Questions tagged [measurement]

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

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54 views

What would be measured if you measure two entangled qubits at exactly the same time?

What would be measured if you measure two entangled qubits at exactly the same time?
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Can Alice and Bob distinguish entangled state coefficients?

Suppose Alice and Bob share the quantum state $\frac{1}{\sqrt 2}(|x\rangle + (-1)^b |y\rangle)$ for some $x\neq y \in \{0,1\}^2$ and $b \in \{0,1\}$. They both do not know $x,y$, and use some ...
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What causes the random variations in the probabilities with respect to the theoretical values, in IBM and QASM simulators?

When I measure 2 and 3 qubits after putting H gate on all of them, there is a variation in probabilities of results in comparison with theoretical values (25% and 12.5%, respectively). This occurs on ...
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1answer
59 views

How can we only use 8192 shots for an experiment with 14 or more qubits?

Let's say you want to do an experiment with 14+ qubits. You apply some arbitrary unitary operator $U \in (\mathbb{C}^2)^{\otimes n} \times (\mathbb{C}^2)^{\otimes n}$ to the state $|\psi\rangle \in (...
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1answer
78 views

Circuit for VQE Expectation Value Finding

I'm looking into the circuit for the VQE, but am stumped at how we can identify the expectation value of the Pauli series. Essentially, how do we find: $$ \langle \psi | H_i | \psi \rangle $$ Given $...
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25 views

Preparing a state given access to projector

Let's say I am given access to a magical box that lets me apply a projector $|\psi\rangle \langle\psi|$, where $|\psi\rangle$ is a quantum state. I do not know anything about $|\psi\rangle$: just that ...
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1answer
85 views

How to measure in another basis

I am new to qiskit and I have to simulate a quantum circuit. I read this documentation https://qiskit.org/textbook/ch-states/single-qubit-gates.html where it is left as an exercise to the reader to ...
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136 views

Prove that Shannon and von Neumann entropies satisfy $H(P)\ge S(\rho)$ with $P$ diagonal of $\rho$

Suppose there is some $n$-qubit state $\rho$. It is well known fact that, given some orthonormal basis $U = \{|u_i\rangle\}$, if $p_i = \langle u_i| \rho |u_i \rangle$ (that is, measuring $\rho$ with $...
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1answer
41 views

Can we measure the quantum circuit sequently when using Qiskit?

In some quantum algorithms, the output of the quanutm circuit is probabilistic. For example. the measurement outcome (once) for a specific qubit "0" indicates success, which means that the ...
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1answer
50 views

How to construct a non-trivial (non-projective) POVM measurement example?

We know that generalized (POVM) measurement is defined by matrices $M_i$ which are Positive semidefinite Add up to a unit matrix, $\sum_i M_i = \mathbb{I}$ and the probability of obtaining outcome $...
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120 views

What's the observable when measuring multiple qubits in the computational basis?

In Nielsen and Chuang, Quantum computing and quantum information, the following definition is given to a projective measurement : Projective measurements are described by an observable $M$ : $$M = \...
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Gate definitions for quantum random access codes

I would like to know how the gates are defined in quantum random access codes? Consider the $2 \to 1$ code described in Lemma 3.1 of this paper. The section defines the encoding and decoding circuits. ...
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There seems to be a bias against states with more 1s, in IBM's calibration matrix generator: What are the consequences and possible solutions?

Qiskit's function CompleteMeasFitter builds a calibration matrix in this way (2 qubit case): Everything is initialized in the state $|00\rangle$, which is the ...
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1answer
33 views

Dose Quantum threshold theorem apply to IBM Quantum Experience

According to Quantum threshold theorem, error rate can be arbitrarily low. But when I use IBM Quantum Experience to measure a simple $|+\rangle$, it gives result of $|1\rangle$ with probability of 52....
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1answer
26 views

What is the matrix for measuring a superposition of general number of qubits in standard basis?

Let's say I have the state of the system of 2 qubits: $\frac{1}{\sqrt{3}}|00\rangle+\frac{2}{\sqrt{3}}|10\rangle$, and I want to measure it in the standard basis. How would I write it mathematically? ...
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2answers
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Error mitigation matrix as backend property: Are any “reliable” mitigation matrices publicly available?

Given that the error mitigation matrix (meas_fitter.filter) does not vary so much for a given backend and number of qubits, then what are the advantages and disadvantages in the determination of the ...
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Calculating bipartite state from joint probability distribution

We can calculate single qubit state by measuring it in pauli observables {$\sigma_{x},\sigma_{y},\sigma_{z}$} and then looking at its probability distribution. How to do this when we are having joint ...
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140 views

How is it possible to guess what state the qubit was in by measuring it?

