Leonardo Banchi

Fundamental limits of repeaterless quantum communications

Using a technique based on quantum teleportation, we simplify the most general adaptive protocols for key distribution, entanglement distillation and quantum communication over a wide class of quantum channels in arbitrary dimension. Thanks to this method, we bound the ultimate rates for secret key generation and quantum communication through single-mode Gaussian channels and several discrete-variable channels. In particular, we derive exact formulas for the two-way assisted capacities of the bosonic quantum-limited amplifier and the dephasing channel in arbitrary dimension, as well as the secret key capacity of the qubit erasure channel. Our results establish the limits of quantum communication with arbitrary systems and set the most general and precise benchmarks for testing quantum repeaters in both discreteand continuous-variable settings.

Nonperturbative Entangling Gates between Distant Qubits Using Uniform Cold Atom Chains

We propose a new fast scalable method for achieving a two-qubit entangling gate between arbitrary distant qubits in a network by exploiting dispersionless propagation in uniform chains. This is achieved dynamically by switching on a strong interaction between the qubits and a bus formed by a nonengineered chain of interacting qubits. The quality of the gate scales very efficiently with qubit separations. Surprisingly, a sudden switching of the couplings is not necessary. Moreover, our gate mechanism works for multiple gate operations without resetting the bus. We propose a possible experimental realization in cold atoms trapped in optical lattices and near field Fresnel trapping potentials.

Quantum fidelity for arbitrary Gaussian states

We derive a computable analytical formula for the quantum fidelity between two arbitrary multimode Gaussian states which is simply expressed in terms of their first- and second-order statistical moments. We also show how such a formula can be written in terms of symplectic invariants and used to derive closed forms for a variety of basic quantities and tools, such as the Bures metric, the quantum Fisher information, and various fidelity-based bounds. Our result can be used to extend the study of continuous-variable protocols, such as quantum teleportation and cloning, beyond the current one-mode or two-mode analyses, and paves the way to solve general problems in quantum metrology and quantum hypothesis testing with arbitrary multimode Gaussian resources.

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.

Perfect wave-packet splitting and reconstruction in a one-dimensional lattice

Particle delocalization is a common feature of quantum random walks in arbitrary lattices. However, in the typical scenario a particle spreads over multiple sites and its evolution is not directly useful for controlled quantum interferometry, as may be required for technological applications. In this paper we devise a strategy to perfectly split the wave-packet of an incoming particle into two components, each propagating in opposite directions, which reconstruct the shape of the initial wavefunction after a particular time

Photonic simulation of entanglement growth and engineering after a spin chain quench

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Pretty good state transfer in qubit chains-The Heisenberg Hamiltonian

. Therefore, a particle in a delta-like initial state becomes exactly delocalized between two distant sites after

Quantum gates between distant qubits via spin-independent scattering

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Spectral problem for quasi-uniform nearest-neighbor chains

. We find the mathematical conditions to achieve the perfect splitting which are satisfied by viable example Hamiltonians with static site-dependent interaction strengths. Our results pave the way for the generation of peculiar many-body interference patterns in a many-site atomic chain (like the Hanbury Brown and Twiss and quantum Talbot effects) as well as for the distribution of entanglement between remote sites. Thus, as for the case of perfect state transfer, the perfect wave-packet splitting can be a new tool for varied applications.

Simulation of non-Pauli channels

The time evolution of quantum many-body systems is one of the most important processes for benchmarking quantum simulators. The most curious feature of such dynamics is the growth of quantum entanglement to an amount proportional to the system size (volume law) even when interactions are local. This phenomenon has great ramifications for fundamental aspects, while its optimisation clearly has an impact on technology (e.g., for on-chip quantum networking). Here we use an integrated photonic chip with a circuit-based approach to simulate the dynamics of a spin chain and maximise the entanglement generation. The resulting entanglement is certified by constructing a second chip, which measures the entanglement between multiple distant pairs of simulated spins, as well as the block entanglement entropy. This is the first photonic simulation and optimisation of the extensive growth of entanglement in a spin chain, and opens up the use of photonic circuits for optimising quantum devices.The complete maximisation of the entanglement between two complementary blocks of spins due to the dynamics of spin chains remains to be observed. Here, Pitsios et al. simulate such dynamics by propagating single photons in an integrated photonic circuit.