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Questions tagged [measurement]

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

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Measuring but not looking at the result

Once a state is measured, but we don't look at the result, is the state now written as a density matrix, that is, the probability that it could land on a measurement operator multiplied by the ...
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1answer
60 views

qiskit - Is there any way to discard the results of a measurement?

I have a circuit composed by n qubits, plus a single one which is an ancilla. I'm making multiple measurements on the ancilla at different stages of the circuit, ...
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1answer
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Measuring order ancilla qubits in surface code

Recently I have been reading about surface codes a little and one thing I came acros was a specific order in which gates should be applied before the ancilla is measured. See for instance figure 2 in ...
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188 views

Are projective measurement bases always orthonormal?

Are projective measurement bases always orthonormal?
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Density matrix after measurement on density matrix

Let's say Alice wants to send Bob a $|0\rangle$ with probability .5 and $|1\rangle$ also with probability .5. So after a qubit Alice prepares leaves her lab, the system could be represented by the ...
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1answer
43 views

Convention for expressing measurement in non-standard basis

If we're measuring in common bases like $|0\rangle$, $|1\rangle$ or $|+\rangle$, $|-\rangle$ we express this by saying we're measuring with $\sigma_z$ or $\sigma_x$, or measuring in the computational ...
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1answer
68 views

How to measure in the standard basis?

I saw some related topics, but none of them give step by step instructions on measuring in standard basis (or some other basis). Could you please give such instructions? Giving an example would be ...
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1answer
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Total mutual information of a quantum system

In the discussions about quantum correlations, particularly beyond entanglement (discord, dissonance e.t.c), one can often meet two definitions of mutual information of a quantum system $\rho^{AB}$: ...
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1answer
103 views

Are the eigenvalues of an observable always -1 and 1?

What are the necessary & sufficient conditions for a matrix to be an observable, and what is the proof that any such matrix has eigenvalues -1 and 1 (if indeed that is the case)? I ask because in ...
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1answer
92 views

Quantum spin measurement

The state of a spin $\frac{1}{2}$ particle is $|0\rangle$ which is eigenstate of $\sigma_z$. What is the most generalized way to show that the results of any spin measurement along any direction in x-...
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Can one ever find the elements of a superposition state?

Given some set of basis states $\{\vert 0\rangle, \vert 1\rangle, \vert 2\rangle...\vert N\rangle\}$ and an unknown superposition of the form $\frac{1}{\sqrt{2}}(\vert i \rangle + \vert j \rangle)$, ...
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1answer
100 views

BB84 attack with entangled qubits example

BB84 attack with entangled qubits example Hi, I'am interested in an attack for BB84 protocol with entangled quibits. Lets say Alice sends a qubit $x$ in state $\left|1\right>_x$ to Bob and Eve ...
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Calculating measurement result of quantum swap circuit

Consider the following circuit, where $F_n$ swaps two n-qubit states. If the inital state is $|0\rangle \otimes |\psi\rangle \otimes |\phi\rangle = |0\rangle|\psi\rangle|\phi\rangle$, the state ...
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Fault tolerant quantum measurement: how is implemented the “majority vote”

As a fundamental component for a quantum computation, the measurement needs to be implemented in a fault tolerant way. As indicated in Chuang and Nielsen Quantum Computation and Quantum Information, ...
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1answer
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Let $\psi$ be a two-qubit state, $U \in \mathbb{C}^{2\times2}$ be a single-qubit unitary. Measure second qubit after applying U to the first qubit?

How can one show that measuring the second qubit of $\psi$ is the same as measuring the second qubit after applying $U \otimes I$ to $\psi$? I know that $\psi = \Sigma_{ij} a_{ij}|i⟩|j⟩$, $(U \otimes ...
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1answer
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How to measure in an arbitrary basis in Q#?

Q# has a measurement operator defined as follows according to the docs: operation Measure (bases : Pauli[], qubits : Qubit[]) : Result Where you give a Pauli gate ...
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1answer
154 views

Is there a classical limit to quantum computing?

Why are quantum computers scalable? With the subjects of spontaneous collapse models and decoherence in mind, it seems to me that the scalability of quantum computers is something which is not only ...
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1answer
79 views

How is measurement modelled when using the density operator?

I've just learned about the density operator, and it seems like a fantastic way to represent the branching nature of measurement as simple algebraic manipulation. Unfortunately, I can't quite figure ...
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1answer
60 views

How to calculate the off-diagonal elements of a density matrix using the measurement result?

For example, one have measured some states like $|0\rangle$ in the computational basis for many times and got the approximate probability of getting 0 and 1 ($P(0)$ and $P(1)$). Then how does he ...
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1answer
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Does the need of many quantum algorithms to be repeated several times impair the efficiency gains?

