Is it possible to reverse the spin of an electron by applying a magnetic field without it losing it's entanglement?
There have been some researches where people have managed to reverse the spin of an electron by applying a magnetic field , however I want to know how ( If possible ) can the electron's spin be reversed without making it lose it's quantum entanglement.
The other entangled particles, probably just one electron will also reverse the spin. This is the basis of quantum cryptology and quantum computing.
The spin of an electron is a model for the quatum state between its mass at ground state and its energy spectrum (Raman effect) thereby it is electromagnetic field conserved by the overall entanglement relation E=m*c^2. You can calculate the spin in an interaction picture (model) (see Mallick, Hamburger, Mallick (2016,2016), Mallick (2014,2015) on www.researchgate.net/Soumitra K Mallick) proof of P vs.NP problem and applications to functor category Dbranes String methods for ECommerce Field Theory Econophysical AGNN GA) . This Physical Chemical Analysis Technology using Functor Category Dbranes calculus experimentally analysis gives rise to "green gravitons" and "green gravitons" in the coupled cybergenetic Network Field (Mallick, Hamburger, Mallick (2016)) lecture notes submitted to Royal Swedish Academy of Sciences also corresponded on this website in answering questions. I hope it answers some of your queries in the matter of Quantum Mechanics that you have put forward. This is in addition to the discussion on this String. Mathematically-Statistically spin is a integration process preserving various kinds of group homology like Lie Groups which requires interaction (experimentally) with the Higgs Field for fundamental particles but not spin.
Soumitra K Mallick
for Soumitra K Mallick, Nick Hamburger, Sandipan Mallick (we are both spinning as well as interacting being on earth!!!)
Dear Debargha
Any unitary operation acting locally on only part of an entangled state will never alter its entangled properties. As an example, take two electrons in the entangled state, a|01>+b|10>, where the notation |01> means that the first particle has its spin pointing up in the z-direction whereas the second has its spin pointing down, and |a|^2+|b|^2=1.
Now imagine that the first particle passes through a magnetic field that points along the x-direction and let us for the sake of argument suppose that the strength of the magnetic field as well as the time the particle spends going through it is such that its spin along the z-direction flips from up to down (or from down to up). The representation of this process mathematically is given by the tensor product of the matrix U=(0 1//1 0) acting on the first system and the identity matrix acting on the second. The effect of this is to transform the state above into a|11>+b|00>. This is still an entangled state. There are many ways to see this but the two easiest ones are; (i) you cannot "factor" this state into a state for system 1 and a state for system 2, or (b) Calculate the reduced density matrix of this state to see that it is a rank-2 state. The second way also allows you to calculate the entanglement content of the state via the von Neumann entropy. Doing this for both the initial and final states you will find that the two have exactly the same von Neumann entropy and thus the same amount of entanglement.
This property is general and is known as the Local Unitary equivalence of entangled states.
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Electromagnetism