Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [measurement]

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

0
votes
1answer
69 views

Why does $|P_U − P_V |$ equal $\langle \psi |U^{\dagger} M U|\psi\rangle −\langle \psi |V^{\dagger} M V |\psi\rangle$?

In QC and QI by Chuang and Nielsen, they state that the $P_U$ of operation $U$ acting on $\psi$ can be reached by $\langle \psi |U^{\dagger} M U |\psi\rangle$. Where $P_U$ (or $P_V$) is the ...
3
votes
1answer
50 views

Do the probability amplitudes describe the probability of projective measurement?

I don't really know the difference between projective measurement and regular measurement or POVM. Until now, wherever I read about the subject I saw that the amplitude describes the probability of ...
5
votes
1answer
59 views

Where does the Xmon simulator from Googles cirq framework its entropy from?

Measurements create entropy as we all know. But computers themselves are deterministic machines. Most devices use processor heat as a source for random number generation as far as I know - which has ...
2
votes
2answers
28 views

What does simultaneous measurement of a mutually commuting set of observables mean?

If I have a mutually commuting set of observables $\{A, B, C, D,...\}$ and when we talk of simultaneous measurements of these observables, do we mean a single apparatus is required for simultaneous ...
6
votes
1answer
39 views

Do weak measurements (with/without weak values) have any application in quantum computation?

I have seen their applications in quantum state tomography but not in computation as such.
10
votes
2answers
677 views

Optimal strategy to a quantum state game

Consider the following game: I flip a fair coin, and depending on the outcome (either heads/tails), I'll give you one of the following states: $$|0\rangle \text{ or } \cos(x)|0\rangle + \sin(x)|1\...
1
vote
1answer
43 views

Measurement of a qubit and storage of the information on a bit

Suppose we have the quantum circuit below with a quantum register of 2 qubits and a classical register of 2 bits. The Hadamard gates and CNOT gate are not important for the question. When we measure a ...
5
votes
1answer
64 views

Is qubit superposition a basis-dependent concept?

The qubit $a\left|0\right>+b\left|1\right>$ is a superposition w.r.t. the basis $\left\lbrace\left|0\right>,\, \left|1\right>\right\rbrace$ because it may collapse to $\left|0\right>$ ...
2
votes
1answer
97 views

Evaluate the given quantum circuit

The input state on the qubit is $|1\rangle\otimes(2|0\rangle+|1\rangle)$. I am assuming this means that the first qubit has the state $|1\rangle$, and the second qubit has the state $2|0\rangle+|1\...
3
votes
1answer
53 views

What are some examples of measuring qubits in different basis states?

What are some examples of measuring qubits in different basis states (it's known that preferable choices are the computation basis states $|0\rangle$, $|1\rangle$ and the Bell basis states $|+\...
3
votes
1answer
40 views

What is the post measurement state given an input and the outcome measurement?

Given a two-qubit state of equal superposition, what is the post-measurement state (should be the same number of qubits that have changed as a result of the measurement) on one of the two qubits and ...
3
votes
1answer
43 views

How is postselection used in quantum tomography?

I refer to this paper but reproduce a simplified version of their argument. Apologies if I have misrepresented the argument of the paper! Alice has a classical description of a quantum state $\rho$. ...
3
votes
0answers
32 views

Why does state preparation of 'off the shelf' qubits not follow from the Born rule (Mermin)?

In Mermin's Quantum Computer Science, section 1.10 (Measurement gates and state preparation), Mermin writes that: This role of measurement gates in state preparation follows from the Born rule if ...
6
votes
3answers
111 views

Measuring qubits in QuTiP

How can you measure qubits in QuTiP? As far as I have seen you can define a Hamiltonian and let it evolve in time. It is also possible to define a quantum circuit, however, measuring and running it ...
1
vote
2answers
568 views

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 ...
2
votes
1answer
79 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, ...
2
votes
1answer
55 views

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 ...
3
votes
2answers
193 views

Are projective measurement bases always orthonormal?

Are projective measurement bases always orthonormal?
7
votes
3answers
166 views

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 ...
2
votes
1answer
50 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 ...
1
vote
1answer
84 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 ...
3
votes
1answer
107 views

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 $\rho^{AB}$: ...
2
votes
1answer
108 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 ...
3
votes
1answer
99 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-...
4
votes
3answers
78 views

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 $\frac{1}{\sqrt{2}}(\vert i \rangle + \vert j \rangle)$, ...
4
votes
1answer
163 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 ...
3
votes
3answers
118 views

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 ...
5
votes
2answers
45 views

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, ...
3
votes
1answer
61 views

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 ...
1
vote
1answer
126 views

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 ...
6
votes
1answer
170 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 ...
3
votes
1answer
98 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 ...
4
votes
1answer
65 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 ...
6
votes
1answer
70 views

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, ...
6
votes
3answers
2k views

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?
4
votes
1answer
132 views

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 ...
5
votes
2answers
93 views

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? ...
4
votes
1answer
100 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 ...
3
votes
1answer
86 views

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 ...
4
votes
3answers
91 views

Use of change of phase gates

As explained in this this answer, when we have different (relative) phases between two states, those two states will yield the same probabilities when measured in the same basis but different ...
12
votes
3answers
1k views

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 $4$ ...
7
votes
2answers
531 views

Measuring in standard basis meaning

What does it mean to measure a qubit (or multiple qubits) in standard basis?
6
votes
1answer
72 views

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 ...
5
votes
0answers
93 views

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 ...
4
votes
2answers
132 views

'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 ...
10
votes
2answers
161 views

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 ...
5
votes
1answer
65 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 ...
4
votes
2answers
131 views

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 \...
13
votes
3answers
910 views

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 ...
7
votes
2answers
175 views

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 ...