# Questions tagged [quantum-state]

Quantum systems can mathematically be described by their 'quantum state'. When the system is closed/isolated, the state is 'pure' and can be written as a sum (i.e. 'superposition') of basis vectors. When the system is a subsystem of an open system, the state is instead usually 'mixed' and cannot be written as a pure state, so has to be written as a density matrix. Consider using the density-matrix tag when relevant

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### How to describe a known quantum state using classical information?

In Nielsen and Chuang, it's said that to describe a known quantum state precisely takes an infinite amount of classical information since $|\psi\rangle$ takes values in a continuous space (from the ...
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### Unitary Transformations for States with Same Entanglement [duplicate]

$\newcommand{\Ket}{\left|#1\right>}$ I know this has been asked before in another context (How to construct local unitary transformations mapping a pure state to another with the same ...
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### How to prove that $\frac{| x_0 \rangle + | x_1 \rangle}{\sqrt{2}}$ hides one of $x_0$ or $x_1$?

I create a quantum state $| \psi \rangle = \frac{| x_0 \rangle + | x_1 \rangle}{\sqrt{2}}$ for a randomly chosen $x_0,x_1$ of 50 bits. I give this quantum state $|\psi \rangle$ to you and you return ...
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### Can quantum circuits/operations have truth tables?

In the caption for the following figure, the word "truth table" is put inside a quotation. I am wondering if this means that the truth table the caption refers to isn't exactly a real truth ...
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### Meaning of a pound sign (#) on a Bloch sphere

For the following Bloch sphere representation of a qubit, what does the highlighted symbol mean? I'm not sure if it means anything or it's just for showing that it's a sphere, not a circle.