As I understand so far, in some algorithms such as Simon's algorithm, swap-test algorithm or quantum k-means algorithm, we repetitively perform a measurement yielding a classical result. Consequently, ...
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Scale for Quantum Computing [closed]

Does something like Mohs' scale exist for quantum computing? (eg. classical=0, hybrid=5, pure quantum=10) Mohs' scale: a scale of hardness used in classifying minerals. It runs from 1 to 10 using a ...
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3answers
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Reverse Quantum Computing: How to unmeasure a qunit

After taking some measure, how can a qunit be "unmeasured"? Is unmeasurement (ie reverse quantum computing) possible?
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1answer
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What are the standard eigenvalues in $\mathbb{C^2}\otimes\mathbb{C^2}$?

In $\mathbb{C^2}$, we generally take $+1$ and $-1$ as the standard eigenvalues, that's what Pauli-X, Pauli-Z measurements, etc will give us. Is there a similar standard while measuring in the Bell ...
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How to check states?

I don't know much about physics so maybe the question is stupid, but I wonder how engineers detect that the state function did not collapse due to the environment while a calculation is performed? ...
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1answer
88 views

Measuring ancillas in Shor's algorithm

When considering Shor's algorithm, we use ancilla qubits to effectively obtain the state $$\sum_x \left|x,f(x)\right>$$ for the function $f(x) = a^x \mod N$. As I have learned it, we then measure ...
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1answer
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Realization of Quantum Shadowgraphy

I recently found out about shadowgraphy and was wondering if a technique like this could be used to: Visually show entanglement Suffice as a measure (e.g. continous partial trace) Most useful ...
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How can I build a circuit to generate an equal superposition of 3 outcomes for 2 qubits?

Given a $2$ qubit-system and thus $4$ possible measurements results in the basis $\{|00\rangle$, $|01\rangle$, $|10\rangle$, $|11\rangle\}$, how can I prepare the state, where: only $3$ of these $4$ ...
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436 views

Measuring in standard basis meaning

What does it mean to measure a qubit (or multiple qubits) in standard basis?
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1answer
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Rank of a measurement

I am thinking about the following question: Assuming that we have some given state $\rho$ and we perform a measurement with $k$ outcomes on this state. Then we can describe the measurement in ...
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Projective measurements: aftermath and restoration

I have some practical difficulties with projective measurements, so I'd welcome inspiration from others. This is beyond the question "Are true Projective Measurements possible experimentally?" in that ...
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'Rectilinear' and 'Diagonal' Basis in BB84 Protocol

A lot of the tutorials on BB84 protocol talks about these two measurement bases, 'Rectilinear' or 'Vertical-Horizontal' and 'Diagonal'. I understand that it is possible to create a physical device ...
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Are true Projective Measurements possible experimentally?

I have heard various talks at my institution from experimentalists (who all happened to be working on superconducting qubits) that the textbook idea of true "Projective" measurement is not what ...
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1answer
64 views

Accessible information of system vs system, apparatus and environment

Suppose we have a quantum system $Q$ with an initial state $\rho^{(Q)}$. The measurement process will involve two additional quantum systems: an apparatus system $A$ and an environment system $E$. We ...
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What does it mean for a result of a measurement to be known/unknown?

Let me start the question with two examples. First, I am reading Nielsen & Chuang section "8.3.3 Bit flip and phase flip channels". There is a description of a quantum operation $\rho \to \...
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3answers
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What does “measurement in a certain basis” mean?

In the Wikipedia article about Bell states it is written: Independent measurements made on two qubits that are entangled in Bell states positively correlate perfectly, if each qubit is measured in ...
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Is it true that observing a quantum state will end the superposition of states? How can I not observe?

I have no background in quantum physics, and no understanding of most formulas used in this context. I'm not looking for an in depth answer, i'd just like to vaguely understand the concept. The way i ...
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2answers
979 views

Do multi-qubit measurements make a difference in quantum circuits?

Consider the unitary circuit model of quantum computation. If we need to generate entanglement between the input qubits with the circuit, it must have multi-qubit gates such as CNOT, as entanglement ...
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Does Barkhausen noise affect the measurement of magnetic particle based qubits?

Q1: I've tried to find out if Barkhausen noise affects the measurement of spin-wave excitations in magnetic particle material based qubits. I prefer implementations such as those described in "...
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Representation of real numbers in quantum computers

In classical binary computers, real numbers are often represented using the IEEE 754 standard. With quantum computers you can of course do this as well - and for measurements this (or a similar ...
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237 views

What makes quantum computations different from randomized classical computations?

One of the many thing that confuse me in the field of QC is what makes the measurement of a qubit in a quantum computer any different than just choosing at random (in a classical computer) (that's not ...
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How does measurement of one qubit affect the others?

To represent a quantum computer's state, all the qubits contribute to one state vector (this is one of the major differences between quantum and classical computing as I understand it). My ...
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609 views

If all quantum gates must be unitary, what about measurement?

All quantum operations must be unitary to allow reversibility, but what about measurement? Measurement can be represented as a matrix, and that matrix is applied to qubits, so that seems equivalent to ...