Let's say that the qubit is in the state $\psi = \alpha|0\rangle+\beta|1\rangle$. We want to find out the values $\alpha$ and $\beta$. If we measure it in, say, the standard basis, then the outcome we ...
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1answer
41 views

How do I measure a single qubit in a two-qubit state?

Let us suppose that I have the state \begin{equation} \frac{1}{\sqrt2}(\alpha|0\rangle|+\rangle+\beta|1\rangle|-\rangle) \end{equation} and I choose to measure the first qubit in the basis $\{(1/\...
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Meaning behind obtaining a hermitian operator for measurement in another basis?

If $$P_{+} = |+\rangle\langle+|=\frac{1}{2}(|0\rangle\langle0|+|0\rangle\langle1|+|1\rangle\langle0| +|1\rangle\langle1|)$$ and $$P_{-} = |-\rangle\langle-|=\frac{1}{2}(|0\rangle\langle0|-|0\rangle\...
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Given a channel $\Phi(X)=\sum_k c_k(X)\sigma_k$, are there always $F_k\ge0$ such that $\Phi(X)=\sum_k \operatorname{tr}(F_k X)\sigma_k$?

Fix a finite number of states $\sigma_k$, and consider a channel of the form $$\Phi(X)=\sum_k c_{k}(X)\sigma_k.$$ For $\Phi$ to be linear and trace-preserving we must have: $$c_k(X+X') = c_k(X) + c_k(...
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What is the Kraus representation of quantum-to-classical channels?

As discussed in Watrous' book, quantum-to-classical channels are CPTP maps whose output is always fully depolarised. These can always be written as $$\Phi_\mu(X) = \sum_a \langle X,\mu(a)\rangle E_{a,...
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Is it possible to detect the phase $\pi$ or 0 for the single qubit circuit X H P?

I found an answer that shows how to detect the phase in cases like $0$, $\pi/8$, $\pi/2$, $\pi/4$ or $\pi$ for circuit to prepare state as H P, where P is a phase gate like $I$, $U1(\pi/8)$, $S$, $T$ ...
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Representing a von Neumann measurement as $[\mathcal{I} \otimes P_i] U(\rho_s \otimes \rho_a)U^{-1} [\mathcal{I} \otimes P_i]$, how do we choose $U$?

Given the state of a system as $\rho_s$ and that of the ancilla (pointer) as $\rho_a$, the Von-Neumann measurement involves entangling a system with ancilla and then performing a projective ...
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1answer
42 views

Randomness using simple parallel Hadamard circuit

I've recently tried to build a Random generator using 5 hadamard gates (shown as U2 below) measured to 5 classical bits in parallel as shown in the circuit image. I've executed this circuit for 8192 ...
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1answer
36 views

What is the representative matrix for a measurement in the Bell-state basis?

I have a few questions about measurement in Bell-state basis. In particular, if $Z = \begin{bmatrix} 1 & 0\\ 0 & -1 \end{bmatrix}$ is for a measurement on the computational basis, then what ...
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1answer
71 views

Question About How Qiskit Reset Gate Affects Other Entangled Qubits

I am trying to understand how the reset gate in Qiskit affects qubits its entangled with. Consider the following circuit with qubits $q_0$ and $q_1$: Where circuit240 takes $|0\rangle$ to $a|0\rangle ...
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99 views

How to measure the sign of quantum amplitudes

I have a quantum state on $ n $ qubits ($ 2^n $ amplitudes) for which I know the amplitudes are real numbers. I want to take the state out as a vector. I can estimate the magnitude of the amplitudes ...
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1answer
68 views

Bra-Ket Notation and Proof of a Ket Equation in Two-Party Shared-Entanglement Setting

Disclaimer: I had posted this question previously on the physics StackExchange, but received no response there. My question is two-part. First, imagine a bipartite quantum state $|\Phi \rangle_{AB}$, ...
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1answer
143 views

Are separable, orthogonal states LOCC distinguishable?

Consider two states $\sigma_0,\sigma_1\in\text{L}(\mathcal{H}_{AB})$, and suppose $\sigma_0,\sigma_1$ are separable and orthogonal. Is it possible to distinguish between $\sigma_0,\sigma_1$ through ...
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Many-photon limit of dispersive shift Hamiltionian

In the context of superconducting quantum computing measuments, consider the dispersive shift Hamiltonian: $$ H/\hbar = \omega_R a^\dagger a + \frac{1}{2} (\omega_Q + \frac{2g^2}{\Delta} a^\dagger a)\...
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36 views

Books about the measurement for Hamiltonian Energy

I am searching for articles/books about the measurement energy of Hamiltonians in adiabatic quantum computing. Do you know of any good resources?
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Can Shor's 9 Qubit Code Correct for a measurement on the first qubit?

