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General Scheme for Perfect Quantum Network Coding with Free Classical Communication

Hirotada Kobayashi, François Le Gall, Harumichi Nishimura +1 more

arXiv:0908.1457Lecture notes in computer scienceJan 1, 200954 citations

Constructing quantum network coding schemes from classical nonlinear protocols (コンピュテーション)

弘忠小林, フランソワルガル, 治道西村 +1 more

電子情報通信学会技術研究報告. COMP, コンピュテーションMay 4, 20110 citations

Single-Shot Secure Quantum Network Coding for General Multiple Unicast Network with Free Public Communication

Go Kato, Masaki Owari, Masahito Hayashi

Lecture notes in computer scienceJan 1, 20179 citations

General Scheme for Perfect Quantum Network Coding with Free Classical Communication

Hirotada Kobayashi, François Le, Gall Harumichi +1 more

This paper considers the problem of efficiently transmitting quantum states through a network. It has been known for some time that without additional assumptions it is impossible to achieve this task perfectly in general — indeed, it is impossible even for the simple butterfly network. As additional resource we allow free classical communication between any pair of network nodes. It is shown that perfect quantum network coding is achievable in this model whenever classical network coding is possible over the same network when replacing all quantum capacities by classical capacities. More precisely, it is proved that perfect quantum network coding using free classical communication is possible over a network with k source-target pairs if there exists a classical linear (or even vector-linear) coding scheme over a finite ring. Our proof is constructive in that we give explicit quantum coding operations for each network node. This paper also gives an upper bound on the number of classical communication required in terms of k, the maximal fan-in of any network node, and the size of the network. x1 x2 s1 ♠ s2 ♠ ❍❍❍❍ ❥ x1 x2 ✟ n1 x1 x1 ⊕ x2 x2 n2 ♠ x1 ⊕ x2✟ ❍❍❍❍ ❥ x1 ⊕ x2This paper considers the problem of efficiently transmitting quantum states through a network. It has been known for some time that without additional assumptions it is impossible to achieve this task perfectly in general — indeed, it is impossible even for the simple butterfly network. As additional resource we allow free classical communication between any pair of network nodes. It is shown that perfect quantum network coding is achievable in this model whenever classical network coding is possible over the same network when replacing all quantum capacities by classical capacities. More precisely, it is proved that perfect quantum network coding using free classical communication is possible over a network with k source-target pairs if there exists a classical linear (or even vector-linear) coding scheme over a finite ring. Our proof is constructive in that we give explicit quantum coding operations for each network node. This paper also gives an upper bound on the number of classical communication required in terms of k, the maximal fan-in of any network node, and the size of the network. x1 x2 s1 ♠ s2 ♠ ❍❍❍❍ ❥ x1 x2 ✟ n1 x1 x1 ⊕ x2 x2 n2 ♠ x1 ⊕ x2✟ ❍❍❍❍ ❥ x1 ⊕ x2

Jan 1, 200957 citations

Nonlinear Quantum Network Coding with Classical Communication Resource

Tao Shang, Chunlei Zhang, Ke Li +1 more

Considering the problem of how to efficiently transmit unknown quantum states in multi-unicast networks, we propose a nonlinear quantum network coding scheme with classical communication resource. On the conditions of free classical communication between adjacent nodes in a network, as well as unlimited capacities of classical channels, perfect quantum network coding is available. By means of local phase deviation correction, we design the encoding procedure of nonlinear coding scheme. Moreover, we provide the upper bound on the total number of classical communication which is required to achieve quantum communication, as well as the analysis of scheme property.Considering the problem of how to efficiently transmit unknown quantum states in multi-unicast networks, we propose a nonlinear quantum network coding scheme with classical communication resource. On the conditions of free classical communication between adjacent nodes in a network, as well as unlimited capacities of classical channels, perfect quantum network coding is available. By means of local phase deviation correction, we design the encoding procedure of nonlinear coding scheme. Moreover, we provide the upper bound on the total number of classical communication which is required to achieve quantum communication, as well as the analysis of scheme property.

IEEE Globecom Workshops (GC Wkshps)Dec 1, 20151 citation

Typical Quantum Network Coding Schemes

Tao Shang, Jianwei Liu

Springer eBooksJan 1, 20200 citations

General scheme for perfect quantum network coding with free classical communication (コンピュテーション)

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