# Tag Info

### What would be the outcome of an experiment wherein the spin of a qubit is measured in two or more orthogonal directions simultaneously?

You can't "measure a qubit in two bases at the same time". A measurement necessarily involves a collapse of the wavefunction, so "measuring in the Z basis" means forcing the state ...
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### In dispersive readout of a qubit coupled to a resonator, how is the measured phase shift used to determine the resonant frequency of the resonator?

In dispersive readout, there are two ways to readout the state of your qubit: amplitude and phase readout, see Chapter V in this great guide on superconducting qubits. In the first case, the probe ...
1 vote

### How can a quantum gate be constructed to evaluate a blackbox function (as in the Deutsch's algorithm)?

You can't feed a quantum state into a classical computer. What you can do however is implement the classical operations on a quantum computer. This can always be done efficiently by simply making all ...
• 14.8k
1 vote

### What would be the outcome of an experiment wherein the spin of a qubit is measured in two or more orthogonal directions simultaneously?

A measurement is a physical process that creates a record of some property of a physical system. Since a measurement is a physical process it is constrained by the laws of physics, which include the ...
• 8,504
Accepted

### What is the dimension considered in the Schmidt Decomposition?

It is the complex dimension. So for an orthonomal basis of $\mathbb{C}^2$, you would choose two vectors which need not be real. Actually this is the case not just for the Schmidt decomposition but ...
• 426

### What is the purpose of the Quantum Fourier Transform or what does it operation achieve?

I've checked through the answer above and it's really a good one especially for newbies! Truth be told, it's my first time to learn about other applications of Quantum Fourier Transform (QFT) rather ...
Accepted

### Joint measurability in quantum mechanics

Two observables are jointly measurable if there always exist a joint probability distribution whose marginal distributions are equal to individual observed probability distributions. This is indeed ...
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### Is there an efficient way to execute a quantum channel using its Choi state?

The answer to this question can be found in Theorem 2 of https://arxiv.org/abs/1809.04552. In general, the optimal retrieval probability of a unitary channel reads $\frac{N}{N-1+d^2}$, where $d$ is ...

### Are states partially ordered in the same way via entanglement and Bell violations?

No. A possible counterexample is given by a trivial Bell inequality $B(\rho)\equiv 0$ (thus $\tilde B(\rho)\equiv0$) and a non-trivial entanglement measure, e.g. entanglement of formation. Then, for a ...
• 20.8k

### Why we use trace-class operators and bounded operators in quantum mechanics?

The effects are not Hilbert Schmidt in general, so to identify them with HS operators would be too restrictive. However, even if density operators are just a part of the Hilbert-Schmidt operators, the ...
• 73.8k
Accepted

### Why we use trace-class operators and bounded operators in quantum mechanics?

I think Tobias Fünke has essentially answerered this question already, but to be as explicit as possible: we need the states to be trace-class so we can obtain normalized probabilities (just as in the ...
• 549
Accepted

### Different Bekenstein bound equations – what’s the difference?

They seem to differ only on the choice of units. The second version uses units with $k = 1$ and the last equation uses units with $k = \hbar = c = 1$. These sorts of unit systems are very common in ...
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1 vote

### How can the Bloch sphere, built from one complex dimension, specify 2-complex dimensional Pauli spinors?

E.Anikin's answer explains lucidly how the spinor has two degrees of freedom. A simple way to look the map between the complex plane and the Bloch sphere it is that one complex dimension is equivalent ...
Accepted

### How can the Bloch sphere, built from one complex dimension, specify 2-complex dimensional Pauli spinors?

It is probably most natural to identify the points of Bloch sphere with density matrices representing pure states of a spinor (two-level system). Arbitrary density matrix of a two-level system can be ...
• 1,011
1 vote
Accepted

### Example of a classical correlation and a quantum correlation

Quantum correlation: The one you identify is correct, let's call that |HH>+|VV> for short; H=horizontal, V=vertical. Same as your |00⟩+|11⟩, right? That state is exactly the same as |DD>+|AA&...
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### Derivation of $P$ representation of the thermal density operator
There is in fact a rather direct method to get $P,Q$, and $W$ representations of thermal states, and more generally of displaced thermal states, by reasoning in terms of the $T(\nu,s)$ operators ...