No-go theorems: when can we go there?

Question

For a field founded on probability and uncertainty, QM seems to have quite a few "rules" describing what is not possible. Are there any circumstances under which the no communication, no cloning or related no-go theorems might conceivably be experimentally violated, for instance using technology or resources not currently available? (It just seems like arguments based on existing experimental data, e.g. modification of delayed choice eraser experiments, get tantalizingly close, but still no cigar.)

(I realize this is a somewhat general, perhaps vague, question. If these types of question are not considered suitable for this forum please feel free to let me know; its my first question posted here.)

Answer 1

There are always assumptions that you can play with. For example, the no-cloning theorem says that the transformation $$|\psi~0\rangle \mapsto |\psi~\psi\rangle$$is necessarily nonunitary and can never work with QM's rules of linearity; the proof is just that the state $$A|00\rangle + B|10\rangle \mapsto A|00\rangle + B|11\rangle$$works out to be an entangled state on the right-hand side, not a product of two coherent states.

So, one assumption is that quantum mechanics is right; you're not going to be able to do much with the reverse. But another assumption is that we're trying to clone the state from A to B rather than just trying to clone the state. In fact you can clone a state in general; just perform all of the experimental procedure that generated qubit 1 on qubit 2.

Similarly, no-communication is a super-robust principle which says that given any density matrix $\rho$ describing two entangled subsystems $A$ and $B$, there is a "reduced" density matrix $\rho_A = \operatorname{Tr}_B \rho$ which describes expectations for all observables of the form $\hat O_A \otimes \hat I_B$ as $\operatorname{Tr}\hat O_A \rho_A;$ we observe that no Hamiltonian of the form $\hat I_A \otimes \hat H_B$ can modify this because it leads to a unitary operator $I_A \otimes U_B$ constructing $$\rho_A' = \operatorname{Tr}_B (I_A \otimes U_B)~\rho~(I_A \otimes U_B)^\dagger = \operatorname{Tr}_B\rho = \rho_A.$$This proves that nothing which B does fundamentally alters what A sees in isolation.

But of course you can then cheat this system by comparing their measurements, especially by ignoring some of them, at which point it really does seem like B is affecting A and sending messages and so forth. That's how the quantum eraser experiment works: there is a "coincidence counter" which quietly erases a bunch of A's contributed data and then goes, "hey, B has an effect on A, even if it has to go back in time to have that effect!"

One of the most productive sets of publications dealt with the no-go theorems about quantum cryptography: given this protocol, it is not possible to hack the system; these two have for sure a private, shared set of bits. The assumption that these publications attacked were, the quantum hardware we're using is ideal. It's not! There's fudge factors, error tolerances, undefined behavior when you blast it with a high-power laser, and with a lot of these real-world properties can make your system look 100% secure when it is compromised.

Answer 2

Similar to the special theory of relativity it all depends on your perspective. For Example Big Bang theory at a very distant and far galaxy might look like a remote explosion of 100 billion galaxies while the rest of the universe is held at a constant or even decreasing size. Since our measurements are derived from the limit of our observable instruments we see the entire universe expanding and live under a "big bang" perspective. God may see a small explosion in a remote area of his universe of unlimited galaxies, perhaps from an "Enlightened" perspective. I think thinking out of the box and taking risk will both reward and stimulate your intellect. But do the hard work as well while keeping a dynamic and open perspective. Also changing the rules of the past is what the present is for. We need to move the present forward to a better place. Choose to grow your mind to make the impossible possible.

Also perpetual motion machines may not be creating energy at all. They may be machines just using energy that has not been used before in such a way. Additonally there are probably still unknown forces and types of energy still to be discovered.

{100 billion Galaxies is an estimate of the number observable galaxies today}

Answer 3

Beating no-go theorems by engineering defects in quantum spin models

https://arxiv.org/abs/1406.7239

You might find this paper interesting

From their Conclusion Section : "There is an ongoing effort in conquering no-go theorems in quantum mechanics either by going beyond the static framework of the quantum formalism [29] or by relaxing quantum dynamical postulates like unitarity [30]. The work presented in this paper shows another path for overcoming the no-go theorems of ordered systems, while still remaining within the quantum realm, by introducing impurities or defects."