相対論的量子測定理論及び相対論的量子情報理論の研究

2013 Fiscal Year Annual Research Report

• Project/Area Number: 13F03757
• Research Institution: Nagoya University
• Principal Investigator: 小澤 正直 名古屋大学, 情報科学研究科, 教授
• Co-Investigator(Kenkyū-buntansha): PALGE Veiko 名古屋大学, 情報科学研究科, 外国人特別研究員
• Keywords: Quantum mechanics / Special relativity / Quantum information / Quantum communication

Research Abstract

The aim of this project is to extend quantum information theory to the relativistic domain by studying how relativity affects entangled systems. In particular, we have investigated how the entanglement of bipartite massive spin-1/2 particles behaves under Lorentz boosts in different geometries. We have obtained analytic characterization of the concurrence of spin-spin entangled systems under different forms of product and entangled momenta where the spin degree of freedom was given by the Werner state and the momenta were assumed to be discrete, and the spins undergo maximal rotation. We have also computed the corresponding state changes using the Fano representation, which provides further geometric insight into the structure of spin orbits.
The significance of these results lies in that they develop the theory of entanglement beyond the non-relativistic regime. Entanglement is the notion that quantum systems an display correlations that are impossible from the classical point of view. In quantum information theory entanglement has come to be recognized. as a physical resource that enables new technologies that perform information processing tasks which are beyond the limits of the classical realm. Since we know that the world is ultimately relativistic at bottom, achieving a relativistic theory of entanglement is important both from the theoretical and practical point of view. These results help reach the goal of understanding and explaining the behavior of quantum information in relativity, as well as lead to possible ways of enhancing applications of quantum information to relativistic system.

Current Status of Research Progress

2: Research has progressed on the whole more than it was originally planned.

Reason

We have obtainde initial results that characterize the behavior of spin-spin entanglement in awide range of relativistic scenarios which involve boost scenarios that maximize the Wigner rotation for the system under consideration. Many different idealizde momenta of both product and entanglde form have been studide, showing novel behavior as well as explaining results that have appearde in the literature.

Strategy for Future Research Activity

While idealizde systems offer valuable insight into the phenomena under investigation, realistic systems involve Gaussian Wave packest. We plan to extend the results obtainde so far to realistic two particle systems with Gaussian momenta with spins in a Bell state. Since the calculations do not admit analytic treatment we plan to carry out calculations using numerical methods. Using geometric framework, we will also focus on single and two particle systems and characterize their behavior in a generalizde multi-boost setting. This goes beyond the usual two-boost model, enabling to devise schemes that bring relativistic effects to speeds that could be experimentally accessible.