Start with Shor's codeword for $|0 \rangle$: $|\psi\rangle = \frac{1}{\sqrt{8}}(|000\rangle + |111\rangle)\otimes(|000\rangle + |111\rangle)\otimes(|000\rangle + |111\rangle)$. Now, assume that ...
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1answer
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How many samples are required to estimate the probabilities of a state?

Suppose that we have a quantum state of the form: $$|\psi\rangle = \sqrt{p}|0\rangle + \sqrt{1-p}|1\rangle$$ In order to get an estimate of the probability of reading $|0\rangle$ or $|1\rangle$, we ...
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1answer
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Efficient diagonalisation of low-rank observables

Let $n$ be the number of qubits we're using, and let $$\mathrm H=\sum_{i=1}^T\alpha_i\mathrm U_i|0\rangle\langle0|\mathrm U_i^\dagger$$ be an $n$-qubit hermitian observable where $T=O(\mathrm{poly}(n))...
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Computing variance under the action of a unitary operator

I wish to calculate the expectation and variance for an observable on a particular qubit of a multi qubit quantum state. I'm using a quantum computing simulation library which allows me to apply ...
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Projective vs general measurements - a missing piece

This may be a very basic and common question (also discussed a lot), but strikingly enough I couldn't find the answer in the books or elsewhere. The projective measurement is given by the PVM on the ...
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Confusion about the state of a system after a measurement

I'm confused about the state of a system after a measurement. Say we have a particle $v$ in the state: $ |\psi\rangle= \sqrt{1/4} \ |0\rangle + \sqrt{3/4} \ |1\rangle $. From my understanding, if one ...
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Which entangled qubit is measured in this example?

Sorry, I am a newbie to quantum computing. I am reading an overview paper (released just a week ago) titled Advances in Quantum Deep Learning: An Overview (Garg & Ramakrishnan, 2020). I am stuck ...
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What are the two measurements per box being done in the Bell Tests in the IBM Quantum Experience “Entanglement and Bell tests” Section

I am confused as to what is being measured in the boxes in the example drawings shown on the Entanglement and Bell Tests section in the IBM Q Experience: https://quantum-computing.ibm.com/docs/guide/...
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Nielsen & Chuang Exercise 4.34 “Measuring an operator”

I need help with the exercise 4.34 from Nielsen & Chuang Book. I am supposed to get a matrix corresponding to the circuit. Thanks
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Measuring Probability of Mixed States

I am a little stuck on understanding the measurement probabilities of a 3 qubit system (QCQI q 4.41). 1)H gates are applied to both $q_1$ and $q_2$ 2) $C^{(1,2)}_3(X)$, a Toffoli, controlled by $q_1$...
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Increasing the von Neumann entropy despite the measurment?

Background Assume we have a density matrix $\rho$ of a sub-ensemble. However, we have an imperfect measuring instrument. While it does perform a measurement, we do not know exactly when it performs ...
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What is the best strategy to get an upper bound to measure $|00\cdots 0\rangle$?

You are given a quantum state$\newcommand{\bra}[1]{\left<#1\right|}\newcommand{\ket}[1]{\left|#1\right>}\newcommand{\bk}[2]{\left<#1\middle|#2\right>}\newcommand{\bke}[3]{\left<#1\...
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168 views

Why can I apply $HS^\dagger$ and then measure in the computational basis to measure $Y$?

I come from a CS background I was reading Neven and Farhi's paper ("Classification with Quantum Neural Networks on near Term Processors"), and I am trying to implement the subset parity problem using ...
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How does Teleportation based Error Correction (TEC) detect and correct loss/erasure errors?

I'm looking at papers like Demonstration of teleportation-based error correction in the IBM quantum computer (page) 10 and Role of syndrome information on a one-way quantum repeater using ...
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1answer
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Showing measurement of a Hermitian Unitary operator gives final states as eigenvectors

This is related to exercise 4.34, The operation described can be written as $(H \otimes I)C^1(U)(H \otimes I)(|0\rangle \otimes |\psi\rangle)$ I can get to the point where the state of the system is ...
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Computation and measurement of readout error in IBM quantum experience

If p(1|0) (p(0|1)) is the probability that a detector registers 1 given that the actual state is 0 (registers 0 given that the actual state is 1), I guess that the readout error should be computed as ...
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2answers
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Readout error in IBM quantum experience processor

Is there a section on the IBM website that shows information about the readout error for the devices of quantum experience? I have only seen the errors for single-qubit (U2) and CNOT gates but nothing ...
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Result of Grover on Qiskit simulator

I have executed this circuit and I don't understand why the result is $|11\rangle$ ? [q[0], q[1]] : solution register [q[2]] : ...

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