# Is quasiclassicality in consistent histories the preferred basis problem in disguise?

Is quasiclassicality in consistent histories the preferred basis problem in disguise? Out of the numerous possible consistent realms in consistent histories — with no canonical choice — we're urged to choose quasiclassical realms. What exactly quasiclassical means though, isn't too clear. In fact, it's starting to seem that if you try to probe too closely what is meant by quasiclassicality, it turns out to be the same thing as the preferred basis problem in other interpretations. Quasiclassical then appears to be a codeword to hide the preferred basis problem under, hoping that no one else will notice this sleight of hand. If quasiclassicality isn't well-defined, then as Kent and Dowker pointed out long ago, a realm which is "quasiclassical" now, whatever that means, can be consistently extended into consistent realms which aren't quasiclassical either in the past or the future, and this is problematic as long as there is no hard criteria to pick out what is quasiclassical.

Consider this example: We have a quantum computer, and we start off with some initial quantum state at time $t_0$. Then, we run a simulation performing a unitary transformation U on this state, ending at time $t_1$. Suppose the quasiclassical projectors at $t_1$ are incompatible with those at $t_0$, i.e. they are not mutually consistent. Consistent histories tells us we can choose a quasiclassical realm at $t_0$ or at $t_1$, but not both simultaneously. Now, consider this scenario: We compute U, then without measuring or disturbing the computer states in any way, we fully uncompute $U^{-1}$, leaving us back with the original state at time $t_2$. Then, once again, without disturbing or observing the internal states in any way, we compute $U$ again, then $U^{-1}$, etc. continuing this sequence as long as we wish. We can now have two mutually incompatible "quasiclassical" realms: one consisting of quasiclassical projectors at even times $t_{2i}$, and the other of quasiclassical projectors at odd times $t_{2i+1}$. According to consistent histories, we always get the same outcomes for projectors at times differing by an even number of "timesteps". In other words, the probability for chains where the projectors differ after an even number of timesteps is zero. So, consistent histories says, in the even realm, the "collapsed" outcome after each even number of timesteps has to repeat itself by being the same. In the odd realm, the same thing can be said about outcomes after an odd number of timesteps. However, both realms can't be combined. Here, we have the case of two mutually incompatible quasiclassical realms. Of course, it might be argued that the internal states of a quantum computer shouldn't be considered quasiclassical, but in that case, what do you mean by quasiclassical?

What if we're currently in a quantum simulation which is programmed to fully uncompute in the future? Is there a quasiclassical realm containing coarse grained descriptions of us which would roughly match what we consider our quasiclassical experiences?

What do the other interpretations say in such a scenario? Copenhagen leaves no room for uncollapses. So, the fact that we can keep uncomputing means no collapse ever takes place, at least not until the very end of the sequence. No collapse means the internal states are never real, not until the very end, at any rate. MWI suggests we keep branching each odd timestep, and then the branches remerge coherently each even timestep, and this process occurs again and again. However, it's not clear why in the corresponding consistent histories interpretation, we ought to end up in the same branch after each odd number of timesteps. In modal interpretations in fact, we end up in a different branch after each odd number of timesteps.

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## 1 Answer

The assertions are absolutely untrue and illogical. The Consistent Histories interpretation is, as the name indicates, based on... consistent histories, not "quasi-classical variables". Consistent histories are described by a very particular "orthogonality" condition for the products of projection operator, products that define alternative histories. Nothing else is needed.

Gell-Mann and Hartle only used the term "quasi-classical variables" informally for some variables for which we have known that classical physics applied rather well – and they talked about them as litmus tests or examples of their interpretation. They're not needed in any way to define their rules of the game. The allowed "preferred bases" are derived from the consistency condition for the histories, not from some informal terms that the interpretation doesn't depend upon.

However, it is true that in general, there may be many mutually incompatible ways to construct a set of consistent histories. There is nothing logically inconsistent about this fact. The Consistent Histories interpretation is really a refinement of the Copenhagen interpretation, it defines what logical systems to make statements about the world are internally consistent and how the probabilities of legitimate propositions are computed from the dynamical quantum mechanical framework, and no other "interpretation" may even sensibly approach the questions you have asked.

The qubits describing a functional quantum computer's immediate state in the middle of a calculation are obviously not quasiclassical variables. They're as non-classical as you can get; indeed, that's the whole point of quantum computing.

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