I stumbled upon the following paper: https://inspirehep.net/record/712299 and the result derived therein, the No-Hiding theorem:

Consider now an arbitrary quantum state (mixed or potentially entangled to some external reference state) which is encoded into a larger Hilbert space through some unitary process. Suppose this encoding process completely hides the information about that state from a particular subsystem of that Hilbert space (i.e., the state of that subsystem shows no dependence on the state being being hidden). We prove that the hidden information is wholly encoded in the remainder of Hilbert space with no information stored in the correlations between the two subsystems [5]. Put differently, we prove that, unlike classical information, quantum mechanics allows only one way to completely hide an arbitrary quantum state from one of its subsystems: by moving it to its other subsystems. More importantly, we prove that this result is robust to imperfections in the hiding process.

This theorem seems to have implications for black hole evaporation, quantum teleportation and in general for thermodynamics:

the no-hiding theorem applies to any process hiding a quantum state, whether by erasure, randomization, thermalization or any other procedure.

More generally, it's a statement about the explicit conservation of quantum information. I'm surprised by the relatively low number of citations, considering the relevance of the theorem. Am I missing something? Have been the theorem disproved or weakened somehow by later results? If not, are there other implications of this theorem?


2 Answers 2


The no-hiding theorem is a fundamental result in quantum mechanics and quantum information. If you read the original paper it says that this theorem has several implications ranging from black hole information loss, quantum teleportation, to thermalisation, erasure, etc. The most important implication of this theorem is that it proves the conservation of quantum information. See for e.g. https://en.wikipedia.org/wiki/No-hiding_theorem

The no-hiding theorem has been experimentally tested also. I guess the low number of citations is nothing to do with the importance of a paper. Sometimes important papers too have low citations and often ignored completely.


In my understanding the theorem and its experimental verification show that quantum information can not be destroyed. This is not the same as saying it is conserved. It does not seem to establish that quantum information can not be created. One might appeal to a t-symmetry argument to extend it that way, but I am uncomfortable with the t-reversed experiment. Its interpretation is knotty.


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