What is the minimum observer energy?

[Jeff Rosenbury]

Question: Suppose I want to measure the polarity of a photon. What is the minimum amount of energy I need to invest? What are the needed forms? (Examples might include rest mass for storage devices, energy in interacting particles, etc.) I'm looking for an ideal device.

Background: I have a B.S.E.E. I'm trying to understand the relationship between QM and information. I found Shannon's definition of information a little constricting as it only deals with information over a channel and not information as a recipient or transmitter. Otherwise His definition seems acceptable (but I'm not up on my IS math as I should be). I'm assuming there is some minimum complexity of a device to count as an observer and cause quantum decoherence. Likely this involves at least the ability to store the results as a bit. My knowledge of QM is self-taught and likely to be spotty, good in some areas, not so good in others. I did well in Calculus but not so well in Linear Algebra.

Assumptions: The energy content of information likely will depend on the temperature of the system, if so, let's use 5.2 Kelvins (critical point of Helium 4). The energy needed might depend on the probability of accuracy of the result, if so let's use 3 sigma or about 99% (whichever is easier to compute). I'm just looking to understand what's happening. Feel free to choose other values if they are useful. Just state the assumptions please.

Speculation: As I understand it, the state function collapses when observed. When it does this it leaks information to the observer. It seems to me a valid observer should be able to, at a minimum, detect and store the information leaked in some form. The detector needs energy. the storage needs energy. The information itself needs energy. Is there anything else needed to be a valid observer? (Perhaps a time stamp?)

Is it possible to leak less information (in the form of lower probability of accuracy perhaps) and partially collapse the function? (Collapse some degrees of freedom, but not others?)

 

[VantagePoint72]

Shannon entropy is for classical information channels and is not valid for quantum mechanics. Its generalization to quantum information is "von Neumann entropy".

A valid observer is just anything capable of becoming entangled with the state we wish to measure. For your photon example, an "observer" is just any kind of measuring device, with at least two states, that can become correlated with the photon such that the device is in one state if the photon is horizontally polarized and in the other if it's vertically polarized. Beyond that, it can be as simple or as complex as you like. Even another photon will do.

And, yes, it is possible to do partial measurements that yield less information and, accordingly, disturb the state less. The extreme example of this is something called weak measurement, in which certain (very sketchy) information about the state may be gained without disturbing it at all.

 

[VantagePoint72]

(Note, also, that quantum decoherence is induced by interactions between the measuring device and the environment, or the system being measured and the environment; not between the system being measured and the measuring device.)

 

[Jeff Rosenbury]

Thank you. Your answers seem to raise more questions, but I'll need more study before I bother you with them.