quantum mechanics - Detecting coherence

Is there a way to know if a particle is acting as a wave or a particle? Alternatively, if an entangled particle was already measured?

A - Yes

So any experiment over an entangled particle that let you know if they are coherent or decoherent, so would let we know that the distant particle is same "state" (coherence or decoherence), so independiently of any quantum state measured, having detected that "the wavicle has been measured", let you send information coded as decoherence time intervals.

B - No

So, does still have sense to talk about a coherence/decoherence "state" if there is no way to detect it?

EDIT

The wave has his meta-existence as a probability of a detectable particle interaction, but.. if there is no way to know about the system coherence or decoherence -before- it have "expressed" his behaviour (it's done always as a particle) then we could say that coherent state is never detectable?, I mean if you have measured a photon by a detector, you already know coherence is lost, but with engangled particles A, B, if you decoherence A, then what happend to B? only we could know that there is no "random"(umpredictable) value anymore.. then could we know if a particle is entangled with other? or explicitly could we know if a particle was measured or decoherenced from another entangled partner ?

Fantastic way to say it: "Suposse you are employed to discover if our entire world is being spied from other distant world via entangled particles and the random we see (and its subsecuent evolution) was already known via an engangled model of our world, so.. there is a way to know if someone had got access from a distant engangled particle?, or there is no way to know if any measured value was already determined or is the current experiment where it's first known and fixed (and last years as a lab note in a yellow paper..) or was the experiment just redundant, because the value was already known in an entangled distant experiment (and by a distant world, with beings laughing at our surprise) it doesn't matter if the value is random, anyway is a known value, and they saw it first"

Answer

the answer is No, at least up to the moment after both particles in the entangled pair are measured. In fact, each particle in the world is always behaving both as a wave and as a particle. One of these two behavior may turn out to be more important - or exclusively important - for the description of a particular experiment. But which one it was can only be determined retroactively.

This is demonstrated by the "delayed choice quantum eraser" experiments, see some comments here:

http://motls.blogspot.com/2010/11/delayed-choice-quantum-eraser.html

It's an experiment in which some sloppy interpreters could think that the particle is already "doomed" and any possible interference pattern that the particle could have created has been damaged. However, the experiment may continue in such a way that the interference pattern is "revived" without any problem. The lesson is that one can never try to determine the "results" of anything before things are actually measured. All intermediate properties - and all histories, using Feynman's approach to quantum mechanics - can contribute and always do contribute to the quantity that matters, namely the probability amplitude whose only goal is to predict the probabilities of outcome at the very end of the experiment. When the measurement is completed, the outcome becomes an objective fact. But there are no objective facts about any system before it is measured.

Just like you can't say whether a particle is coming through slit 1 or slit 2 before you measure it - and if you don't interrupt the particle, both possible histories actually contribute to the interference pattern which is what you measure after many repetitions of the double slit experiment - you are also unable to say that a particle behaves "only as a particle" or "only as a wave" before anything is measured. Once again, both possible intermediate histories must be allowed to contribute to what's going on. The wave function has to be carefully evolved in time. And even though some portions of the wave function may later become irrelevant because they describe histories that were not realized, you can never make such a reduction prematurely. And you can't even imagine that in principle, one of the answers was already correct.

So be sure that you can't transmit any information by entangled particles faster than light. It's not possible by the measurements of their usual quantum numbers and it's not possible by your seemingly more sophisticated procedure which is actually not more sophisticated but it is the same thing with different types of measurements.

Finally, you wrote that because I answered No, it doesn't make sense to talk about a coherent state. Well, a coherent state is a particular state that exists in a Hilbert space. (More precisely, a "coherent state" means something else than you say - it's a term denoting states of a shifted harmonic oscillator ground state - but you mean "some state that exhibits coherence.)

And if you make infinitely many repetitions of many experiments to test the character of a state, you may prove that it is a particular state, e.g. your "coherent state", up to an overall phase. So the coherent state surely exists both as a mathematical object as well as an actual situation that leads to very particular predictions that differ from the predictions of any other state. So it's just incorrect to say that it makes no sense to talk about this state - or any other state. It makes a perfect sense.

What isn't right is to claim that a particular particle - or any other quantum object - is determined to have one property or another before it is measured. Indeed, whenever the wave function admits that both properties (up or down spin; or coherent or incoherent behavior) may be true, you must patiently admit that both possilibities are true until the very moment when all the measurements are completed. Then you may perhaps do some retroactive interpretations of what happened. But it's important that there can't be any interpretation before the measurements are over, and not even God knows whether two particles are coherent or incoherent with each other before all the manipulations with the particles are over and the particles are actually measured.

That's how quantum mechanics works. States in the Hilbert space exist and maybe realized, but they can only be tested by statistically comparing their probabilistic predictions with repetitions of the same experiments. If you want to discuss a much more specific experiment and notion of "coherence", you will have to clarify your question a bit.

Best wishes Lubos