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 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 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.
Abstract We propose a scheme where one can exploit auxiliary resources to achieve quantum multicast communication with network coding over the butterfly network. In this paper, we propose the quantum 2-pair multicast communication scheme, and extend it to k-pair multicast communication over the extended butterfly network. Firstly, an EPR pair is shared between each adjacent node on the butterfly network, and make use of local operation and classical communication to generate entangled relationship between non-adjacent nodes. Secondly, each sender adds auxiliary particles according to the multicast number k, in which the CNOT operations are applied to form the multi-particle entangled state. Finally, combined with network coding and free classical communication, quantum multicast communication based on quantum measurements is completed over the extended butterfly network. Not only the bottleneck problem is solved, but also quantum multicast communication can be completed in our scheme. At the same time, regardless of multicast number k, the maximum capacity of classical channel is 2 bits, and quantum channel is used only once.
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.
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, s1 to t1 and s2 to t2 , 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 ∣ψ1⟩ from s1 to t1 and ∣ψ2⟩ from s2 to t2 simultaneously with a fidelity strictly greater than 1/2.(ii) If one of ∣ψk⟩ and ∣ψ2⟩ is classical, then the fidelity can be improved to 2/3.(iii) Similar improvement is also possible if Cbi⟩ and 1Cb2⟩ are restricted to only a finite number of (previously known) states.This allows us to design an interesting protocol which can send two classical bits from s1 to t1 (similarly from s2 to t2 ) but only one of them should be recovered.
Quantum entanglement plays a central role in many quantum communication protocols. It allows distant particles to share correlations beyond the limits of classical interactions. Entanglement is essential for superdense coding, quantum teleportation, and secure cryptographic key distribution in quantum communication. It is also a pillar for developing quantum networks, where the management and distribution of entanglement are crucial for connecting distant nodes. Although perfect entanglement is a sought-after ideal, experimental imperatives, including entanglement distribution over long distances, often limit the quality of entangled states. An important question is whether weaker entanglement still offers advantages. First, we study more general tasks than dense coding to show that simpler measurements, combined with entanglement, allow advantageous and sometimes even optimal qubit communication protocols to be obtained. We also demonstrate that simple measurements can generate quantum correlations that cannot be modelled by two classical communication bits and can constitute an optimal protocol with quantum resources. We implement a novel Bell-type inequality tailored for certifying full network non-locality (FNN) to develop certification methods guaranteeing security on an entanglement-based network. Our experiment uses two pairs of polarised entangled photons in a network configuration with three nodes, briefly referred to as a bilocal network scenario. Finally, we show that weakly entangled states can improve communication over a qubit channel using only separate (local) measurements on isotropic non-steerable two-qubit states, without interference, of individual photons, across two communication tasks: secret sharing and its stochastic variant.