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Quantum Physics

Title: Quantum Network Coding

Abstract: Since quantum information is continuous, its handling is sometimes surprisingly harder than the classical counterpart. A typical example is cloning; making a copy of digital information is straightforward but it is not possible exactly for quantum information. The question in this paper is whether or not quantum network coding is possible. Its classical counterpart is another good example to show that digital information flow can be done much more efficiently than conventional (say, liquid) flow.
Our answer to the question is similar to the case of cloning, namely, it is shown that quantum network coding is possible if approximation is allowed, by using a simple network model called Butterfly. In this network, there are two flow paths, s_1 to t_1 and s_2 to t_2, which shares a single bottleneck channel of capacity one. In the classical case, we can send two bits simultaneously, one for each path, in spite of the bottleneck. Our results for quantum network coding include: (i) We can send any quantum state |psi_1> from s_1 to t_1 and |psi_2> from s_2 to t_2 simultaneously with a fidelity strictly greater than 1/2. (ii) If one of |psi_1> and |psi_2> is classical, then the fidelity can be improved to 2/3. (iii) Similar improvement is also possible if |psi_1> and |psi_2> are restricted to only a finite number of (previously known) states. (iv) Several impossibility results including the general upper bound of the fidelity are also given.
Comments: 27pages, 11figures. The 12page version will appear in 24th International Symposium on Theoretical Aspects of Computer Science (STACS 2007)
Subjects: Quantum Physics (quant-ph)
Journal reference: Proceedings of 24th International Symposium on Theoretical Aspects of Computer Science (STACS 2007), Lecture Notes in Computer Science 4393, pp. 610-621, 2007
DOI: 10.1007/978-3-540-70918-3_52
Cite as: arXiv:quant-ph/0601088
  (or arXiv:quant-ph/0601088v2 for this version)

Submission history

From: Harumichi Nishimura [view email]
[v1] Fri, 13 Jan 2006 07:32:55 GMT (35kb)
[v2] Sat, 9 Dec 2006 04:12:43 GMT (110kb)