Questions tagged [measurement]

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

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How do I get correct measurement probabilities in ZX calculus?

I'm learning ZX-calculus, but I'm getting confused when trying to obtain some simple results to compute probabilities for different outcomes. Here's a simple example where I'm getting lost. Here, <...
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3 votes
2 answers
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Projective measurement operation in Qiskit

I would like to implement the operation $\pi = \begin{bmatrix} 1 & 0 \\ 0 & 0 \end{bmatrix}$ on qiskit but I don't know how to do that. If I use the reset ...
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Is there an alternative algorithm to extract a probability of states of qubit after measuring?

Let a simple quantum circuit consist of one qubit and one classical bit. Initially, a qubit has the $|0\rangle$-state and then goes through some sequence of quantum gates, see the circuit below. The ...
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Encoded Fusion Based Ring Resource State

In the article on Fusion Based Quantum Computing, they presented that a fusion of 4qubits encoded states, is creating an encoded ring resource state. My question is - when we make fusion (Type 2) to 2 ...
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qiskit : how to measure multiple pauli strings

This seems like a basic operation, but I can't see how it's done in qiskit. The solution here Measuring tensor products of Pauli operators doesn't work anymore. I get an error "qiskit has no ...
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1 vote
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Formal measurement of the probability of an outcome of a Qubit in the hadamard base

I am fairly new to Quantum Computing and have a question which might be trivial for all of you, but I am really struggling with it. From Quantum Computation and Quantum Information I have learned, ...
1 vote
1 answer
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Is a generalized 2D cluster state still a universal resource?

Let $G = (V, E)$ be a $\sqrt{n} \times \sqrt{n}$ grid graph. Consider preparing a 2D cluster state as follows. $$|\psi_{\mathsf{C}}\rangle = \underset{(i, j) \in E}{\Pi} (\mathsf{CZ})_{i, j} | + \...
4 votes
1 answer
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Is the post-measurement state always pure after a partial measurement?

Imagine I have two potentially entangled qudits and measure the first one using some Hermitian operator $M$ that has only one eigenstate per eigenvalue and get some outcome $m$. Can I know for sure ...
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How can you extract all the state probabilities in e.g. Grover's search?

In the Qiskit tutorial for e.g. Grover's algortihm, there is a 3-qubit implementation on a real quantum computer https://qiskit.org/textbook/ch-algorithms/grover.html#3.1.2-Experiment-with-Real-...
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How can one impliment Bennett's partial measurement onto a binomial subspace for state distillation?

I'm reading the seminal paper on entanglement distillation by Bennett et. al. The idea is that Alice and Bob have $n$ identical copies of an imperfect (but pure) Bell state. The initial state is ...
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1 vote
1 answer
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Going from projective measurement to unitiary operators for qiskit

I have a solution to the Peres-Mermin magic squares game (Wikipedia quantum pseudo-telepathy) I simulate the six measurements using projective (non-unitary) measurement operators like in Nielson and ...
5 votes
1 answer
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If $[M,N]=0$, is the probability distribution obtained measuring $M$ after $N$ the same as the one obtained measuring $N$?

Let $|\psi\rangle$ be a fixed state and $M$ and $N$ two commuting operators corresponding to projective measurements. Consider the probability distribution $p$ obtained by measuring $N$ on $|\psi\...
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1 answer
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How to compute projective probabilities of a given measurement outcome using Stim?

I am looking to calculate the projective probabilities for each measurement outcome in a Clifford circuit and then output its corresponding tableau state. I am performing the measurement in the Z ...
1 vote
3 answers
171 views

CNOT entangling a third qubit and how measurement impacts entanglement

I'm trying to understand entanglement, superposition and the effects of measurement on entangled qubits a bit better. About entanglement: I know that the circuit below will entangle the two qubits: ...
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Measuring qubits vs measuring operators

I'm having trouble unifying these two ideas. When I read examples using, say, qiskit, it's typical to measure a qubit, so that to find the probability of measuring a state $|\psi \rangle$ in the state ...
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Exact Probabilities of Outcomes for Clifford Circuits with Mid-Circuit Measurements Using Stim

I am trying to find the exact probabilities of specific measurement outcomes for Clifford circuits with mid-circuit measurements. Essentially, I am looking for a function that takes an arbitrary ...
4 votes
1 answer
91 views

Swap test vs measurement in a specific basis

I have two states $|\psi\rangle$ and $|\phi\rangle$. The swap test allows to estimate $|\langle \psi | \phi \rangle|^2$ by using the controlled SWAP gate and a couple of Hadamard gates. To obtain the ...
3 votes
1 answer
186 views

What is the most general way to describe post-measurement states?

