First you have to prepare a whole bunch of photons in the same state, so that you can characterize what that state is. Let's say you prepare N >> 1 photons in the same state (say, using a laser). Next you send them all through a linear polarizer at some angle. If they all get through, you know that was the polarization of the state. If they don't, turn the polarizer a little and do it again. Keep doing that until they all get through, now you know their polarization (and you know how the state is prepared, so you can assume it will always work that way). If they never all get through, they must not be linearly polarized, so you bring out the circular polarizer and do it again. If that doesn't work either, they are elliptically polarized, so you maximize the circular and the linear outputs, and use that to figure out the superposition you had originally.nard said:Suppose we have a photon whose polarization state is unknown, what measurement can be done to determine the state of that photon?
You need many measurements to characterize the state. However, once you understand how the preparation of the state links up with the measurements, you can "learn how it works", and not have to do it again every time.How many times are we supposed to make the measurement in order to confirm our results?
A mixed state will never let all the photons through any polarizer, and when the pure state doesn't either, you will get different results when you start using both linear and circular polarizations-- the pure state will have a different signature that will tell you all the photons are in the same state. For the mixed state, the outcomes will not be consistent with all the photons being in the same state, they have to be a mixture of different pure states.How can we distinguish a mixed state to a pure state?
The state of a photon refers to its polarization, or the direction of its electric field. A pure state photon has a well-defined polarization, meaning it only has one direction of electric field. A mixed state photon, on the other hand, has a combination of different polarizations, resulting in an average direction of electric field.
2.There are several methods for measuring the state of photons. One common method is using a polarizer, which only allows light of a certain polarization to pass through. By rotating the polarizer and measuring the intensity of light passing through, scientists can determine the polarization of the photons. Another method is using quantum state tomography, which involves making multiple measurements on a large number of photons to reconstruct the full state.
3.The state of a photon is important in many applications, such as quantum computing and quantum cryptography. In these fields, the ability to control and manipulate the state of photons is crucial. By determining whether a photon is in a mixed or pure state, scientists can better understand and utilize its properties for various applications.
4.The state of photons can be affected by various factors, such as the material they are passing through, the angle at which they are being observed, and external magnetic or electric fields. These factors can alter the polarization of the photons and result in a mixed state.
5.Scientists have developed various techniques for manipulating and controlling the state of photons. These include using special materials called waveplates to change the polarization of photons, using quantum gates to manipulate the state of multiple photons at once, and using feedback control systems to maintain a desired state. Additionally, the state of photons can also be manipulated through interactions with other particles, such as in the process of entanglement.