Scientific Progress and Accomplishments:

During this period, we have analyzed several issues related to the foundations of quantum mechanics using an information-theoretic formulation of quantum entanglement. This formalism has been applied to the study of quantum communication channels and quantum error-correcting codes. We have also investigated the simulation of quantum computation using a quantum Monte Carlo technique. This work is a direct continuation of our previous research during the year 1995-96.

Plans for the coming year:
Our research directions for the coming year under the QUIC program will be centered on two main avenues:

1. We plan to pursue our research effort on the simulation of quantum computation using a quantum Monte Carlo method. This will include the investigation of alternative approaches to the Hubbard-Stratonovich method, as well as the analysis of possible techniques to circumvent the "sign-problem" (which currently prevents the simulation of any complex quantum circuit).

2. We will investigate new applications of the unified framework for quantum information that we have developed in our earlier work. In particular, we plan to study information-theoretic aspects of quantum copying, and, more specifically, to derive entropic bounds on quantum copying. We will also focus on noisy quantum channels in an attempt to obtain better entropic bounds on the achievable rate of reliable quantum information transmission. This will extend our previous work on quantum error correction (cf. the quantum Singleton bound). Finally, we will investigate quantum non-separability using this information-theoretic framework.

List of Participating Scientific Personnel:

Dr. Steven Koonin, Professor of Theoretical Physics
Dr. Nicolas Cerf, Senior Research Fellow in Physics, Kellogg Radiation Laboratory; also Visiting Scientist at the Jet Propulsion Laboratory, NASA.
Dr. Chris Adami, Senior Research Fellow in Computational Neural Systems
Scott Noble, undergraduate student, Summer 97 (Subject: Monte Carlo simulation of quantum circuits)
Francois Lekien, undergraduate student, Summer 97 (Subject: Algorithms to search for quantum error-correcting codes)
Bob Gingrich, 2nd-year graduate student, started his thesis in September 97 (Subject: Quantum inseparability and quantum information)

List of Manuscripts/Publications:

1. “Negative Entropy and Information in Quantum Mechanics,” N. J. Cerf and C. Adami, Phys. Rev. Lett. 79 (1997), 5194.
[KRL-MAP-191 and quant-ph/951202200]
2. “Negative Entropy in Quantum Information Theory,” N. J. Cerf and C. Adami,
in: New Developments on Fundamental Problems in Quantum Physics, ed. M. Ferrero and A. van der Merwe, Fundamental Theories of Physics 81, (Kluwer, Dordrecht, 1997), p. 77. [quant-ph/9610005]
3. “Quantum Information Theory of Entanglement and Measurement,” N. J. Cerf and C. Adami, Physica D (1997), in press. Also in: Proc. of the 4th Workshop on Physics and Computation, Boston 1996, ed. T. Toffoli, M. Biafore, and J. Leao (New England Complex Systems Institute, Cambridge, MA, 1996), p. 65. [KRL-MAP-199 and quant-ph/9605039]
4. “Physical Reality and Quantum Paradoxes,” C. Adami and N. J. Cerf, (submitted to Lecture Notes in Computer Science, Springer-Verlog, 1998). [KRL-MAP-204]
5. “Entropic Bell Inequalities,” N. J. Cerf and C. Adami, Phys. Rev. A 55 (1997) 3371. [KRL-MAP-205 and quant-ph/9608047]
6. “von Neumann Capacity of Noisy Quantum Channels,” C. Adami and N. J. Cerf, Phys. Rev. A 56 (1997) 3470. [KRL-MAP-206 and quant-ph/9609024]
7. “Information-Theoretic Interpretation of Quantum Error-Correcting Codes,” N. J. Cerf and R. Cleve, Phys. Rev. A 56 (1997) 1721. [KRL-MAP-209 and quant-ph/9702031]
8. “Accessible Information in Quantum Measurement,” N. J. Cerf and C. Adami, submitted to Phys. Rev. Lett. [KRL-MAP-207 and quant-ph/9611032]
9. “Monte Carlo Simulation of Quantum Computation,” N. J. Cerf and S. E. Koonin, Math. and Computers in Simulation (1997), in press. Also in: Proc. of the IMACS (International Association for Mathematics and Computers in Simulation) Conference on Monte Carlo Methods, 1997. [KRL-MAP-212 and quant-ph/9703050]
10. “Optical Simulation of Quantum Logic,” N. J. Cerf, C. Adami, and P. G. Kwiat, Phys. Rev. A. (1998) in press. [KRL-MAP-211 and quant-ph/9706022]
11. “Entropic Bounds on Coding for Noisy Quantum Channels,” N. J. Cerf, Phys. Rev. A. (1998) in press. [KRL MAP-215 and quant-ph/9707023]
12. “Quantum Conditional Operator and a Criterion for Separability,” N. J. Cerf, C. Adami, and R. M. Gingrich, submitted to Phys. Rev. A. [KRL MAP-217 and quant-ph/9710001]