In Quantum Computing, there is something known as the Holevo bound - which basically says that a q-bit cannot deliver more than a bit of information into our spacetime, although it can carry more.
The question is - where is the extra information kept?
The usual answer is that the extra info lies embedded in a superimposition of entangled states, and that any accessing of the information destroys the superimposition and with it, the extra information itself.
So far, so good.
But a number of experiments make it appear as far too simple an explanation. For starters, the extra information can be shown to be carried by a single photon, and only a later actualization decision determines which part of the information becomes actualized within our spacetime (so that the above explanation would necessitate a photon superimposed with itself, which then leads to a superimposition of spacetime). In other words, a form of time travel must be allowed (the photon being then 'told' by its future state which part of the information it should carry and which part it should not even take on board.)
But in other experiments (Michael Goggin et al.), the time travel possibility is not enough to explain what is going on, and the inescapable conclusion is that the photon not only carries more info than is accessible, but more information that could be stored in simple particle superimposition states.
Where is that information?
Is it carried in a parallel universe, as David Deutsch says, and therefore inaccessible to us in this space time?
Or, as Hamlet famously put it, is there more to it than we conceptualize, and the parallel universe idea is nothing but a reflection of our tendency to think in familiar boxes, and space time itself an illusion, woven by quantum correlations which are more fundamental than spacetime itself? (Spacetime being then, in effect, a byproduct of quantum correlations, which pops up when choices are made and the other latent possibilities become thus barred from becoming realized)? If the latter view is the case, then how many Spacetimes are precipitated that way, and does this explanation then, in effect, rejoin David Deutsch's?
A qubit is a position on a circle, while a bit is only a piece of yes/no information. So the qubit is implicitely containing more information. This information can play a role in the computation process, but not in the output. I think that the parallel universe metaphor is an exageration. We also, as humans, when solving a task and giving an answer, try to clean out the information about how we came to this answer. The succession of patterns, recalls and darkness we had in our mind by finding the answer is not important for the user waiting for the answer. If we cannot clean it, then the answer is just not ready. Nobody needs the "additional information".
I cannot think of other explanation than what you wrote as "the usual answer." Qbits exist only as intermediate quantum states, and the final answer of the quantum computer should be retrieved as bits. Thus, quantum computers are not a replacement of classical computers. Quantum computers are only faster for special types of calculations where you can use the fact that you have quantum superpositions available to you at the same time, to do some kind of computational parallelism; namely for calculations of processes with many intermediate states developing into final states. (See for example https://www.youtube.com/watch?v=g_IaVepNDT4)
The development of a quantum computer is a promising challenge for work in specific areas of science. Unfortunately, there is insufficient knowledge of the quantum laws to implement this idea. But most importantly, in a variety of scientific research does not disrupt the development of ideas.
Dear Chris,
It's interesting, what type of investigations do you perform, why you need such definitions? Because if one would simulate quantum computations on usual architecture, it could be noted that O(2^n) bits are needed to hold all hidden information about quantum state for n qbits. So if the structure of our space (or spacetime) is such that we can analogously perform the computations with hidden O(2^n) bits without fundamental possibility of getting all this temporary information, one just need to use this roperty of quantum object.
The information content that can be extracted from a classical bit has completely different meaning than that could be from a quantum bit. This stems from the Measurement postulate of quantum mechanics. How much information can be extracted from a quantum bit rely on how many measurement settings can be used to extract the same bit of information. If there is only one then it is a single classical bit and if there are many then it has quantum features added to it. Information in quantum world always comes with the overhead of huge statistics that goes into the measurement process as the choice of measurement itself is a random variable, and hence comparing it to classical information can be quite tricky. I would say information is hidden in the quantum randomness/fuzziness associated with each quantum state, and can only be extracted with many identical copies of the same state, or have parallel worlds where simultaneous measurements along different directions are performed.
@Mihai,
your psychological analogy is instructive:
The evolution of a quantum state (say a many-particle wave function) between measurements corresponds to the flow of thoughts (which you nicely describe as 'succession of patterns, recalls and darkness') in the mind of a human individual who tries to come up with the solution to some problem.
The result of a measurement corresponds to what the human individual writes down in clear words as a solution (after his thoughts happened to come to a conclusion).
It is evident that the actual flow of thoughts was a much more complex entity than the result. However, the boundary conditions set by real life let only the result count. Most of our fellow scientists will have suffered from the fact that there are human individuals who tend to never reach a conclusion and offer partial descriptions of their thought flow instead.
