Timeline for Can a nonlinear evolution be linear at the level of reduced states?
Current License: CC BY-SA 4.0
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| Feb 15, 2023 at 13:06 | vote | accept | bb2002 | ||
| Feb 15, 2023 at 10:48 | comment | added | Norbert Schuch | @bb2002 Yes - there will always be a states $|\phi\rangle$ which will have non-zero overlap with the non-linear elements, i.e. its expectation value will be non-linear. Then you can rotate it onto |00>. | |
| Feb 15, 2023 at 10:26 | comment | added | bb2002 | For example, the two-qubit states $| \Phi^+ \rangle \langle \Phi^+|$ and $\mathbb{I}/4$ share the same reduced states. But applying $U$ mapping Bell's basis states to computational basis states, the reduced states will no longer coincide in the two scenarios. | |
| Feb 15, 2023 at 10:00 | comment | added | bb2002 | Thanks for the clear answer! I have a follow up question: consider a map of the kind you described, where the nonlinearity is hidden in the correlations but cannot be witnessed at the level of local mmts (without "sharing notes"). My intuition tells me that there always exist a global unitary which, when applied to the transformed state, shifts the nonlinearity in at least one of the reduced states. Is this true? | |
| Feb 14, 2023 at 17:12 | history | edited | Norbert Schuch | CC BY-SA 4.0 |
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| Feb 14, 2023 at 16:51 | history | answered | Norbert Schuch | CC BY-SA 4.0 |