Questions tagged [measurement]

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

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51 views

Can we characterise how correlated the expectation values associated with a pair of observables are?

Consider a state $\rho$ and two observables $P$ and $Q$. Is there a good way to characterise how correlated the associated expectation values are? Be it in terms of mutual information or something ...
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1answer
60 views

Question about quantum error correction and density matrixs

I am now studying QEC and feel confused. If I have a density matrix before the correction: The circuit is: $\rho = p^0(1-p)^3|\varphi\rangle \langle\varphi|+p^1(1-p)^2\sum_{i=1}^3X_i|\varphi\rangle \...
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What is the meaning of measuring a Bell state with Pauli operators?

There will be a certain value of getting the probability when measuring any Bell's state with Pauli operators such as observable X, Y, or Z. What is the meaning behind all this measurement? the result ...
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34 views

How to relate the result of measuring Pauli operators on Bell states with the quantum entanglement? [closed]

how to relate the result of measuring Pauli operators such as observable X and observable Y on the Bell's state with the quantum entanglement? In which way to say that there are correlated to each ...
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1answer
69 views

What are the possible results of measuring $X$ and $Z$ on the state $|01\rangle+|10\rangle$?

When calculating the probability of getting +1 on X-basis on the first qubit of Bell's state $|01\rangle+|10\rangle$, the result is 1/2 with the state after measurement |++⟩ while the probability of ...
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1answer
39 views

How to calculate the exponential of all elements in an input array using qiskit? [closed]

How can I perform an operation similar to Numpy.exp() in qiskit?
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1answer
71 views

What is the probability of finding the second qubit as $0$ in the state $|\psi\rangle=\frac1{\sqrt2}|00\rangle+\frac12|10\rangle-\frac12|11\rangle $?

Assuming two qubits start in the state: $|\psi\rangle = \frac{1}{\sqrt 2}|00\rangle + \frac{1}{2}|10\rangle- \frac{1}{2}|11\rangle $ What is the probability of measuring the second qubit as 0? And ...
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1answer
36 views

Details for implementing the measurement of a simulation

I am trying to work out how to program a simulation of a quantum computer program. I think I understand all the steps, of implementing a simulation, except the simulation of the measurement. I will ...
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3answers
124 views

What can I conclude about $\langle \phi|\pi_1\pi_2|\phi\rangle$ if $\langle \phi|\pi_i|\phi\rangle\ge e$?

If I have two projectors $\pi_1, \pi_2$ such that for some $|{\phi}\rangle$: $\langle {\phi}| \pi_1 |{\phi}\rangle \geq e$ and $\langle {\phi}| \pi_2 | {\phi}\rangle \geq e$ What can I conclude about ...
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1answer
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Probabilities of entangled state. Quantum measurement [duplicate]

I confused about how to calculate the PROBABILITIES and getting a certain result of measuring Bell's states with Pauli matrices as the operator. When you measure something, the state involved would be ...
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2answers
158 views

What is the result of measuring $\sigma_x$ on the state $|01\rangle+|10\rangle$?

I confused about how to calculate the probabilities and getting a certain result of measuring Bell's states with Pauli matrices as the operator. When you measure something, the state involved would be ...
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3answers
78 views

How to identify index $k$ when presented with a state $\vert \psi_k\rangle$ from orthonormal states $\{\vert \psi_i\rangle\}_{1\le i\le n}$?

A passage on page 86 of Quantum Computation and Quantum Information by Michael A. Nielsen & Isaac L. Chuang has been bugging me for a while, Suppose the states $\vert \psi_i\rangle$ are ...
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1answer
34 views

Cirq - Measure Density Matrix Function Getting First Element

Hello I am using measure density matrix function like that: ...
3
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2answers
60 views

Proof of the no-communication theorem

Let $A, B$ be (finite-dimensional) Hilbert spaces, and $\rho$ some mixed state of $A \otimes B$. I am trying to show that a measurement performed on the '$A$-subsystem' does not affect $\rho^B = \text{...
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1answer
70 views

Cirq-Measuring a State with Rotation Matrix

I have this state: $$p |\text{GHZ}\rangle \langle \text{GHZ}| + (1-p)\rho$$ And after creating this state I have this code lines: ...
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Can I partially collapse the wavefunction in Qiskit?

I'm trying to do something similar to this question, where I want to partially measure the system before getting the output. In particular, say I have 4 qubits. I want to measure two of them, and then ...
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1answer
34 views

Trace distance bound after partial trace

Let's say I have a pair of states among three parties Alice(A), Bob(B) and Eve(E), $\rho_{ABE}$ and $\rho_{UUE}$ where the first two parties hold uniform values U.} I know that the trace distance ...
2
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1answer
58 views

Measuring Pauli strings using generators

I am trying to find the ground state of a Hamiltonian using VQE. I have decomposed the Hamiltonian into a set of Pauli strings. To decrease the number of actual measurements that has to be done, can I ...
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1answer
47 views

Partial Measurement of Quantum Circuit in Qiskit

I want to do partial measurement of quantum circuit containing two qubits in entangled state. I want to first measure one qubit and record the result. Thereafter, record the measurement of second ...
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0answers
35 views

How to use the measurement in quantum phase estimation?

