I've heard a few times recently the phrase "Information only exists in a physical state". It come from the quantum computing world where they claim quantum changes the game when it comes to representing information.
As one who has spent his career studying theoretical information that has never and never will exist in a physical state, how can we reckon with such a statement? For starters let's consider the set of all primes--how does that infinite set exist in our finite world?
Information is physical but not directly, but rather as its description. We can discuss a computational process or more generally a mathematical model that captures the set of all primes and we can and have store that description physically.
Let's consider a single prime, the recently discovered Mersenne prime \(2^{136279841}-1\). Note how we must describe the number in a very compressed format, certainly not as a collection of \(2^{136279841}-1\) ping pong balls or even \(2^{136279841}-1\) atoms, far more than the roughly \(2^{365}\) atoms in the observable universe.
In a similar fashion, a large language model stores information through its weights--not a direct encoding of the sentences it can generate.
Now let's think of quantum computing. The quantum algorithm is always classically defined. All the information in quantum states has a classical description. An entangled quantum state may require an exponentially large explicit description, but the algorithm generating it provides a short classical physical description. So if we allow information to only physically represented by its description then it's hard to argue that quantum is somehow special. There are differences to how quantum works but when we try to simplify the message, it can confuse people into thinking quantum is more powerful than it really is.
Are you saying that information does *not* only exist in a physical state? Or are you saying that, if we think of information in terms of its smallest possible representation, then it does exist only in a physical state, but those finite physical states still allow us to reason about infinitely long strings which cannot be be explicitly represented (and in that case, the quantum world is really no different)?
ReplyDeleteThis is me trying to interpret that statement "All information must exist in a physical state", not try to argue whether or not it is true, a philosophical debate I'd rather not wade into.
DeleteIn college, an astrophysicist friend of mine computed the weight of an e-mail message. He started with (average) e-mail message length, converted to entropy, then to energy, then mass.
ReplyDeleteI'm not sure how serious he was being; but it is thought-provoking that the units (sort of) make sense.
I think the point of the slogan is mostly to encourage taking seriously the encoding into a physical system in any context where one is discussing potential implementations. I'm not aware of anyone trying to use that slogan to increase quantum hype.
ReplyDeleteHere is an example.
ReplyDeleteWhen the person in this video says, “it's as if you're playing a game of chess and somebody introduces a new rule,” it’s a good point. See, for example, the square-root of NOT gate discussed in “Machines, Logic and Quantum Physics” https://arxiv.org/pdf/math/9911150.
DeleteThe abstract of the aforementioned paper answers the question in the title of this blog post extremely well. Its first sentence is: “Though the truths of logic and pure mathematics are objective and independent of any contingent facts or laws of nature, our knowledge of these truths depends entirely on our knowledge of the laws of physics.” If you agree with the arguments in the rest of the paper, then saying that information is physical is actually quite a deep statement far removed from hype.
Pure information exists outside a carrier medium. It will just resemble a sine wave. The name itself means sinus or cavity or empty space. Thus, information although typically bound, does partake of reification or the proces of “will it flush”
ReplyDeletePure information exists outside a carrier medium. It will just resemble a sine wave. The name itself means sinus or cavity or empty space. Thus, information although typically bound, does partake of reification or the proces of “will it flush”
ReplyDeleteIf P=BPP then is this statement false? 'An entangled quantum state may require an exponentially large explicit description, ..'?
ReplyDeleteThe introduction to https://arxiv.org/pdf/1405.5563 by David Deutsch and Chiara Marletto contains a good explanation of why physicists think information is physical.
ReplyDeleteAs Seth Lloyd says in one of his Nature papers, “Computers are physical systems: what they can and cannot do is dictated by the laws of physics.” This is the arXiv version of the paper: https://arxiv.org/pdf/quant-ph/9908043. There are 86 references backing up this statement.
ReplyDeleteI almost feel sorry for the physicists who limit their view of computing to the world as they know it. Computing is so much more than that.
ReplyDeleteIt’s possible to consider computing in scenarios that aren’t the world as we know it. For example, we do not know whether closed timeline curves exist in our universe but David Deutsch’s paper, “Quantum mechanics near closed timelike lines” uses the quantum theory of computation to gain insights into chronology violation.
DeleteScott Aaronson has an interesting paper called “Quantum Computing, Postselection, and Probabilistic Polynomial-Time.” He says that his “original motivation was to analyze the computational power of “fantasy” versions of quantum mechanics, and thereby gain insight into why quantum mechanics is the way it is.”