Background Generally speaking, the description of post-measurement states associated with a POVM seems to always pass through, in some form or another, the formalism of Kraus operators. For example: ...
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4 votes
1 answer
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Given a state $\rho$ and operator $0\le \Lambda\le I$, what does $\sqrt\Lambda \rho \sqrt\Lambda$ represent?

An expression that is found in a good number of results is $\sqrt\Lambda\rho\sqrt\Lambda$, for some pair of positive semidefinite operators $\rho,\Lambda\ge0$. For example, in the gentle operator ...
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Frequency of VNA for resonator and Qubit measurements

why is it that most researchers use a VNA with a much higher frequency range (typically 26.5 GHz) than the frequency of the resonates or Qubit, which is usually around 4-6 GHz. As VNAs get much more ...
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1 vote
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How does interference help to bias the measurement of a qubit towards a desired state?

I just read that : A fundamental idea in quantum computing is to control the probability a system of qubits collapses into particular measurement states. Quantum interference, a byproduct of ...
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2 answers
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Why after breaking the entanglement does the phase disk in the second qbit not match the result?

I am new in IBM composer quantum and I have a doubt. I have the next circuit After reinitializing q0 and reading it. (breaking entanglement) The phase disk for qubit q1 says that 100% is 0, but the ...
0 votes
1 answer
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In a state $\alpha \vert HL \rangle + \beta \vert VR \rangle$ can a particle be measured in the $\{|L\rangle,|R\rangle\}$ basis?

Given a pair of entangled particles: $\alpha \vert HL \rangle + \beta \vert VR \rangle$ where: $\alpha^2 + \beta^2=1$ $H$ and $V$ are orthonormal vectors. $L$ and $R$ are orthogonal vectors (but not ...
1 vote
2 answers
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What projective measurement discriminates between a set of pairwise orthogonal states?

If we know a set of $K$ states $\{\lvert\psi_j\rangle:j\in[K]\}$ such that they are pairwise orthogonal, and we are given an unknown state $\lvert\psi_i\rangle$, what sort of projective measurement ...
0 votes
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Finding the Exact Probability Distribution for the Outcomes of a Quantum Circuit with Mid-Circuit Measurements

I would like to find the exact probabilities of the possible outcomes of a circuit that includes mid-circuit measurements. So, as a specific example, consider the following circuit: I would like to ...
2 votes
1 answer
60 views

Quantum instrument vs POVM

In the Wikipedia article https://en.wikipedia.org/wiki/Measurement_in_quantum_mechanics#Generalized_measurement_(POVM) They say that the Kraus decomposition of the POVM operators is needed to express ...
1 vote
1 answer
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Is measurement of $M\otimes I$ equivalent to measurement of $M$ on first subsystem?

Let $\rho$ be a state in $H_A\otimes H_B$ and $\rho_A$ its reduced state on $H_A$ (obtained by tracing out $H_B$). Is the probability distribution corresponding to the observable $M\otimes I$ on $\rho$...
0 votes
1 answer
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Question about proof that non-orthogonal states can't be reliably distinguished in QCQI

$$ \newcommand{\ket}[1]{\left|#1\right\rangle} \newcommand{\bra}[1]{\left\langle#1\right|} $$ The beginning portion of Box 2.3 on page 87 of QCQI is as follows: "Suppose such a measurement is ...
1 vote
1 answer
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qml.probs with another computational basis state

I am working with pennyLane library in Python and I have a circuit that involves several operations to 10 qubits. I want to measure the occupation probability of a target state. The function qml.probs(...
2 votes
1 answer
137 views

Understanding Paddle Quantum's MBQC simulation

Paddle Quantum have a toolkit for simulating measurement-based QC patterns in Python, and I'm having a hard time understanding how this works. For example, the following code snippet considers the ...
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How to understand Tensor observables and Combined measurements from the perspective of quantum mechanics?

This doubt comes from https://pennylane.readthedocs.io/en/stable/introduction/measurements.html pennylane mentioned two measurements, I can't tell the difference between the two. Such as $H=0.5Z+1Y$...
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Alternative measurements cost

Most of QKD protocols depends on performing measurements on different basis: Some performs the measurements on two basis (standard basis (Z) and the Hadamard basis (X)). some performs the ...
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2 answers
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Qiskit - How to get statevector for each shot?

I have a simple circuit which I run for 10 shots: ...
0 votes
1 answer
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Why does having two classical registers sometimes only yeild one bit?

