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# Questions tagged [entanglement]

For questions about the principle and application of quantum entanglement. It is a physical phenomenon which occurs when pairs or groups of particles are generated, interact, or share spatial proximity in ways such that the quantum state of each particle cannot be described independently of the state of the other(s), even when the particles are separated by a large distance—instead, a quantum state must be described for the system as a whole. (Wikipedia)

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### Why use superpositions to write states even when they are not entangled?

I am reading book "Dancing with Qubits. How quantum computing works". I had learned the rule of entangled state: when quantum state is separable(i.e. it can be written as such a tensor ...
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### Is there a relation between quantum entanglement and inclusion-exclusion principle?

If an entangled state is not simply the multiplication of each particle wave function: $$|\Psi_{ABC}\rangle \neq |\Psi_{A}\rangle|\Psi_{B}\rangle|\Psi_{C}\rangle$$ then can we apply the inclusion ...
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### What is the quantum strategy required to win the Magic Squares game

This question is about the Magic Squares game. Links here, here and link here in which two players try to win a game. It's a cooperative game - either the team wins or the team loses. It is claimed ...
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### what does the multiplication of Quantum state represent? [duplicate]

According to my understanding of QC/QM: A matrix is a function/operation which when applied on vectors, changes/rotates them. Ket and bra notation is used to denote quantum state. Question 1: ...
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### Depth circuit optimization for 6-qubits GHZ state

Standard implementation of the generalized GHZ circuit has a depth that grows linearly with the number of qubits. I am looking for an optimized version in the case of 6 qubits. Is there any?
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### Are there separable states $\rho$ with separable pure decompositions requiring $\operatorname{rank}(\rho)^2$ components?

This question is tightly related to What separable $\rho$ only admit separable pure decompositions with more than $\mathrm{rank}(\rho)$ terms?. In there, examples were given of separable states $\rho$ ...
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### does CNOT gate cause entanglement?

I have just started learning Quantum computing. Pairs of qubits that are “entangled,” which means the two members of a pair exist in a single quantum state. Changing the state of one of the qubits ...
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### What does equality of partial traces, ${\rm Tr}_1\rho={\rm Tr}_1\sigma$, say about a pair of states $\rho,\sigma$?

Let $\rho,\sigma$ be a pair of bipartite quantum states such that ${\rm Tr}_1\rho={\rm Tr}_1\sigma$. What does this tell us about $\rho,\sigma$? More precisely, is there a way to write more explicitly ...
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### Relationship between entanglement and complex vector space

In the article Quantum Algorithm Implementations for Beginners I found the following sentence Entanglement makes it possible to create a complete $2^n$ dimensional complex vector space to do our ...
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### Kind of errors on entangled states

I see on this chapter that, when noise applies to an even number of entangled qubits, such noise can be considered as operating only on half of those qubits. This is interesting, but I'm not sure if I'...
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### Why von Neumann entropy requires diagonalization and linear entropy doesn't?

The linear entropy for a state $\rho$ is defined as $S_L = 1 - Tr[\rho^2]$, while as von Neumann entropy as $S_{N} = -Tr[\rho \ln \rho]$. According to quantiki, the computation of $S_{N}$ requires ...
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In this (freely available) article, just below equation 14, it says The SWAP operator has the maximum operator entanglement entropy... The operator entanglement entropy, denoted by $E(U)$ for an ...