Long-distance quantum communication over noisy networks without long-time quantum memory

Abstract

The problem of sharing entanglement over large distances is crucial for implementations of quantum cryptography. A possible scheme for long-distance entanglement sharing and quantum communication exploits networks whose nodes share Einstein-Podolsky-Rosen (EPR) pairs. In Perseguers et al. [Phys. Rev. A 78, 062324 (2008)] the authors put forward an important isomorphism between storing quantum information in a dimension D and transmission of quantum information in a D + 1-dimensional network. We show that it is possible to obtain long-distance entanglement in a noisy two-dimensional (2D) network, even when taking into account that encoding and decoding of a state is exposed to an error. For 3D networks we propose a simple encoding and decoding scheme based solely on syndrome measurements on 2D Kitaev topological quantum memory. Our procedure constitutes an alternative scheme of state injection that can be used for universal quantum computation on 2D Kitaev code. It is shown that the encoding scheme is equivalent to teleporting the state, from a specific node into a whole two-dimensional network, through some virtual EPR pair existing within the rest of network qubits. We present an analytic lower bound on fidelity of the encoding and decoding procedure, using as our main tool a modified metric on space-time lattice, deviating from a taxicab metric at the first and the last time slices.Suppose we have a network of laboratories with some fixed distance between neighboring ones, and one of them wants to establish quantum communication with another one. We assume that neighboring labs can directly exchange quantum communication with some small, fixed error. This can be used e.g. to share some noisy Einstein-Podolsky-Rosen (EPR) pairs between the neighboring labs. We also assume that all operations performed within each lab may be faulty with some fixed, small probability. If two distant labs can achieve quantum communication with the help of all the labs in the network, then they can exploit it to share cryptographic key that will be known only to these two labs. This scenario was put forward in [1], and is an alternative to quantum repeaters [2,3]. It is also closely related to entanglement percolation [4]. In [1] the question was posed whether for a 2-dimensional network, in principle, one can perform quantum communication over an arbitrary distance, provided that one can execute gates between the adjacent nodes (i.e. local gates), and the size of the system in each node is constant (i.e. it does not depend on the distance), so that the nodes do not need quantum memory. The answer was affirmative. Namely, the authors represented nearest neighbour quantum computation on a line as a teleportation process on quantum 2-dimensional square networks, where entangled pairs are shared between adjacent nodes (i.e. between those that are separated by a size of an elementary cell a of the network). 1-dimensional system for quantum computation is formed by all nodes belonging to a chosen line forming a diagonal of elementary ce...

Fundamental rate-loss trade-off for the quantum internet

“…This class of QKD protocols leads to a square root improvement in the secret key rate over conventional QKD schemes (without quantum repeaters) bounded by the TGW bound. Nonetheless, it is implementable21 without the need of matter quantum memories or quantum error correction, which is in a striking contrast to quantum repeaters18222324252627282930313233343536. In particular, those intercity QKD protocols are modifications of the measurement-device-independent QKD39 (mdiQKD), and all of them use a single (untrusted) intermediate node C in the middle of communicators Alice and Bob.…”

“…Actually, there are many quantum repeater schemes18222324252627282930313233343536, depending on the assumed devices of the repeater nodes { C 1 , C 2 , …, C n }. For instance, a protocol assumes repeater nodes equipped with atomic-ensemble quantum memories as well as optical devices1823.…”

“…For instance, a protocol assumes repeater nodes equipped with atomic-ensemble quantum memories as well as optical devices1823. To obtain better scaling, instead of the atomic-ensemble quantum memories, another protocols222728293234 use matter qubits satisfying3536 all the criteria given by DiVincenzo40. Moreover, there is even an all-photonic scheme35 that does not use matter quantum memories at all and works by using only optical devices.…”

“…For example, the point-to-point quantum communication over 1,000 km needs18 to take almost one century to provide just one secret bit or one ebit for Alice and Bob under the use of a typical standard telecom optical fibre with loss of about 0.2 dB km −1 . Therefore, for the request from far distant Alice and Bob, the quantum internet necessitates long-distance quantum communication schemes utilizing intermediate nodes, such as intercity quantum key distribution (QKD) protocols192021 and quantum repeaters18222324252627282930313233343536. In particular, these schemes would be in greater demand for the quantum internet than the point-to-point quantum communication, analogously to the current Internet, where a client communicates with a far distant client via repeater nodes routinely and even unconsciously.…”

Aggregating quantum repeaters for the quantum internet

“…More importantly, Eq. (14) proves that, although a best protocol may use multi-party entanglement purification or quantum network coding, the communication performance is merely, at most, twice of that of the aggregated quantum repeater protocol based only on linear networks.…”