Quantum Communication, Teleportation, and Maxwell’s Demon

1. Quantum Communication, Teleportation, and Maxwell’s Demon Jason Grinblat Felix Terkhorn

2. Quantum Communication Classical information theory: if we want to send a message with an object that can be put into N states, then we can send at most N distinct messages (e.g. 0 and 1)

3. Classical theory: the state of a system can be described completely by the constituents of the system • This is untrue of a quantum system, due to quantum entanglement

4. Quantum Entanglement • First investigated by Einstein, Podolsky, and Rosen (EPR) • Constituent systems of a quantum system can be “entangled”; the macro-system then has additional properties

5. Non-locality: two physically separated systems can be entangled • Bennett and Wiesner developed a hypothetical communication system based on the non-locality of quantum entanglement

6. The experiment involves the transmission of a two-bit message using two physical bits, but only one of those bits comes from the sender The receiver begins with two photons, which are “entangled.” He stores one of the photons, and sends the other to the sender. Both photons must be kept isolated from their environments in order to maintain entanglement.

7. Once he receives the photon, the sender performs one of four operations on that photon with a “quantum gate”. The four operations are: do nothing, rotate 180 degrees around the x-axis, y-axis, or z-axis. After performing the operation, the sender sends the photon back to the receiver. By examining both the photons jointly with a different quantum gate, the receiver is able to determine which of the four messages was sent.

8. Quantum Teleportation • Classical “science fiction” proposal of teleportation: Measure and record the state of every atom, transmit this information to the receiver, and reproduce, or clone, each atom • The uncertainty principle asserts that one cannot experimently determine an unknown state, so classical teleportation is not possible

9. Suppose person A is given an a particle. Previously it was thought that the only way to give person B an object in the same state as person A’s object was to send the object itself or to give the state characteristics of that object to another particle and send that to the receiver

10. Bennett, Brassard, Crepeau, Jozsa, Peres, and Wootters have shown that an unknown quantum state can be transferred from one place to another • Suppose the sender and receiver are each given a particle of the entangled EPR pair. The sender then performs a measurement on his particle and the particle in the unknown state; this is the same measurement in fact that was performed in the second step of the quantum communication experiment

11. The sender then transmits the results to the receiver using ordinary means. The receiver uses this information to perform one of four operations on his particle, using some quantum gate. In fact, these four operations are the same four described in the first step of the quantum communication experiment. The result is that the receiver’s particle is now in the same state as the unknown particle, effecting “teleporting” the original particle

12. Implementation • Neither of these two experiments have been performed yet. While we can implement quantum gate which performs the four operations, we do not yet have the technology to build the quantum gate that performs the needed measurement (referred to as a “Bell measurement”). • Weinfirter and Zeilinger from the University of Innsbruck are working on techniques to build this gate.

13. Even while the results remain theoretical, they still force us to revise our theory of information in light of quantum mechanics.

14. Maxwell’s Demon • “A hypothetical being of intelligence but molecular order of size imagined to illustrate limitations of the second law of thermodynamics.” (Webster’s Third International Dictionary) • Second Law of Thermodynamics: Energy spontaneously tends to flow only from being concentrated in one place to becoming diffused and spread out.

15. Maxwell’s Demon • Imagine a room full of some gas heated to an average temperature T. You partition that room into two halves, A & B. Naturally, some of the molecules of gas will be hotter than T, and some will be cooler than T. • Happily straddling the wall between the two rooms is a very small but clever demon. This demon has been magically endowed with the power to observe single nearby molecules in the room, and without expending any effort (work), the demon is able to open and close a door between the two rooms.

16. Maxwell’s Demon • It is the demon’s job to allow fast molecules to pass from chamber A to chamber B, and to allow slow molecules to pass from chamber B to chamber A. • By doing this, chamber B will heat up, and chamber A will cool down, thus violating the Second Law, since the overall effect of his efforts is to allow energy to flow into a place of higher concentration without any work being done.

17. Maxwell’s Demon • Several attempts were made to exorcise the demon. • In 1929, Leo Szilard reduced the problem. The demon was now replaced by a simple engine with a block of memory. As the engine moves molecules from left to right, or right to left, it records their original state. This act of recording does not increase the entropy of the system.

18. Maxwell’s Demon • However, in 1982, Bennett showed that at the completion of the sorting process, the “demon engine” would be required to erase its memory. During the erasure, the entropy in the environment must increase, and so the Second Law is preserved.