Uncertainty Relation in Quantum Information Theory
July 13, 2015 3:53 pmInformation is a key quantity in science and plays a significant role in many economic sectors such as communication technologies, cryptography, or data storage. In quantum communication and information technology the transfer and encryption of information is studied; in the quantum regime phenomena such as the Heisenberg uncertainty principle have to be taken into account as well. Our current experimental work is presented in the journal “Physical Review Letters” and has been chosen as “Editor’s Suggestion“. 1
In 2015, physicists in Australia, the US and Japan, by using the so-called information entropy, precisely analyzed uncertainty in terms of “knowledge” and “predictability” and established a trade-off relation between them. An illustration of the proposed experimental scheme is depicted below.
Randomly selected eigenstates of A and B are sent into a measurement apparatus M. After a correction operation C, and a precise measurement of B, the information- theoretic noise and disturbance are calculated.
For our experiment, the spins of neutrons produced the 250 kW TRIGA reactor at the Atominstitut – TU Wien were determined by successive measurements. Unlike in classical computer science, where classical bits can have only the values 0 or 1, the spin represents a so-called quantum bit (qubit) of information. For spin measurements an uncertainty principle applies, just like for position and momentum. One cannot simultaneously measure the spin in the x-direction and in the y-direction precisely. Thus, one can view the neutron spins as a carrier of qubits and thus test the information-theoretical uncertainty. It was possible to test the trade-off relation for “knowledge” and “predictability“. The higher the knowledge of spin in the x-direction acquired by the measurement of the qubit, the lower was the predictability of its spin in the y-direction, and vice versa. Quantum information prohibits having both high knowledge and high predictability. Further, protocols for quantum error correction were applied to determine how much information loss is reversible and can therefore be regained and how much information will be inevitably destroyed by a measurement. The correctness of the postulated relationship between knowledge and predictability was clearly demonstrated, with the utmost precision. Details of the experimental procedure can be found here.
(left) Noise (straight blue line), uncorrected disturbance (dashed green line), and optimally corrected disturbance (dotted red line) vs polar angle θ of M. (right) Disturbance vs noise with and without optimal correction procedure.
The new results quantify the limits of the transmission of information through quantum channels and thus are very important in many areas of quantum information technology. Noisy communication channels, information loss along such channels, and the quantum encryption of data may be better understood.
Press Release TU Wien (german only)
1. G. Sulyok, S. Sponar, B. Demirel, F. Buscemi, M.J. Hall, M. Ozawa, and Y. Hasegawa, Physical Review Letters 115, 030401 (2015) [quant-ph/1504.04200].↩