As instructive as your psychological analogy is the computational analogy: In a program written in some formal language (such as C++) a bit corresponds to a variable of type bool and a qbit corresponds to a variable of type pair where C is the type complex and R is the type of real numbers. Making use of some multiprecision library (such as boost/multiprecision for C++) one can spend any number of bits for the representation of a real number. The time-evolution algorithm of the program will make use of all these bits: If we compare a simulation run for a, say, three-qbit system realized with 1000 bit reals and a run with 1001 bit reals we will observe that the trajectories starting from the same initial state will finally diverge from each other, and thus will give completely different probabilities for specified qbit measurements. This logical analogy makes clear that a qbit behaves like a complicated machine that needs many classical bits for describing its state. Only the result from measurements on this machine can be described by a bit. The inner working of the qbit is a complex process (just as the thought process in the psychological analogy) whereas the measurement result is as simple as a single character, say, 0 or 1.
Dear Ulrich,
Fair enough, but in the case of the human brain a case can be made as to where the extraneous information is held at every intermediate step of the way ( to wit, inside the brain. This extra info will eventually be discarded, as indeed only the upshot counts.) In the case of the qbit though, where is that extra info held during the intermediary process stages?
Quantum mechanics, as Dieter Zeh once put it , is an experiments-based science, since Quote nobody in their right mind would ever come up with a theory as weird as QM if it weren't for the need to explain experimental results Unquote. The experimental results in the case of this extra intermediary info tell us clearly where it can't possibly be held, but not where it is or possibly could be held - which is the question here, although I realize that the answer is, at this stage, elusive.
Very often, puzzling questions in physics turn out to be precious engines of progress - the reason why we can't answer them point up our areas of ignorance and/or of incomplete theories.
Dear Chris,
as it appears to me, your question relates two things which (as also Durga noticed) are quite different. Your question could be generalized to: Where the information is held which gives a quantum state his 'individuality', i.e. let it be this state (and not a different one) that it is. The qbit context in which you put your question suggests a wrong answer by suggesting that at least |0> and |1> are sufficiently characterized states. Actually, these notations say nothing unless we are given the operators in Hilbert space to which they are eigenvectors (to the eigenvalues indicated by the notation). In addition to this operator we also need a Hamilton operator for describing time-evolution between measurements. Without such additional structure we could not answer the question into which state the state |0> will evolve during the next millisecond. If we have the Hamiltonian we can compute complex numbers c1 and c2 such that this state can be proved to be c1|0> + c2|1>. If anything is the 'intermediary info' you are looking for, it is this pair of numbers. (In this language the initial info would be the pair (1,0) of numbers). More generally, all info characterizing a quantum state is the Hilbert state vector, or its representation as a wave function in space-time, or a list of complex numbers as in Heisenberg's matrix mechanics. Which (if any) of these structures describes what 'really goes on' in a quantum dynamical process is, of course, an open question these days.
Dear Ulrich,
you are answering from a well-trodden theoretical standpoint ... My question is how to interpret specific experimental results (especially Michael Goggin's et al.), which appear to show that the wonted theoretical arguments, which you also quote here (and to which also Prof. Tabata alluded), actually do not work in providing possible satisfactory answers to the experimental outcomes that are seen. This is the reason why the likes of David Deutsch and others have drawn in speculations about parallel universes, etc. Maybe we are missing something, which is what my question is all about.
Dear Chris,
all these modern quantum optics experiments show us the consequences of standard quantum mechanics. What they show is not that the 'wonted theoretical arguments' are insufficient but that some common-sense-like assumptions e.g. concerning the flow of information and the involvement of classical bits do not work.
Should you have identified any experimental result that can't be derived from a standard quantum mechanical description it would be nice if you would give a reference. I would be happy to withdraw my bold initial statement if evidence proves it wrong.
Dear Ulrich,
1- Recapping - Timelike entanglements are well-established - described by a number of researchers , see especially http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.110404
with further background & / or supporting texts such as by Stephen Breierly et al., (http://arxiv.org/abs/1501.03505) and others by Ämin Baumeler (http://arxiv.org/pdf/1312.5916.pdf) , etc. So far so good.
2- Now the presence of extra volatile info has been investigated by a number of people, but there is nothing new or odd there, we fully expect the presence of this volatile info (http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.102.010401 , http://arxiv.org/abs/1309.3678 , etc.)
3- But e.g.this is where the plot thickens - www.pnas.org/content/108/4/1256 describes a set of experiments addressing possible modes, left fallow or unaddressed in previous experiments (to cut a long story short, it uses duplicate pre-entangled particles, enabling a calibrating of entanglement of the original with the stand-in particles, and minimizing the subsequent involvement and entanglement of the original particle. Despite such minimal residual entanglement, there is no loss of extra information by the original particle, now minimally entangled. If your explanation held, then there would unavoidably be a loss of extra info. So we're back to the question: where is that information encoded, as it cannot be embedded in the entanglement as per this experiment? I think it is Brierley who said that no one has a clue, as of yet at least.
Others have, from different angles, also looked at this (David Deutsch) and speculated about the location of the volatile info ....
Dear Chris,
I can't take the time to find out wether in your cited material there is 'any experimental result that can't be derived from a standard quantum mechanical description'. It would help if you would communicate your top candidate for such a result.
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