Andrea Mari

Positive Wigner functions render classical simulation of quantum computation efficient.

We show that quantum circuits where the initial state and all the following quantum operations can be represented by positive Wigner functions can be classically efficiently simulated. This is true both for continuous-variable as well as discrete variable systems in odd prime dimensions, two cases which will be treated on entirely the same footing. Noting the fact that Clifford and Gaussian operations preserve the positivity of the Wigner function, our result generalizes the Gottesman-Knill theorem. Our algorithm provides a way of sampling from the output distribution of a computation or a simulation, including the efficient sampling from an approximate output distribution in the case of sampling imperfections for initial states, gates, or measurements. In this sense, this work highlights the role of the positive Wigner function as separating classically efficiently simulable systems from those that are potentially universal for quantum computing and simulation, and it emphasizes the role of negativity of the Wigner function as a computational resource.

Measures of quantum synchronization in continuous variable systems.

We introduce and characterize two different measures which quantify the level of synchronization of coupled continuous variable quantum systems. The two measures allow us to extend to the quantum domain the notions of complete and phase synchronization. The Heisenberg principle sets a universal bound to complete synchronization. The measure of phase synchronization is, in principle, unbounded; however, in the absence of quantum resources (e.g., squeezing) the synchronization level is bounded below a certain threshold. We elucidate some interesting connections between entanglement and synchronization and, finally, discuss an application based on quantum optomechanical systems.

Quantum state majorization at the output of bosonic Gaussian channels

Quantum communication theory explores the implications of quantum mechanics to the tasks of information transmission. Many physical channels can be formally described as quantum Gaussian operations acting on bosonic quantum states. Depending on the input state and on the quality of the channel, the output suffers certain amount of noise. For a long time it has been conjectured, but never proved, that output states of Gaussian channels corresponding to coherent input signals are the less noisy ones (in the sense of a majorization criterion). Here we prove this conjecture. Specifically we show that every output state of a phase-insensitive Gaussian channel is majorized by the output state corresponding to a coherent input. The proof is based on the optimality of coherent states for the minimization of strictly concave output functionals. Moreover we show that coherent states are the unique optimizers.

Speeding up and slowing down the relaxation of a qubit by optimal control

We consider a two-level quantum system prepared in an arbitrary initial state and relaxing to a steady state due to the action of a Markovian dissipative channel. We study how optimal control can be used for speeding up or slowing down the relaxation towards the fixed point of the dynamics. We analytically derive the optimal relaxation times for different quantum channels in the ideal ansatz of unconstrained quantum control (a magnetic field of infinite strength). We also analyze the situation in which the control Hamiltonian is bounded by a finite threshold. As by-products of our analysis, we find that (i) if the qubit is initially in a thermal state hotter than the environmental bath, quantum control can not speed up its natural cooling rate; (ii) if the qubit is initially in a thermal state colder than the bath, it can reach the fixed point of the dynamics in finite time if a strong control field is applied; (iii) in the presence of unconstrained quantum control, it is possible to keep the evolved state indefinitely and arbitrarily close to special initial states which are far away from the fixed points of the dynamics.

Mutual information as an order parameter for quantum synchronization

Spontaneous synchronization is a fundamental phenomenon, important in many theoretical studies and applications. Recently, this effect has been analyzed and observed in a number of physical systems close to the quantum-mechanical regime. In this work we propose mutual information as a useful order parameter which can capture the emergence of synchronization in very different contexts, ranging from semiclassical to intrinsically quantum-mechanical systems. Specifically, we first study the synchronization of two coupled Van der Pol oscillators in both classical and quantum regimes and later we consider the synchronization of two qubits inside two coupled optical cavities. In all these contexts, we find that mutual information can be used as an appropriate figure of merit for determining the synchronization phases independently of the specific details of the system.

A generalization of the entropy power inequality to bosonic quantum systems

The conjectured entropy-power inequality, which determines the lower bound of channel capacity, is mathematically proved even in the quantum regime.

Opto- and electro-mechanical entanglement improved by modulation

One of the main milestones in the study of opto- and electro-mechanical systems is to certify entanglement between a mechanical resonator and an optical or microwave mode of a cavity field. In this work, we show how a suitable time-periodic modulation can help to achieve large degrees of entanglement, building upon the framework introduced in Mari and Eisert (2009 Phys. Rev. Lett. 103 213603). It is demonstrated that with suitable driving, the maximum degree of entanglement can be significantly enhanced, in a way exhibiting a nontrivial dependence on the specifics of the modulation. Such time-dependent driving might help to experimentally achieve entangled mechanical systems also in situations when quantum correlations are otherwise suppressed by thermal noise.

Directly estimating nonclassicality.

We establish a method of directly measuring and estimating nonclassicality--operationally defined in terms of the distinguishability of a given state from one with a positive Wigner function. It allows us to certify nonclassicality, based on possibly much fewer measurement settings than necessary for obtaining complete tomographic knowledge, and is at the same time equipped with a full certificate. We find that even from measuring two conjugate variables alone, one may infer the nonclassicality of quantum mechanical modes. This method also provides a practical tool to eventually certify such features in mechanical degrees of freedom in opto-mechanics. The proof of the result is based on Bochners theorem characterizing classical and quantum characteristic functions and on semidefinite programming. In this joint theoretical-experimental work we present data from experimental optical Fock state preparation.

Majorization and additivity for multimode bosonic Gaussian channels

We obtain a multimode extension of the majorization theorem for bosonic Gaussian channels, in particular, giving sufficient conditions under which the Glauber coherent states are the only minimizers for concave functionals of the output state of such a channel. We discuss direct implications of this multimode majorization for the positive solution of the famous additivity problem in the case of Gaussian channels. In particular, we prove the additivity of the output Rényi entropies of arbitrary order p > 1. Finally, we present an alternative, more direct derivation of a majorization property of the Husimi function established by Lieb and Solovej.

Optimal continuous variable quantum teleportation with limited resources

Given a certain amount of entanglement available as a resource, what is the most efficient way to accomplish a quantum task? We address this question in the relevant case of continuous variable quantum teleportation protocols implemented using two-mode Gaussian states with a limited degree of entanglement and energy. We first characterize the class of single-mode phase-insensitive Gaussian channels that can be simulated via a Braunstein-Kimble protocol with nonunit gain and minimum shared entanglement, showing that infinite energy is not necessary apart from the special case of the quantum limited attenuator. We also find that apart from the identity, all phase-insensitive Gaussian channels can be simulated through a two-mode squeezed state with finite energy, albeit with a larger entanglement. We then consider the problem of teleporting single-mode coherent states with Gaussian-distributed displacement in phase space. Performing a geometrical optimization over phase-insensitive Gaussian channels, we determine the maximum average teleportation fidelity achievable with any finite entanglement and for any realistically finite variance of the input distribution.