2001 Fiscal Year Final Research Report Summary
Research on the Collaboration between Quantum Mechanics and Information Processing
| Project/Area Number |
12440111
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (B)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
物理学一般
|
|---|
| Research Institution | The Graduate University for Advanced Studies |
|---|
Principal Investigator |
IMOTO Nobuyuki The Graduate University for Advanced Studies, The Graduate University for Advanced Studies, 教授 (00313479)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
KOASHI Masato The Graduate University for Advanced Studies, 先導科学研究科, 助教授 (90322099)
|
|---|
| Project Period (FY) |
2000 – 2001
|
| Keywords | Quantum Information Processing / Quantum Cryptography / Quantum Computing / Quantum Electronics |
|---|
| Research Abstract |
We derived a formula that determines the optimal number of qubits per message that allows asymptotically faithful compression of the quantum information carried by an ensemble of mixed states. The set of mixed states determines a decomposition of the Hilbert space into the redundant part and the irreducible part. After removing the redundancy, the optimal compression rate is shown to be given by the von Neumann entropy of the reduced ensemble.
We also investigated entanglement sharing among multi-qubit systems, especially its behavior in the limit of large number qubits. Quantum entanglement cannot be unlimitedly shared among an arbitrary number of qubits. The degree of bipartite entanglement decreases as the number of entangled pairs in an N-qubit system increases. We analyze a system of N qubits in which an arbitrary pair of particles is entangled. We show that the maximum degree of entanglement (measured in the concurrence) between any pair of qubits is 2/N. This tight bound can be achieved when the qubits are prepared in a pure symmetric (with respect to permutations) state with just one qubit in the basis state |0> and the others in the basis state |1> .
|
