Final Report Summary - MEMORY QUANTUM ICT (Information Transfer with Correlated Noise and Memory Effects in Quantum Comminication Technologies) Description of the work performed since the beginning of the project In the first 12 months of the project, the applicant Dr. Filippo Caruso has mainly worked on three different topics (towards objectives 1, 2, 3 and 4 of the proposal): (i) correlated memory (qubit and Bosonic) channels and new characterisation of such maps in terms of many-body correlation functions [F. Caruso, V. Giovannetti, and M. Palma, Phys. Rev. Lett. 104, 020503 (2010) ]; (ii) noise-assisted transport in quantum networks [A. W. Chin, A. Datta, F. Caruso, S. F. Huelga, M. B. Plenio, New J. Phys. 12, 065002 (2010) ]; (iii) role of entanglement in quantum transport phenomena [F. Caruso, A. W. Chin, A. Datta, S. F. Huelga, and M. B. Plenio, Phys. Rev. A 81, 062346 (2010) ].Concerning (i), in collaboration with Dr. V. Giovannetti of Scuola Normale Superiore (Pisa, Italy) and Prof. G. M. Palma of Physics Department of Palermo University (Palermo, Italy), a new representation of correlated quantum channels, based on a teleportation protocol, has been introduced. This yielded a characterisation of the noise of such memory maps in terms of many-body correlation functions. In particular, it provided a relatively simple method for determining how reliable a correlated channel is to transmit quantum information by analyzing the entanglement properties of the physical system which mediates the teleportation. As a specific case, the latter can be a multipartite pure or mixed graph state. Finally, this new approach was generalised to Bosonic memory channels.As regards (ii), the applicant has provided physically intuitive mechanisms for the effect of noise on transmission dynamics of open quantum networks, i. e. basically line broadening effects and destructive interference suppression. In other words, it has been explicitly demonstrated how noise alters the pathways of transport across an open quantum system, suppressing ineffective paths and facilitating direct ones to the "receiver" side. The impact of non-Markovian effects, i. e. temporally correlated noise, has been also investigated.Concerning (iii), the evolution of quantum entanglement during quantum network transport dynamics has been studied. In particular, the influence of Markovian as well as spatially and temporally correlated (non-Markovian) noise on the generation of entanglement across distinct network sites has been analyzed under different conditions. Additionally, the entangling power of such complex dynamics was numerically quantified. While quantum information processing tends to favor maximal entanglement, near-unit transfer efficiency is achieved as the result of an intricate interplay between coherent and noisy processes where the initial part of the evolution displays intermediate values of entanglement.During the second half of the fellowship, Dr. Filippo Caruso has basically worked on the following issues (towards objectives 1, 3 and 5 of the proposal): (iv) quantitative characterisation of quantum communication networks in terms of channel capacities, in presence of noise [F. Caruso, S. F. Huelga, and M. B. Plenio, Phys. Rev. Lett. 105, 190501 (2010) ]; (v) optimal unitary representation of multimode Bosonic Gaussian channels in terms of a minimal number of environmental modes [F. Caruso, J. Eisert, V. Giovannetti, and A. S. Holevo, Phys. Rev. A 84, 022306 (2011) ]; (vi) proposal for the experimental realisation of noise-assisted communication networks in terms of quantum optical cavities [F. Caruso, N. Spagnolo, C. Vitelli, F. Sciarrino, and M. B. Plenio, Phys. Rev. A 83, 013811 (2011) ].The work in (iv) has shown a clear example in which noise, in terms of dephasing, may enhance the capability of transmitting not only classical but also quantum information, encoded in quantum systems, through communication networks. Indeed, although the unavoidable presence of noise is thought to be one of the major problems to solve in order to implement quantum information technologies in realistic physical platforms, some frameworks have been found where the noise is instead very useful. In particular, quantum and classical capacities for a large family of quantum channels have been analytically and numerically derived, showing that these information transmission rates can be strongly enhanced by introducing dephasing noise in the complex network dynamics. Even more surprisingly, the presence of noise may lead to a finite quantum capacity where the noiseless system has vanishing capacity. Furthermore, a possible application of these results in the context of quantum cryptography was also shown. More specifically, there does exist a counter-intuitive situation where the presence of the eavesdropper (introducing noise in the network dynamics) actually