Few years back, I had applied for enrolling into Ph.D program at an Indian University. However, the university didn’t accept my proposal for a part-time Ph.D. Below is an abstract of the problem statement I proposed. It’s titled “Signal Processing Framework for Quantum Communication Systems”. This is still an open problem and I would be glad if someone takes it up.
Abstract: Signal processing in Communication systems is based upon the classical properties of signals. In classical physics, the effects of measurement, cloning, uncertainty and detection have no or little impact on the signal. As we move from classical communication systems to the system built using quantum mechanical properties of matter, effects such as measurement, cloning, uncertainty and detection have profound impact on the way system works. In , quantum signal processing was studied for the two quantum mechanical properties namely measurement and detection. This thesis intends at developing a formal framework that takes into account the measurement and detection of signals, no-cloning theorem, Uncertainty of canonically conjugate variables, superposition principle and other quantum mechanical properties [2-5].
The following studies are to be aimed to be done as part of thesis
1. Impact of quantum mechanical properties such as No-Cloning theorem classical signal processing algorithms
2. Validity of Shannon’s sampling theorem for quantum band-pass signals*
3. Effects of Energy-Time uncertainty in transforming signals from Time domain to frequency domain**
4. Design of basic modulation/demodulation techniques for signal processing.
*Original proposal of Shannon’s sampling theorem and Nyquist rate was performed on classical communication systems. The author is unaware of any study on this based on quantum mechanical properties.
**Note: In classical signal processing, theoretical signal transformations from frequency domain to time domain doesn’t impact the final result , whereas there is a possibility that due to energy-time uncertainty, transforming signals from time domain to frequency domain might introduce an uncertainty. This needs to be thoroughly studied from the signal processing prospective.
 Yonina Chana Eldar, Alan V. Oppenheim, Quantum Signal Processing, PhD Thesis, MIT, 2002.
(Available at http://dspace.mit.edu/handle/1721.1/16805)
 E.B. Manoukian, Quantum Theory – A wide Spectrum, Springer, 2006.
 K.T. Hecht, Quantum Mechanics, Springer, 2000.
 A.C. Phillips, Introduction to Quantum Mechanics, John Wiley and Sons, 2003.
 Gary E. Bowman, Essential Quantum Mechanics, Oxford University Press, 2008.
 Simon Haykin, Communication Systems, John Wiley and Sons, 1983.