Each period in history comes with its own paradigm of how the physical world operates. The deterministic, clockwork universe of Newton’s day has given way to the modern information-centric view of the world as a vast computer. If our reality is a computation, then we know it must be a quantum computation, and this comes with many new counterintuitive features such as superposition, entanglement, and non-locality, all of which provide novel opportunities for reality hacking.

We already know that quantum computers have transcended the limits of classical Turing machines, which our digital computers are modeled after: they can break RSA asymmetric encryption, perform ultra-fast database searches, encode information more efficiently, perform quantum teleportation, etc. When quantum computers become practical some day, it will almost certainly have a major impact on society.

Imagine a world where we could send information instantaneously across any distance, receive information from the future and effectively engineer any reality we want. The current thinking is that this is out-of-reach even for quantum processes. There are theorems that ‘prove’ it to be impossible and, of course, there is Einstein’s Special Theory of Relativity that places the speed of light as the limit on how fast physical bodies and information can move though space-time.

Nevertheless, there are still those who are not completely convinced it is impossible. After all, in the quantum computing paradigm, time is reversible—irreversibility only appears to arise after quantum systems undergo decoherence , i.e. interaction with the environment. The system as a whole is still reversible. Also, the non-locality of quantum mechanics makes it seem that nature has the ability of instantaneous information transfer but is unwilling to share it with us.

Recently I’ve been talking with Jack Sarfatti about his idea for superluminal communication. His idea is to use two coherent (Glauber) states and entangle them with a normal qubit (such as a trapped ion). Coherent states have an interesting feature of being non-orthogonal yet are still distinguishable, among others. Two communicating parties, conventionally known as Alice and Bob, may be able to use this scheme for superluminal communication, as the modulation of the coherent states controlled by Alice would bias Bob’s qubit state. There are a few quirks with the scheme: there is a normalization anomaly, which Jack believes is a violation of the Born probability rule and the quantum mechanical formalism produces slightly different answers depending on the exact way the calculation is performed (even across ‘equivalent’ methods). Nevertheless, all calculations do show a modulation term and this seems to indicate something interesting is going on.

Here is my calculation, which agrees with Sarfatti’s—note the Alice-controlled modulation term biasing Bob’s qubit in the final result…

The joint state of Alice and Bob is:

The density matrix is:

Due to the non-zero overlap of Alice’s coherent states

we consider the probability of Bob’s qubit collapsing onto B to have contributions from both of Alice’s coherent states:

Calculating the first term, we have:

Using the tensor-product identity

and noting the orthogonality of

we see that all terms except the first drop out and so we have:

Calculating the second term:

we see that all terms except the first drop out as previously, resulting in:

Combining terms, we get the following expression:

which, for the special case of

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