improves the communication between the two parties (Alice and Bob), without however eavesdropping any amount of information.As regards (v), the minimal number of quantum Gaussian environmental modes required to provide a unitary dilation of a multimode Bosonic Gaussian channel, for both pure and mixed environments, has been investigated. These analytical computations relied, on one hand, on the properties of the generalised Choi-Jamiolkowski state and, on the other hand, on an explicit construction of the minimal dilation for arbitrary Bosonic Gaussian channel. The achieved results allowed introducing a new quantity reflecting "noisiness" of Bosonic Gaussian channels, also useful to address some issues concerning transmission of information in continuous variables systems.As concerns (vi), an experimentally realisable optical network scheme for the demonstration of the basic mechanisms underlying noise-assisted transmission of classical and quantum information was proposed. The system consisted of a network of coupled quantum-optical cavities, injected with a single photon. In particular, introducing dephasing in the photon path, this scheme exhibited a characteristic enhancement of the transmission efficiency that can be observed with presently available technology.Main results achieved so far The main results of Caruso's investigations are: a) the introduction of a new class of correlated (qubit and Bosonic) quantum channels by means of the quantum teleportation protocol and their characterisation in terms of many-body correlations functions (published in Physical Review Letters); b) finding that noise may actually assist the transmission of classical and quantum information over complex networks and the quantitative (analytical and numerical) characterisation of such enhancement in terms of channel capacities (published in Physical Review Letters); c) proposal for the experimental realisation of noise-assisted communication networks by using optical cavities (published in Physical Review A).Expected final results and their potential impact and use The achieved results are expected to advance the knowledge about correlated quantum channels and their capacities, and to open up new possibilities for further research in this field, which is crucial to pave the way for implementing quantum information technologies in realistic physical platforms.In particular, the work in (i), by means of a teleportation representation of correlated Pauli channels and their CV generalisations, allows one to establish and further develop a formal connection between correlated quantum maps and the physics of many-body systems. Moreover, it can be easily generalised to higher dimensions, i. e., d-level systems (qudit). This analysis provides new techniques for characterising realistic channels, such as optical fibers, and for improving information transmission rates beyond the corresponding memoryless scenario. Furthermore, this new relation between many-body systems and memory channels is expected, on one side, to lead to novel tools for the exploration of realistic noisy communication channels, and, on the other one, to provide new insights into the exciting area of many-body physics.The results in (iv) are easily generalisable to Bosonic systems and are valid for any Hamiltonian preserving the number of excitations, other forms of noise, and also for non-Markovian evolutions. Therefore, the proposed scheme and, in particular, the simple but interesting case of a three-site quantum network could be experimentally investigated relatively easily by considering, for instance, quantum information platforms using trapped ions or cold atoms where dephasing noise can be introduced in a controlled manner. Besides, they advance the state-of-the-art knowledge in quantum network information theory and, in the long time perspective, might be used for large communication networks based on quantum effects and for new applications related to quantum cryptography.The work (vi) may open interesting perspectives for a deeper investigation of the fundamental mechanisms underlying noise-enhanced transmission of classical and quantum information. More specifically, this type of experiment can also trigger significant activity in two different areas, namely the modeling of complex environments via controlled interactions and the development of noise-assisted protocols for quantum communication.Finally, the obtained results may have a very direct impact on experimental efforts towards realistic and possibly commercial quantum information and communication technologies. The latter should be made use of at Community level to enhance European Union scientific excellence and attractiveness, and to open up new horisons for new devices involving ultra-fast secure (e. g., high-speed optical) communication and miniaturised more powerful (e. g., solid-state) processors
