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There are examples of time evolution of quantum dynamics with history dependence, such as these quantum random walk examples which make use of a memory parameter to influence the distribution of the random walk.

I am wondering whether the rules of quantum mechanics allow the construction of a very complex quantum system such that two interacting quantum states can exchange a similar kind of memory parameter in a way such that they evolve and adapt like microbes in ecosystems

Are there examples of history dependent quantum systems that display some kind of inheritance property similar to how biological organisms can exchange their genetic material in order to evolve?

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I think the answer is (surprisingly!) no for finite systems. Quantum mechanics evolves in a unitary way, which means that information is not lost. Evolution involves a selection step where candidate individuals are evaluated and removed; one can say the process of moving information from the environment into the genome occurs by making random variations where the bad ones are erased. This is not unitary.

(In infinite systems one might just save the qubits of unwanted individuals and never erase anything)

In fact, in quantum mechanics it is not possible to make a self-replicator and it is hard to make a universal constructor. This is all surprising because we are surrounded by replicating creatures. But we are exploiting decoherence and the arrow of time: evolution and replication in some sense require the classical limit since it allows copies of states to be made and the erasure of information. One cannot run evolution in reverse.

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  • $\begingroup$ So does this fix a preferred interpretation of quantum mechanics to one that involves a non-linear wave function collapse? (As a "many worlds" style no collapse interpretation is essentially just treating the entire giant classical-style system of the whole Universe as a huge plug-in to the linear Schrodinger equation.) Does this allow us to provide a precise mathematical description (formal language not natural language) of the when-time of the collapse as opposed to "it's a measurement" (which has no precise mathematical information as to when to invoke the "random number generator call" $\endgroup$ – The_Sympathizer Mar 14 '18 at 10:10
  • $\begingroup$ of the nonlinear collapse) or at least point us to the way to do so? $\endgroup$ – The_Sympathizer Mar 14 '18 at 10:10
  • $\begingroup$ Also, regarding universal constructors - the paper says that no constructor can be made to construct an arbitrary quantum state. However is an exact copy really necessary? What happens if you allow the copy to be imperfect? Clearly the two daughter cells formed when, say, a bacterium splits, are not exact copies of each other in any mathematical sense of the term and do not need to be, much less having mathematically identical (which has probability exactly 0) quantum states. $\endgroup$ – The_Sympathizer Mar 14 '18 at 10:14
  • $\begingroup$ @The_Sympathizer - I seriously doubt this tells us anything about interpretations of quantum mechanics. Imperfect construction is where things become interesting: classical systems can be identical on the coarse-grained level, and hide the necessary differences in the quantum decoherence. $\endgroup$ – Anders Sandberg Mar 14 '18 at 20:47

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