and ...
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### Do I need to use classical bits in measurement?

I wonder if I have to add classical bits while performing measurement for a single-qubit quantum circuit. The difference to initialize the circuit is ...
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