Efficient and reliable entanglement distribution forms the core of quantum network architecture. The Quantum Max-Flow concept defines the upper boundary for efficiently transmitting entanglement within quantum tensor networks (Calegari, Freedman, and Walker, Journal of the American Mathematical Society, 2010). Despite the general invalidity of the Quantum analog of the Max-Flow Min-Cut theorem, this paper introduces a precise Quantum Max-Flow Min-Cut Theorem tailored to quantum tensor networks enhanced by ancilla entanglement. Specifically, our research establishes infinite ’n’ values for any quantum tensor network, where the Quantum Max-Flow matches the Quantum Min-Cut by attaching a maximally entangled state with dimension ’n’ to each edge. Our protocol exclusively relies on quantum teleportation and guarantees unambiguous success. This work highlights the potential of quantum repeaters, enabled by ancilla entanglement, to efficiently distribute entanglement throughout quantum networks.
Efficient and reliable entanglement distribution forms the core of quantum network architecture. The Quantum Max-Flow concept defines the upper boundary for efficiently transmitting entanglement within quantum tensor networks (Calegari, Freedman, and Walker, Journal of the American Mathematical Society, 2010). Despite the general invalidity of the Quantum analog of the Max-Flow Min-Cut theorem, this paper introduces a precise Quantum Max-Flow Min-Cut Theorem tailored to quantum tensor networks enhanced by ancilla entanglement. Specifically, our research establishes infinite ’n’ values for any quantum tensor network, where the Quantum Max-Flow matches the Quantum Min-Cut by attaching a maximally entangled state with dimension ’n’ to each edge. Our protocol exclusively relies on quantum teleportation and guarantees unambiguous success. This work highlights the potential of quantum repeaters, enabled by ancilla entanglement, to efficiently distribute entanglement throughout quantum networks.
The classical max-flow min-cut theorem describes transport through certain idealized classical networks. We consider the quantum analog for tensor networks. By associating an integral capacity to each edge and a tensor to each vertex in a flow network, we can also interpret it as a tensor network and, more specifically, as a linear map from the input space to the output space. The quantum max-flow is defined to be the maximal rank of this linear map over all choices of tensors. The quantum min-cut is defined to be the minimum product of the capacities of edges over all cuts of the tensor network. We show that unlike the classical case, the quantum max-flow=min-cut conjecture is not true in general. Under certain conditions, e.g., when the capacity on each edge is some power of a fixed integer, the quantum max-flow is proved to equal the quantum min-cut. However, concrete examples are also provided where the equality does not hold. We also found connections of quantum max-flow/min-cut with entropy of entanglement and the quantum satisfiability problem. We speculate that the phenomena revealed may be of interest both in spin systems in condensed matter and in quantum gravity.
Most quantum communication tasks need to rely on the transmission of quantum signals over long distances. Unfortunately, transmission of such signals is most often limited by losses in the channel, the same issue that affects classical communication. Simple signal amplification provides an elegant solution for the classical world, but this is not possible in the quantum world, as the no-cloning theorem forbids such an operation and, thus, an alternative approach, a quantum repeater, is needed. Quantum repeaters enable one to create a known maximally entangled state between the end points of the network by first segmenting the network into pieces, creating entanglement between the segments, and then, connecting those entanglement to create the required long range entanglement. Quantum teleportation then allows an unknown quantum message to be transmitted between them using the long-range entangled state. This form of quantum communication will be at the heart of the future quantum Internet. In this review, we will detail various approaches to quantum repeaters, and discuss their expected performance and limitations.
