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When is $\rho_{AB} = \rho_{A} \otimes \rho_{B}$ true?

A pure or mixed density operator of the form $$\rho = \rho_1 \otimes \rho_2 \tag{1}$$ on a bipartite Hilbert space $H=H_1 \otimes H_2$ is called a product state. Not all states are product states; ...
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2 votes

Can you measure an electrons spin in multiple ways before measuring its entangled partner?

If you start with an entangled Bell state like $\frac{1}{\sqrt2}(|{\uparrow}{\downarrow}\rangle + |{\downarrow}{\uparrow}\rangle)$, then after your first measurement along the vertical axis, the ...
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1 vote
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Do qutrits violate monogamy of entanglement?

In this example $A$ and $B$ are not entangled at all. Parties $A$ and $B$ being (maximally) entangled means that the reduced state on $\mathcal H_A\otimes\mathcal H_B$ is (maximally) entangled. In ...
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Detecting when a particle has been measured

No. If one of the particles lies outside the lightcone of the other when the measurement is performed, no information regarding the measurement can leak to that region of space-time. The idea behind ...
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1 vote
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Proof of the expression for entanglement entropy from correlation matrix

It should, of course, be cautioned that the quantum state corresponding to the correlation matrix $C$ is a Gaussian state -- for a pure state, this simply means it's a Slater determinant, but more ...
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1 vote

Proof of the expression for entanglement entropy from correlation matrix

The general strategy for non-interacting bosons or fermions in this case is as follows. First, note that the quantity you are interested (entropy) is basis independent. Thus, you can move into a basis ...
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1 vote

System with no entanglement but consuming quantum discord

(zero entanglement, zero discord): aside from the standard example of a Werner state, another very simple one is the state $\frac12(\mathbb{P}_0\otimes\mathbb{P}_0+\mathbb{P}_1\otimes\mathbb{P}_+)$ ...
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