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General Scheme for Perfect Quantum Network Coding with Free Classical Communication
, 2009
"... 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 additiona ..."
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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 sourcetarget pairs if there exists a classical linear (or even vectorlinear) 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 fanin 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
Perfect Quantum Network Communication Protocol Based on Classical Network Coding
, 2009
"... This paper considers a problem of quantum communication between parties that are connected through a network of quantum channels. The model in this paper assumes that there is no prior entanglement shared among any of the parties, but that classical communication is free. The task is to perfectly tr ..."
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This paper considers a problem of quantum communication between parties that are connected through a network of quantum channels. The model in this paper assumes that there is no prior entanglement shared among any of the parties, but that classical communication is free. The task is to perfectly transfer an unknown quantum state from a source subsystem to a target subsystem, where both source and target are formed by ordered sets of some of the nodes. It is proved that a lower bound of the rate at which this quantum communication task is possible is given by the classical mincut maxflow theorem of network coding, where the capacities in question Consider a communication network consisting of a set V of several nodes, each of which can hold a small number of qubits and which have no prior entanglement among them. Furthermore, these nodes are connected via a set E of edges which correspond to quantum communication channels, each of a certain capacity. Let G = (V,E) be the weighted graph corresponding to this network. Consider the following communication problem: given a set S ⊆ V
Constructing quantum network coding schemes from classical nonlinear protocols
 In Proc. 2011 IEEE Intl. Symp. Info. Theory
, 2011
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Quantum Network Coding for General Graphs
, 2006
"... Abstract. It is shown that quantum network coding is always possible for a general graph G if G has a classical network coding protocol based on the linear operation over F4. 1 ..."
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Abstract. It is shown that quantum network coding is always possible for a general graph G if G has a classical network coding protocol based on the linear operation over F4. 1
On quantum network coding
"... We study the problem of errorfree multiple unicast over directed acyclic networks in a quantum setting. We provide a new informationtheoretic proof of the known result that network coding does not achieve a larger quantum information flow than what can be achieved by routing for twopair communic ..."
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We study the problem of errorfree multiple unicast over directed acyclic networks in a quantum setting. We provide a new informationtheoretic proof of the known result that network coding does not achieve a larger quantum information flow than what can be achieved by routing for twopair communication on the butterfly network. We then consider a kpair multiple unicast problem and for all k ≥ 2 we show that there exists a family of networks where quantum network coding achieves ktimes larger quantum information flow than what can be achieved by routing. Finally, we specify a graphtheoretic sufficient condition for the quantum information flow of any multiple unicast problem to be bounded by the capacity of any sparsest multicut of the network. C
Quantum Random Access Codes with Shared Randomness
"... thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. We consider a communication method, where the sender encodes n classical bits into 1 qubit and sends it to the receiver who performs a certain ..."
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thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. We consider a communication method, where the sender encodes n classical bits into 1 qubit and sends it to the receiver who performs a certain measurement depending on which of the initial bits must be recovered. This procedure is called n p ↦ → 1 quantum random access code (QRAC) where p> 1/2 is its success probability. It is known that 2 0.85 ↦− → 1 and 3 0.79 ↦− → 1 QRACs (with no classical counterparts) exist and that 4 p ↦ → 1 QRAC with p> 1/2 is not possible. We extend this model with shared randomness (SR) that is accessible to both parties. Then n p ↦ → 1 QRAC with SR and p> 1/2 exists for any n ≥ 1. We give an upper bound on its success probability (the known 2 0.85
Quantum Random Access Codes with Shared Randomness
, 2009
"... We consider a communication method, where the sender encodes n classical bits into 1 qubit and sends it to the receiver who performs a certain measurement depending on which of the initial bits must be recovered. This procedure is called n p ↦ → 1 quantum random access code (QRAC) where p> 1/2 is ..."
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We consider a communication method, where the sender encodes n classical bits into 1 qubit and sends it to the receiver who performs a certain measurement depending on which of the initial bits must be recovered. This procedure is called n p ↦ → 1 quantum random access code (QRAC) where p> 1/2 is its success probability. It is known that 2 0.85 ↦− → 1 and 3 0.79 ↦− → 1 QRACs (with no classical counterparts) exist and that 4 p ↦ → 1 QRAC with p> 1/2 is not possible. We extend this model with shared randomness (SR) that is accessible to both parties. Then n p ↦ → 1 QRAC with SR and p> 1/2 exists for any n ≥ 1. We give an upper bound on its success probability (the known 2 0.85 ↦− → 1 and 3 0.79