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We study the mutual coupling of chaotic lasers and observe both experimentally and in numeric simulations that there exists a regime of parameters for which two mutually coupled chaotic lasers establish isochronal synchronization, while a third laser coupled unidirectionally to one of the pair does not synchronize. We then propose a cryptographic scheme, based on the advantage of mutual coupling over unidirectional coupling, where all the parameters of the system are public knowledge. We numerically demonstrate that in such a scheme the two communicating lasers can add a message signal (compressed binary message) to the transmitted coupling signal and recover the message in both directions with high fidelity by using a mutual chaos pass filter procedure. An attacker, however, fails to recover an errorless message even if he amplifies the coupling signal.

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We have entered the Noisy Intermediate-Scale Quantum Era. A plethora of quantum processor prototypes allow evaluation of potential of the Quantum Computing paradigm in applications to pressing computational problems of the future. Growing data input rates and detector resolution foreseen in High-Energy LHC (2030s) experiments expose the often high time and/or space complexity of classical algorithms. Quantum algorithms can potentially become the lower-complexity alternatives in such cases. In this work we discuss the potential of Quantum Associative Memory (QuAM) in the context of LHC data triggering. We examine the practical limits of storage capacity, as well as store and recall errorless efficiency, from the viewpoints of the state-of-the-art IBM quantum processors and LHC real-time charged track pattern recognition requirements. We present a software prototype implementation of the QuAM protocols and analyze the topological limitations for porting the simplest QuAM instances to the public IBM 5Q and 14Q cloud-based superconducting chips.

Theoretical physicist here! I've enquired on this in r/Physics and r/math and r/AskPhysics but I'd like to get some insights of philosophers and desperately want some literature you guys can recommend into this.

I've been recently wondering about this and was hoping somebody might be able to grant me some insights into this (books/papers and the like). I've done a brief search online but haven't found too many interesting points that have tackled the issue the way I've thought about it.

Essentially, I've viewed math as kind of a fundamental truth. We establish axioms and then derive results using rigour and logic, but there's no real way to validate truth. Mathematics is basically entirely a subset of logical truth. Observations don't establish that you're right. Several proofs leading to one result don't necessitate that the result/theorem is right.

Now for a long time, I've viewed Physics as being a part of this subset. Anything fundamental like the law of conservation of energy (yes, it can be viewed as derivative of Noether's theorem but bare with me) can be established as a subset of everything that can be put in terms of mathematical machinery. In this particular case, dE/dt = 0. There's no reason for why it should be a conserved quantity beyond the fact that the universe manifests in that way. It's just a particular case of something we've observed and view as the truth.

Mathematics allows for the investigation of "other" universes where you could have other conservation laws or different geometries. So, the physical universe is one particular subset of the generalised universe (or if you'd like, a multiverse). I suppose that's what motivates this strip. This is where I've found most opinions to be centred on (or convergent).

Recently however, I've realised that the universe need not be mathematical in structure. Mathematics allows us to explore future predictions of particular events and we are indeed quite lucky to have been able to predict a lot of them using powerful mathematical machinery. But if there comes forth an observation where we can't find any mathematics to describe a physical phenomenon, then there's always definitely a possibility that there doesn't exist any logical way to describe it. Of course, as a theoretical physicist, we have hope (dare I say, faith) that we can find such mathematical machinery but there's obviously some possibility that we simply can't explain it. Perhaps there's some mathematics where we can prove that we can't explain it...? (Aside : Has there ever been any cases of this happening? Ik that there exists undecidability and incompleteness in mathematics, but have those kind of concepts been used in Physics?)

Physics imo, is simply reliant on observation and inference. These basic tenets formulate its basis in the scientific method. The scientific method cannot be wrong because it is self-correcting. In this way, theoretical physics is a subset of mathematics because it is all the physics that can be explained by mathematics, logic and observation. It has two constraints, but experimental physics is simply reliant on observation. It has no mathematical constraint whatsoever. The universe need not adhere to any logic we can understand (or not understand). It simply is.

In some ways, theoretical physics forms its basis in observational and logical truth.

Mathematics forms its basis in logical truth.

Experimental physics forms its basis in observational.

(I'd like to stress that the next few sentences aren't intended to show any kind of superiority amongst any fields. They are just my opinions and observations.)

To this end, the job of the theoretical physicist is closer to the truth because there are verifiable theories and assertions. The job of the mathematician is much harder imo because logical truth can be extremely difficult since some parts of mathematics simply have no verifiable claims. The job of the experimental physicist can be extremely counter-intuitive (and ofc difficult since the universe is not ideal) if it doesn't fit with any mathematics that we can bring forth .

The theoretical physicist has 2 clues -- Observational and logical truth. Mathematicians and experimental physicists have only one clue. Their pursuit of the truth is more difficult but in that quest, the latter two are further apart to the former.

Ultimately, I don't think all of physics is necessarily mathematics. Physics appears as the pinnacle (or the 'purest' pardon my words) of scientific observation but it isn't a subset of mathematics. Any observations taken by a physicist fall under the purview of 'truths', these have no reason to be a part of mathematics. Some can be explained and generalised but there can definitely be some which don't have to be explained using any mathematical and logical structure.

Does this make sense? What are your thoughts on it? Is there any literature on this that I could briefly touch on? I'm aware that this may appear philosophical but I haven't done a lot of philosophy (metaphysics?) so I won't get there yet.