# Tagged Questions

Quantum information is the study of the informational content of quantum states. The most common object of study is the "qubit", the information in a two-state quantum system such as spin-1/2 or photon polarization.

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### Entanglement of 3-qubit states

Given a separable 3-qubit state φ = φ0 ⊗ φ1 ⊗ φ2 with φi= ai0|0> + ai1|1>, |0>, |1> being the computational base. φ thus can be written as φ = b000|000> + b001|001> + b010|010> + b011|011> + ...
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### How can I measure the security of Quantum Key Distribution (QKD)?

QKD protocol is a technique that allow two parties to share common secret key for cryptographic purpose and defined as being secure, by definition. But I am still wondering how can we measure that QKD ...
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I'm having trouble understanding why I'm getting the wrong answer when simplifying a quantum circuit: The relevant matrices are \begin{align*} H = \frac{1}{\sqrt{2}}\left[\begin{matrix} 1 & 1 \...
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### Quantum Logic Gates

In classical computation, a bit can have the value of either 1 or 0 and one can apply a logic gate to this bit. As far as I understand, in classical computation, no matter what gate is used, the value ...
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### How to calculate fidelity of a specific quantum channel?

Let $\gamma$ be a completely trace preserving operator such that $\gamma(\rho) \to (1-\epsilon)\rho+\epsilon(|\phi\rangle \langle\phi|)$. Here $\rho$ is density matrix of two dimensional hilbert space ...
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### How do Rabi oscillations act on the relative phase of state kets

Suppose we have a system with a lower state $\left|{\downarrow}\right\rangle$ and and upper state $\left|{\uparrow}\right\rangle$, coupled by a pulsed electromagnetic field. I thought that from an ...
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### How to prove that quantum computers can't solve problems outside PSPACE quickly?

What are general methods to prove that certain complexity class is not proper superset of PSPACE class, and how to apply them in quantum case (for BQP class, for example).
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### Effect of the translation operator affected by spin?

I'm reading an introductory review on quantum walks and at some point it incorporates spin into the translation operator in a way that I don't follow. Initially it states that the translation by ...
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### Is it possible to reverse engineer quantum computer?

Case: I give you a "live" box with quantum signals going through it (while performing calculations) and which contains quantum logic gates. You don't know exact internal structure of box, but you're ...
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### What is spontaneous symmetry breaking in QUANTUM systems?

Most descriptions of spontaneous symmetry breaking, even for spontaneous symmetry breaking in quantum systems, actually only give a classical picture. According to the classical picture, spontaneous ...
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### No-Cloning and Uncertainty: Connections or Misconception

In chapter 9 of Scott Aaronson's book "Quantum Computing Since Democritus", he make interesting but peculiar claims relating the no-cloning theorem and the Heisenberg Uncertainty Principle (HUP). Here ...
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### To what extent is it true that quantum computation cannot be simulated on classical computers, and how can we prove it?

I have read several times, for example in chapter 3 of Computer-aided-design Methods for Emerging Quantum Computing Technologies by David Dov Yehuda Feinstein (PhD thesis, Southern Methodist ...
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### Can spatial coherence be maintained in fiber optic cables over time?

I am doing research with a double slit experiment, using a beam splitter and 2 lengths of fiber optic cable, whose ends brought close together form the effective double slit. I notice that the ...
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### Using open system dynamics to define a quantum state

Background The density matrix of a closed quantum system with Hilbert space $\mathscr H$ evolves according to the von Neumann equation \begin{align*} i\hbar\dot\rho=[H,\rho]. \end{align*} Given a ...
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### Meaning of the Reduced Density Operator

I am confused about what it is exactly that a reduced density operator describes. To illustrate, I came across the following seemingly paradoxical argument. Consider a bipartite system $AB$, ...
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### Are coherent states of light 'classical' or 'quantum'?

Coherent states of light, defined as $$|\alpha\rangle=e^{-\frac{|\alpha|^2}{2}}\sum_{n=0}^\infty \frac{\alpha^n}{\sqrt{n!}}|n\rangle$$ for a given complex number $\alpha$ and where $|n\rangle$ is a ...
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### Quantum computer able to compute non-computable elements? [closed]

I just recently read the journal article (below) about the Orchestrated Objective Reduction theory put forth by Roger Penrose and Stuart Hammeroff. According to this theory, the phenomenon of '...
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### Can quantum computer provide random or just pseudo-random number, or none of both? [closed]

Can quantum computer provide random or just pseudo-random number, or none of both? It's a bit confusing me, since collapse of wave function once measured.
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### Entangled qubit measurement

I came across this while reading lecture notes and I have no idea how they got the $M_0$ and $M_1$. The way I see it, the matrix $U$ is a block matrix:  \left[ \begin{array}{ c c } P &...
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### Quantum Discord and entropy

I'm trying to understand certain aspects of Quantum Discord. The idea is that a quantum system might have non-classical correlations despite it not being in an EPR-like state. So the discord is ...
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### dependence of braiding matrix element on the fusion product of anyons

In the case of Majorana fermions (MFs), one knows that if one braids MF $a$ with MF $b,$ then braiding matrix element $R^{c}_{ab}$ depends on the state $c$ which is the fusion outcome of $a$ and $b$. ...
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