Gaetana Spedalieri

High-rate measurement-device-independent quantum cryptography

Stefano Pirandola, Carlo Ottaviani, Gaetana Spedalieri, Christian Weedbrook, Samuel L. Braunstein, Seth Lloyd, Tobias Gehring, Christian S. Jacobsen, and Ulrik L. Andersen Department of Computer Science, University of York, York YO10 5GH, United Kingdom Department of Physics, University of Toronto, Toronto M5S 3G4, Canada and QKD Corp., 112 College St., Toronto M5G 1L6, Canada MIT – Department of Mechanical Engineering and Research Laboratory of Electronics, Cambridge MA 02139, USA Department of Physics, Technical University of Denmark, Fysikvej, 2800 Kongens Lyngby, Denmark

Optimality of Gaussian Discord

In this Letter we exploit the recently solved conjecture on the bosonic minimum output entropy to show the optimality of Gaussian discord, so that the computation of quantum discord for bipartite Gaussian states can be restricted to local Gaussian measurements. We prove such optimality for a large family of Gaussian states, including all two-mode squeezed thermal states, which are the most typical Gaussian states realized in experiments. Our family also includes other types of Gaussian states and spans their entire set in a suitable limit where they become Choi matrices of Gaussian channels. As a result, we completely characterize the quantum correlations possessed by some of the most important bosonic states in quantum optics and quantum information.

Continuous-variable quantum cryptography with an untrusted relay: Detailed security analysis of the symmetric configuration

We consider the continuous-variable protocol of Pirandola et al. [Nature Photonics 9, 397-402 (2015), see also arXiv.1312.4104] where the secret-key is established by the measurement of an untrusted relay. In this network protocol, two authorized parties are connected to an untrusted relay by insecure quantum links. Secret correlations are generated by a continuous-variable Bell detection performed on incoming coherent states. In the present work we provide a detailed study of the symmetric configuration, where the relay is midway between the parties. We analyze symmetric eavesdropping strategies against the quantum links explicitly showing that, at fixed transmissivity and thermal noise, two-mode coherent attacks are optimal, manifestly outperforming one-mode collective attacks based on independent entangling cloners. Such an advantage is shown both in terms of security threshold and secret-key rate.

Reply to 'Discrete and continuous variables for measurement-device-independent quantum cryptography'

Stefano Pirandola, Carlo Ottaviani, Gaetana Spedalieri, Christian Weedbrook, Samuel L. Braunstein, Seth Lloyd, Tobias Gehring, Christian S. Jacobsen, and Ulrik L. Andersen Computer Science and York Centre for Quantum Technologies, University of York, York YO10 5GH, United Kingdom Department of Physics, University of Toronto, Toronto M5S 3G4, Canada Department of Mechanical Engineering and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge MA 02139, USA Department of Physics, Technical University of Denmark, Fysikvej, 2800 Kongens Lyngby, Denmark

Theory of channel simulation and bounds for private communication

We review recent results on the simulation of quantum channels, the reduction of adaptive protocols (teleportation stretching), and the derivation of converse bounds for quantum and private communication, as established in PLOB [Pirandola, Laurenza, Ottaviani, Banchi, arXiv:1510.08863]. We start by introducing a general weak converse bound for private communication based on the relative entropy of entanglement. We discuss how combining this bound with channel simulation and teleportation stretching, PLOB established the two-way quantum and private capacities of several fundamental channels, including the bosonic lossy channel. We then provide a rigorous proof of the strong converse property of these bounds by adopting a correct use of the Braunstein-Kimble teleportation protocol for the simulation of bosonic Gaussian channels. This analysis provides a full justification of claims presented in the follow-up paper WTB [Wilde, Tomamichel, Berta, arXiv:1602.08898] whose upper bounds for Gaussian channels would be otherwise infinitely large. Besides clarifying contributions in the area of channel simulation and protocol reduction, we also present some generalizations of the tools to other entanglement measures and novel results on the maximum excess noise which is tolerable in quantum key distribution.

Covariance Matrices under Bell-like Detections

We derive a simple formula for the transformation of an arbitrary covariance matrix of (n + 2) bosonic modes under general Bell-like detections, where the last two modes are combined in an arbitrary beam splitter (i.e., with arbitrary transmissivity) and then homodyned. In particular, we consider the realistic condition of non-unit quantum efficiency for the homodyne detectors. This formula can easily be specialized to describe the standard Bell measurement and the heterodyne detection, which are exploited in many contexts, including protocols of quantum teleportation, entanglement swapping and quantum cryptography. In its general form, our formula can be adopted to study quantum information protocols in the presence of experimental imperfections and asymmetric setups, e.g., deriving from the use of unbalanced beam splitters.

Asymmetric quantum hypothesis testing with Gaussian states

We consider the asymmetric formulation of quantum hypothesis testing, where two quantum hypotheses have different associated costs. In this problem, the aim is to minimize the probability of false negatives and the optimal performance is provided by the quantum Hoeffding bound. After a brief review of these notions, we show how this bound can be simplified for pure states. We then provide a general recipe for its computation in the case of multimode Gaussian states, also showing its connection with other easier-to-compute lower bounds. In particular, we provide analytical formulas and numerical results for important classes of one- and two-mode Gaussian states.

A limit formula for the quantum fidelity

Quantum fidelity is a central tool in quantum information, quantifying how much two quantum states are similar. By using the notion of generalized overlap, which occurs in the definition of the quantum Chernoff bound, we propose here a limit formula for the quantum fidelity between a mixed state and a pure state. As an example of an application, we apply this formula to the case of multimode Gaussian states, achieving a simple expression in terms of their first- and second-order statistical moments.

Quantum reading under a local energy constraint

Nonclassical states of light play a central role in many quantum information protocols. Their quantum features have been exploited to improve the readout of information from digital memories, modelled as arrays of microscopic beam splitters [S. Pirandola, Phys. Rev. Lett. 106, 090504 (2011)]. In this model of quantum reading, a nonclassical source of light with Einstein-Podolski-Rosen correlations has been proven to retrieve more information than any classical source. In particular, the quantum-classical comparison has been performed under a global energy constraint, i.e., by fixing the mean total number of photons irradiated over each memory cell. In this paper we provide an alternative analysis which is based on a local energy constraint, meaning that we fix the mean number of photons per signal mode irradiated over the memory cell. Under this assumption, we investigate the critical number of signal modes after which a nonclassical source of light is able to beat any classical source irradiating the same number of signals.

Channel Simulation in Quantum Metrology

Abstract In this review we discuss how channel simulation can be used to simplify the most general protocols of quantum parameter estimation, where unlimited entanglement and adaptive joint operations may be employed. Whenever the unknown parameter encoded in a quantum channel is completely transferred in an environmental program state simulating the channel, the optimal adaptive estimation cannot beat the standard quantum limit. In this setting, we elucidate the crucial role of quantum teleportation as a primitive operation which allows one to completely reduce adaptive protocols over suitable teleportation-covariant channels and derive matching upper and lower bounds for parameter estimation. For these channels,wemay express the quantum Cramér Rao bound directly in terms of their Choi matrices. Our review considers both discrete- and continuous-variable systems, also presenting some new results for bosonic Gaussian channels using an alternative sub-optimal simulation. It is an open problem to design simulations for quantum channels that achieve the Heisenberg limit.