Reading the quantum phase estimation algorithm on Wikipedia, I am wondering how exactly the measurements are used to obtain the phase $\delta$. I understand that the value of phase is encoded into the ...
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1answer
33 views

Bit Flip, Seperable state and Several Question about Cirq

1)I want to use noise model for my state and bit_flip is not defined on cirq. ...
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2answers
208 views

How to compute the measurement probability in swap test?

The figure of a circuit and the state are as follows. The final state before the measurement is $|O_{out}\rangle=\frac{1}{2}|0\rangle(|\phi\rangle|\psi\rangle+|\psi\rangle|\phi\rangle)+\frac{1}{2}|1\...
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Conditional Time Evolution increases entropy?

Question Does the below calculation conclusively show the idea of conditional time evolution (if state measured is $x$ I do $y$ else I do $z$ ) increases the Von Neumann entropy? Has this already ...
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1answer
140 views

How do I efficiently implement a POVM using a fixed universal gate set and the ability to measure in the standard basis?

Let's say I am given a Hamiltonian \begin{equation} H = \sum_{i = 1}^{m} H_{i}, \end{equation} where $H$ acts on $n$-qubits, and each $H_{i}$ acts non-trivially on at most $k$ qubits. The eigenvalues ...
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1answer
59 views

How does a projective measurement distinguish between two states in a $d$-dimensional Hilbert space?

Let $\mathcal{H}$ be a $d$ -dimensional Hilbert space, and let $|\psi\rangle,|\phi\rangle \in \mathcal{H}$ be two quantum states. Show that if $|\psi\rangle$ and $|\phi\rangle$ are orthogonal, then ...
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1answer
166 views

Are perfectly LOCC-indistinguishable states necessarily identical?

Let $\rho,\sigma\in\text{L}(\mathcal{H}_{XAB})$ be given by $$ \rho = \sum_x |x\rangle\langle x|\otimes p_x\rho_x, \quad \sigma = \sum_x |x\rangle\langle x|\otimes q_x\sigma_x, $$ and consider ...
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How to make a measurement in a subspace?

I am currently reading this paper by Xin et al. (2020) in which they perform a measurement in a particular subspace. In the caption of Figure 6 (last sentence) they say " At the end of the ...
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1answer
40 views

Noise model for 3 Qubit $|GHZ \rangle$ state measurement circuit

I found this example code in Qiskit documentation. Does this code signify that it is simulating noise as per the IBM Valencia quantum chip. If yes, what kinds of noise does it simulate? I executed the ...
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1answer
49 views

Is there any difference between a quantum- and classically-controlled gate if I know my basis?

Consider an unrealistic 2-qubit plus 1 ancilla bit-flip error correction code (images generated by quirk), where I know by some means or other that an error may have happen on qubit0 (represented by ...
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1answer
48 views

Show that for any measurement operator $M_m$ there exists unitary $U_m$ such that $M_m=U_m\sqrt{E_m}$ with $E_m$ POVM

Exercise 2.63 of Nielsen & Chuang asks one to show that if a measurement is described by measurement operators $M_m$, there exists unitary $U_m$ such that $M_m = U_m \sqrt{E_m}$ where $E_m$ are ...
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1answer
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IBM Melbourne quantum computer performance and errors

What is the reason for high variation in measurement probability results of a simple 3/4 qubit measurement circuit on IBM Melbourne machine in comparison with the same circuit being run on IBM Vigo/...
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1answer
122 views

XX and YY and ZZ Hamiltonians in vqe

I'm trying to implement a vqe in cirq and I have sort of a brain knot. I have a 4 qubit chain with periodic boundary condition. So in fact a 2x2 qubit grid. Now 2 of them each are coupled. How do I ...
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44 views

Calculating outcomes of projective measurements

I'm pretty new to quantum computing, and I'm wondering how I can compute the outcome of a projective measurement of a spin along the +Z axis followed by a projective measurement along the -Z axis. I ...
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2answers
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Generate a random bit sequence of 512 bits [duplicate]

How can I generate a random bit sequence of 512 bits on IBM Q experience using 3 or 5 qubits? Putting a hadammard gate and measuring would only give me smaller bit sequence due to limitation in number ...
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1answer
65 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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2answers
56 views

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
82 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
149 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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0answers
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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
313 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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3answers
161 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
44 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 ...
2
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1answer
79 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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3answers
156 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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