We find a protocol transmitting two quantum states crossly in the butterfly network only with prior entanglement between two senders. This protocol requires only one qubit transmission or two classical bits (cbits) transmission in each channel in the butterfly network. It is also proved that it is impossible without prior entanglement. More precisely, an upper bound of average fidelity is given in the butterfly network when prior entanglement is not allowed. The presented result concerns only the butterfly network, but our techniques can be applied to a more general graph.
We find a protocol transmitting two quantum states crossly in the butterfly network only with prior entanglement between two senders. This protocol requires only one qubit transmission or two classical bits (cbits) transmission in each channel in the butterfly network. It is also proved that it is impossible without prior entanglement. More precisely, an upper bound of average fidelity is given in the butterfly network when prior entanglement is not allowed. The presented result concerns only the butterfly network, but our techniques can be applied to a more general graph.
Abstract Distributing quantum state and entanglement between distant nodes is a crucial task in distributed quantum information processing on large-scale quantum networks. Quantum network coding provides an alternative solution for quantum-state distribution, especially when the bottleneck problems must be considered and high communication speed is required. Here, we report the first experimental realization of quantum network coding on the butterfly network. With the help of prior entanglements shared between senders, two quantum states can be transmitted perfectly through the butterfly network. We demonstrate this protocol by employing eight photons generated via spontaneous parametric downconversion. We observe cross-transmission of single-photon states with an average fidelity of 0.9685 ± 0.0013, and that of two-photon entanglement with an average fidelity of 0.9611 ± 0.0061, both of which are greater than the theoretical upper bounds without prior entanglement.
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 ⊕ x2
Network coding is often explained by using a small network model called Butterfly. In this network, there are two flow paths, s_1 to t_1 and s_2 to t_2, which share a single bottleneck channel of capacity one. So, if we consider conventional flow (of liquid, for instance), then the total amount of flow must be at most one in total, say 1/2 for each path. However, if we consider information flow, then we can send two bits (one for each path) at the same time by exploiting two side links, which are of no use for the liquid-type flow, and encoding/decoding operations at each node. This is known as network coding and has been quite popular since its introduction by Ahlswede, Cai, Li and Yeung in 2000. In QIP 2006, Hayashi et al showed that quantum network coding is possible for Butterfly, namely we can send two qubits simultaneously with keeping their fidelity strictly greater than 1/2. In this paper, we show that the result can be extended to a large class of general graphs by using a completely different approach. The underlying technique is a new cloning method called entanglement-free cloning which does not produce any entanglement at all. This seems interesting on its own and to show its possibility is an even more important purpose of this paper. Combining this new cloning with approximation of general quantum states by a small number of fixed ones, we can design a quantum network coding protocol which ``simulates'' its classical counterpart for the same graph.
We find a protocol transmitting K quantum states crossly in the quantum networks with K pair sender-receiver and one bottleneck channels only with sharing quantum correlations between senders. In these networks senders want to multi cast perfect quantum states to receivers. Perfect send on the quantum networks is impossible just using some additional resources like quantum correlation. This protocol has been used maximum entangled states and Quantum Discord which is best indicator of the quantum nature of the correlation to sharing between senders. At first, to send perfect K states in quantum network applied some maximum entanglement states to teleport quantum states, Enistein - Podolsky - Rosen (EPR) states as simple and two qubit states and Grrenberger- Horne - Zeilinger (GHZ) states and W states as kinds of three qubit states. Then reached that there is no difference between sharing these maximum entanglement states and must send same amount of classical bits in bottleneck channel. In the second part of this paper of sharing Quantum Correlation (quantum discord) perfect send of two quantum states is possible in the Butterfly network with fidelity equal one.
We investigate the classical and quantum networking regimes of the butterfly network and a group of larger networks constructed with butterfly network blocks. By considering simultaneous multicasts from a set of senders to a set of receivers, we analyze the corresponding rates for transmitting classical and quantum information through the networks. More precisely, we compare achievable rates (i.e., lower bounds) for classical communication with upper bounds for quantum communication, quantifying the performance gap between the rates for networks connected by identity, depolarizing and erasure channels. For each network considered, we observe a range over which the classical rate non-trivially exceeds the quantum capacity. We find that, by adding butterfly blocks in parallel, the difference between transmitted bits and qubits can be increased up to one extra bit per receiver in the case of perfect transmission (identity channels). Our aim is to provide a quantitative analysis of those network configurations which are particularly disadvantageous for quantum networking, when compared to classical communication. By clarifying the performance of these 'negative cases', we also provide some guidance on how quantum networks should be built.
Although perfect quantum network coding has been proved to be achievable, it is still puzzling whether it is feasible whenever one or more of the channels are replaced by the hidden ones emerging from quantum entanglement. The question is answered in this paper. First, we propose a quantum network coding protocol over a butterfly network with two hidden channels. Second, we investigate a more general situation, where d-level quantum letters are transmitted through the network containing arbitrarily distributed hidden channels, and prove that quantum network coding on such networks is still achievable.