I was running some qiskit code on qasm_simulator to test something and I realized that, when I have two separate classical registers, sometimes only one bit is generated, and I'm trying to understand ...
2 votes
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Distinguishing $n$ pure states in an $n$ dimensional Hilbert space

Suppose we have $n$ pure states in an $n$ dimensional Hilbert space, and we would like to distinguish them using POVM or PVM. We get any one of the pure states with equal probability, and we may set ...
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2 votes
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Calculating the probability of a result after measurement using Ry, Rz, and Rx matrices

Broadly: I have noticed on the qiskit developer (assessment) exam there are many questions asking to calculate the probability after measurement however I generally have no idea how to do this without ...
1 vote
1 answer
81 views

Get probabilistic state of a quantum circuit using Ry gate

Starting with a 2 qubit (each initialized as $|00\rangle$) I need to apply an $R_y(\theta)$ gate to get the following probabilistics: 24% $|00\rangle$ 56% $|01\rangle$ 6% $|10\rangle$ 14% $|11\...
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4 votes
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In what contexts are different notations used for indicating measurement outcomes?

I have seen a few different notations for denoting measurement outcomes. Does anyone know of which notation is more widely used in various contexts? For instance, I like referring to this Wikipedia ...
1 vote
1 answer
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Is quantum non-demolition measurement necessary for quantum computation?

Most quantum computing algorithms are based on probability distriubtion measurement and it requires a lot of iteration of the experiment; for example, when dealing with 2 qubits in an experiment, the ...
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Ion trap computational basis measurement

I'm studying the ion trap quantum computation and I'm wondering if a certain computational basis measurement, for example $|0\rangle$ state measurement, is possible in ion trap. The fig.3 and 4 in the ...
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2 votes
1 answer
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Readout Error in Qiskit: What is a reasonable model?

The Readout Error in Qiskit is described here: https://qiskit.org/documentation/stubs/qiskit.providers.aer.noise.ReadoutError.html Although it is easy to obtain such an error for 1-qubit for IBMs ...
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Expected Minimum Clique Coverage?

I'm curious if there is literature on this and, if there is, where to find it. Here I'm using ``clique" to mean a set of observables which all commute with each other. I also include the identity ...
1 vote
1 answer
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Conditional measurement using classical bit in qiskit

I am trying to implement Figure 6 in Implementing a distance-based classifier with a quantum interference circuit by Schuld et. al The specific part that I'm struggling with is the controlled (on |0&...
3 votes
2 answers
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Is a "Bell measurement" equivalent to a projective measurement in a different basis?

Let \begin{align} H = \frac{1}{\sqrt{2}}\begin{bmatrix} 1 & 1 \\ 1 & -1\end{bmatrix}\in M_2(\mathbb C), \quad \mathrm{CNOT} = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 &...
2 votes
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What does distinguishability mean in this case?

In a lecture, we were given the following example to explain the operational significance of the trace distance. Suppose that Alice prepares one of two (known) states $\rho_0$ or $\rho_1$ with equal ...
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How to interpret the measurement $\mu$ giving a fidelity equal to the Bhattacharyya coefficient: ${\rm F}(P,Q)={\rm B}(P,Q|\mu)$?

(Bhattacharyya coefficient vs state fidelity) Given two vectors $u,v$ with nonnegative entries, their Bhattacharyya coefficient is $$\mathrm B(u,v)\equiv \sum_a \sqrt{u_a v_a}.$$ Given two positive ...
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2 votes
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Measurement Base of Fusion Gate

I am reading this article on "Fusion-based quantum computation" and they claim there about Fusion Gate type-2 that it collapses the state to 2 types of eigenstates, and returns 2 results - $...
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1 vote
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What's a circuit to compute the expectation value of an observable?

Apologies if the question is naive. I want to compute the expectation value of some operator for a particular model. It seems I can do that with Hadamard test. I have the circuit for the ground state ...
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What's the structure of the measurement $\mu$ that optimally discriminates an ensemble $\{(p_i,\rho_i)\}_i$?

As discussed e.g. in this post, given two states $\rho$ and $\sigma$, the measurement that allows to optimally discriminate between them (i.e. the measurement providing the highest average probability ...
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1 vote
3 answers
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Is there a way to know if a probability amplitude is negative or positive?

I have a quantum system that outputs a state similar to: $|\psi\rangle = \frac{1}{2}(|00\rangle + |01\rangle + |10\rangle \pm |11\rangle)$. So my question is: is there a way (by measurement or by ...

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