The state $(|00\rangle-|11\rangle)/\sqrt2$ is an entangled state. If we think about the state $(|11\rangle-|00\rangle)/\sqrt2$, is this also entangled, but with maybe a phase change? The above two can not be similar? Maybe, the second state is entangled but not maximally?


1 Answer 1


The kets $|\psi\rangle$ and $e^{i\theta}|\psi\rangle$ represent the same quantum state for any $|\psi\rangle$ and any phase factor $e^{i\theta}$ with $\theta\in[0,2\pi)$. No observable quantity depends on the global$^1$ phase $e^{i\theta}$ of a state.

In particular,




represent the same state. The state is maximally entangled.

$^1$ Relative phase, i.e. phase on a proper subset of kets in a sum, does have observable consequences.


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