Quantum networks create a completely new way for communication, and the most important function of a quantum network is to generate long-distance quantum entanglement to serve a number of quantum applications. As the scale of the network expands, in order to establish end-to-end entanglement between two remote nodes, entangled pairs need to be generated and distributed among multiple repeaters along the path from the source to the destination, which requires a specific protocol to negotiate resource allocations and quantum operations among the repeaters. Thus, to realize such remote entanglement distribution in a quantum network, designing a stable and reliable protocol becomes urgent and necessary. In this article, we focus on how to guarantee the generation rate of entangled pairs between any two quantum nodes to meet the requirements of various quantum applications in a large-scale quantum network. We present a connection-oriented entanglement distribution protocol inspired by the connection-oriented communication model in classical networks. Our protocol is located in the network layer of the quantum network to enable end-to-end quantum communication. Three main features are provided by the proposed protocol: 1) it is reliable and can guarantee the successful entanglement generation; 2) it can reduce the influence of quantum decoherence via reducing the latency caused by resource competition; and 3) it can guarantee the rate of generating entanglement between two quantum nodes according to the requirement of quantum applications.
Transmitting unknown quantum states to distant locations is crucial for distributed quantum information protocols. The seminal quantum teleportation scheme achieves this feat while requiring prior maximal entanglement between the sender and receiver. In scenarios with noisy entangled states, optimal teleportation fidelity characterizes the efficacy of transmitting the state, demanding the proper selection of local operations at the sender's and receiver's ends. The complexity escalates further in long-range communication setups, prompting the consideration of a repeater-based approach, which incorporates arrays of nodes with multiple segments to facilitate the efficient transmission of quantum information. The fidelity of the communication line gets degraded even if a single segment is affected by noise. In such cases, the general wisdom employs the standard entanglement swapping protocol involving maximally entangled states across the noiseless segments and applying maximally entangled basis measurement at the corresponding nodes to achieve optimal fidelity. In this Letter, we propose a more efficient protocol for a certain class of noisy states, achieving the same fidelity as the standard protocol while consuming less amount of entanglement. Our approach ensures optimal teleportation fidelity even when the end-to-end state gets noisier, and thus promises efficient utility of quantum resources in repeater-based distributed quantum protocols.
The distribution of quantum entanglement between remote clients offers opportunities for secure communication, distributed quantum computation, and quantum-enhanced sensing. A key technology for allowing such a quantum network to extend over large distances is the quantum repeater, which typically employs a long-lived quantum memory with an optical interface. The past decade has seen tremendous progress in experimentally realizing the fundamental building blocks of these repeaters, but open questions remain on what architectures achieve optimal entanglement flows in multi-user quantum networks. Here, we propose a quantum router architecture comprising many quantum repeater nodes in a flexible photonic switchboard architecture to broker entanglement flows across such networks. We compute the rate and fidelity of entanglement distribution using this architecture using an event-based simulation platform. We find that the router's photonic switchboard improves the entanglement fidelity with the number of qubits per node, without a significant drop in the entanglement distribution rate. The proposed quantum router architecture uses present-day photonic switch technology such as photonic integrated circuits, opening a path to near-term deployable multi-user quantum networks.
We consider quantum and private communications assisted by repeaters, from the basic scenario of a single repeater chain to the general case of an arbitrarily-complex quantum network, where systems may be routed through single or multiple paths. In this context, we investigate the ultimate rates at which two end-parties may transmit quantum information, distribute entanglement, or generate secret keys. These end-to-end capacities are defined by optimizing over the most general adaptive protocols that are allowed by quantum mechanics. Combining techniques from quantum information and classical network theory, we derive single-letter upper bounds for the end-to-end capacities in repeater chains and quantum networks connected by arbitrary quantum channels, establishing exact formulas under basic decoherence models, including bosonic lossy channels, quantum-limited amplifiers, dephasing and erasure channels. For the converse part, we adopt a teleportation-inspired simulation of a quantum network which leads to upper bounds in terms of the relative entropy of entanglement. For the lower bounds we combine point-to-point quantum protocols with classical network algorithms. Depending on the type of routing (single or multiple), optimal strategies corresponds to finding the widest path or the maximum flow in the quantum network. Our theory can also be extended to simultaneous quantum communication between multiple senders and receivers.