Advances in Quantum Teleportation

Quantum teleportation is one of the most important protocols in quantum information. By exploiting the physical resource of entanglement, quantum teleportation serves as a key primitive in a variety of quantum information tasks and represents an important building block for quantum technologies, with a pivotal role in the continuing progress of quantum communication, quantum computing and quantum networks. Here we review the basic theoretical ideas behind quantum teleportation and its variant protocols. We focus on the main experiments, together with the technical advantages and disadvantages associated with the use of the various technologies, from photonic qubits and optical modes to atomic ensembles, trapped atoms, and solid-state systems. Analysing the current state-of-the-art, we finish by discussing open issues, challenges and potential future implementations.Comment: Nature Photonics Review. Comments are welcome. This is a slightly-expanded arXiv version (14 pages, 5 figure, 1 table

Entanglement-assisted communication of classical and quantum information

We consider the problem of transmitting classical and quantum information reliably over an entanglement-assisted quantum channel. Our main result is a capacity theorem that gives a three-dimensional achievable rate region. Points in the region are rate triples, consisting of the classical communication rate, the quantum communication rate, and the entanglement consumption rate of a particular coding scheme. The crucial protocol in achieving the boundary points of the capacity region is a protocol that we name the classically-enhanced father protocol. The classically-enhanced father protocol is more general than other protocols in the family tree of quantum Shannon theoretic protocols, in the sense that several previously known quantum protocols are now child protocols of it. The classically-enhanced father protocol also shows an improvement over a time-sharing strategy for the case of a qubit dephasing channel--this result justifies the need for simultaneous coding of classical and quantum information over an entanglement-assisted quantum channel. Our capacity theorem is of a multi-letter nature (requiring a limit over many uses of the channel), but it reduces to a single-letter characterization for at least three channels: the completely depolarizing channel, the quantum erasure channel, and the qubit dephasing channel.Comment: 23 pages, 5 figures, 1 table, simplification of capacity region--it now has the simple interpretation as the unit resource capacity region translated along the classically-enhanced father trade-off curv

The apex of the family tree of protocols: Optimal rates and resource inequalities

We establish bounds on the maximum entanglement gain and minimum quantum communication cost of the Fully Quantum Slepian-Wolf protocol in the one-shot regime, which is considered to be at the apex of the existing family tree in Quantum Information Theory. These quantities, which are expressed in terms of smooth min- and max-entropies, reduce to the known rates of quantum communication cost and entanglement gain in the asymptotic i.i.d. scenario. We also provide an explicit proof of the optimality of these asymptotic rates. We introduce a resource inequality for the one-shot FQSW protocol, which in conjunction with our results, yields achievable one-shot rates of its children protocols. In particular, it yields bounds on the one-shot quantum capacity of a noisy channel in terms of a single entropic quantity, unlike previously bounds. We also obtain an explicit expression for the achievable rate for one-shot state redistribution.Comment: 31 pages, 2 figures. Published versio

Absolutely Maximally Entangled states, combinatorial designs and multi-unitary matrices

Absolutely Maximally Entangled (AME) states are those multipartite quantum states that carry absolute maximum entanglement in all possible partitions. AME states are known to play a relevant role in multipartite teleportation, in quantum secret sharing and they provide the basis novel tensor networks related to holography. We present alternative constructions of AME states and show their link with combinatorial designs. We also analyze a key property of AME, namely their relation to tensors that can be understood as unitary transformations in every of its bi-partitions. We call this property multi-unitarity.Comment: 18 pages, 2 figures. Comments are very welcom

A Quantum Light Source for Quantum Information Applications in the Telecom C-Band

Semiconductor quantum dot (QD) quantum light sources have long been established as suitable candidates for many quantum information applications, due to the on-demand emission of highly pure and highly indistinguishable single and entangled photons. A key factor in the development of this technology is the operation over the standard telecommunication optical fibre network infrastructure, where the minimum absorption wavelength window is centred on the telecom C-band (1530 – 1565 nm). Initial experiments in this work demonstrated single-photon emission of a QD light source emitting directly in the telecom C-band, under both continuous wave (CW) and 1-GHz pulsed excitation regimes. The QDs were further characterised in terms of fine-structure splitting (FSS) and coherence time, in order to determine their suitability for quantum entanglement and interference-based applications. Long coherence times were observed in the majority of the QDs considered, allowing the demonstration of Hong-Ou-Mandel-type two-photon interference of subsequently emitted photons under CW excitation. The post-selected interference visibility was found to be limited by only the detector resolution and single-photon purity. A further demonstration of high-visibility interference under the same limitations was then made using QD photons and dissimilar photons from a laser, forming the basis of a fibre-based quantum relay. Working further towards a quantum relay, polarisation-entangled photon pairs in the telecom C-band were then generated using the radiative cascade of the biexciton, where a record high fidelity to the ©+ Bell state was observed under both CW and 1-GHz pulsed excitation regimes. While an anomalous effect of the FSS was observed in a majority of the studied QDs, a further characterisation of the FSS in terms of the QD polarisation eigenstates confirmed the emission of entangled photon pairs from such an anomalous-splitting QD. Finally, the work of this thesis was combined to demonstrate a proof-of-principle quantum relay using a QD light source in the telecom C-band. The relay was operated first under CW excitation where polarisation encoded laser input qubits were used and high-fidelity quantum teleportation was observed. In an effort to demonstrate a more technologically relevant application, the quantum relay was subsequently operated at 1 GHz in order to demonstrate the teleportation of initially time-bin encoded laser input qubits. A high mean teleportation fidelity was again observed, demonstrating the potential of this telecom C-band QD quantum light source in the future of long-distance quantum information applications

Practical limitations on robustness and scalability of quantum Internet

As quantum theory allows for information processing and computing tasks that otherwise are not possible with classical systems, there is a need and use of quantum Internet beyond existing network systems. At the same time, the realization of a desirably functional quantum Internet is hindered by fundamental and practical challenges such as high loss during transmission of quantum systems, decoherence due to interaction with the environment, fragility of quantum states, etc. We study the implications of these constraints by analyzing the limitations on the scaling and robustness of quantum Internet. Considering quantum networks, we present practical bottlenecks for secure communication, delegated computing, and resource distribution among end nodes. Motivated by the power of abstraction in graph theory (in association with quantum information theory), we consider graph-theoretic quantifiers to assess network robustness and provide critical values of communication lines for viable communication over quantum Internet. In particular, we begin by discussing limitations on usefulness of isotropic states as device-independent quantum key repeaters which otherwise could be useful for device-independent quantum key distribution. We consider some quantum networks of practical interest, ranging from satellite-based networks connecting far-off spatial locations to currently available quantum processor architectures within computers, and analyze their robustness to perform quantum information processing tasks. Some of these tasks form primitives for delegated quantum computing, e.g., entanglement distribution and quantum teleportation. For some examples of quantum networks, we present algorithms to perform different quantum network tasks of interest such as constructing the network structure, finding the shortest path between a pair of end nodes, and optimizing the flow of resources at a node.Comment: Happy about the successful soft landing of Chandrayaan-3 on the moon by ISRO. 35 pages, 32 figures. Preliminary versio