2004 Fiscal Year Final Research Report Summary
Analysis of non-locality of quantum mechanics in terms of quantum trajectories and quantum teleportation of continuous variables
| Project/Area Number |
14540382
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
物理学一般
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| Research Institution | Kyoto Sangyo University |
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Principal Investigator |
TOYAMA Masafumi Kyoto Sangyo University, Faculty of Engineering, Professor, 工学部, 教授 (60180189)
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| Project Period (FY) |
2002 – 2004
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| Keywords | Non-locality of quantum mechanics / Quantum entanglement / Bohm trajectory / Quantum teleportation / Point interaction / Quantum register / Coupled channels / Confining potential |
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| Research Abstract |
1.Analysis of non-locality of quantum entanglement in configuration space in terms of Bohm trajectories
We analyzed non-local correlations in Bohm trajectories of two particles that are entangled in configuration space. We used a one-dimensional wave-packet model that explicitly describes the space-time evolution of a two-particle entangled state. This analysis substantiates the geometrical, schematic approach that was used earlier by Rice to demonstrate non-locality in the Bohm theory of quantum mechanics. We further discussed a subtle aspect of the non-local correlations that was not revealed in Rice's analysis. We also examined a three-particle entangled state with a one-dimensional wave-packet model.
2.A non-relativistic time-dependent model for teleportation of a quantum state of position and momentum
We constructed a time-dependent model for teleportation of an unknown quantum state of position and momentum. We used a correlation function of the Gaussian type for the two-particle entangled state. With this model, we analyzed a situation where a time-evolution of a post-measurement state generated at the receiver's site cannot be ignored and the receiver is ignorant of the Hamiltonian that describes the time-evolution. We illustrated how the time-evolution of the post-measurement state deteriorates the fidelity of the quantum teleportation. We also illustrated a special situation in which a two-mode input state is transformed into a one-mode state by teleportation. In addition, we discussed an optimal situation in which a high teleportation probability and a high degree of teleportation fidelity can be achieved.
3.Related problems
We examined generalized point interactions of various types to apply them to a new model of quantum register. In addition, we examined quantum decay process accelerated by tunneling, transmission and reflection of a wave packet with a small width and so on.
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