The Wehrl entropy has Gaussian optimizers

We determine the minimum Wehrl entropy among the quantum states with a given von Neumann entropy, and prove that it is achieved by thermal Gaussian states. This result determines the relation between the von Neumann and the Wehrl entropies. The key idea is proving that the quantum-classical channel that associates to a quantum state its Husimi Q representation is asymptotically equivalent to the Gaussian quantum-limited amplifier with infinite amplification parameter. This equivalence also permits to determine the p->q norms of the aforementioned quantum-classical channel in the two particular cases of one mode and p=q, and prove that they are achieved by thermal Gaussian states. The same equivalence permits to prove that the Husimi Q representation of a one-mode passive state (i.e. a state diagonal in the Fock basis with eigenvalues decreasing as the energy increases) majorizes the Husimi Q representation of any other one-mode state with the same spectrum, i.e. it maximizes any convex functional.Comment: Proof extended to multimode state

New lower bounds to the output entropy of multi-mode quantum Gaussian channels

We prove that quantum thermal Gaussian input states minimize the output entropy of the multi-mode quantum Gaussian attenuators and amplifiers that are entanglement breaking and of the multi-mode quantum Gaussian phase contravariant channels among all the input states with a given entropy. This is the first time that this property is proven for a multi-mode channel without restrictions on the input states. A striking consequence of this result is a new lower bound on the output entropy of all the multi-mode quantum Gaussian attenuators and amplifiers in terms of the input entropy. We apply this bound to determine new upper bounds to the communication rates in two different scenarios. The first is classical communication to two receivers with the quantum degraded Gaussian broadcast channel. The second is the simultaneous classical communication, quantum communication and entanglement generation or the simultaneous public classical communication, private classical communication and quantum key distribution with the Gaussian quantum-limited attenuator

Uncertainty relations with quantum memory for the Wehrl entropy

We prove two new fundamental uncertainty relations with quantum memory for the Wehrl entropy. The first relation applies to the bipartite memory scenario. It determines the minimum conditional Wehrl entropy among all the quantum states with a given conditional von Neumann entropy and proves that this minimum is asymptotically achieved by a suitable sequence of quantum Gaussian states. The second relation applies to the tripartite memory scenario. It determines the minimum of the sum of the Wehrl entropy of a quantum state conditioned on the first memory quantum system with the Wehrl entropy of the same state conditioned on the second memory quantum system and proves that also this minimum is asymptotically achieved by a suitable sequence of quantum Gaussian states. The Wehrl entropy of a quantum state is the Shannon differential entropy of the outcome of a heterodyne measurement performed on the state. The heterodyne measurement is one of the main measurements in quantum optics and lies at the basis of one of the most promising protocols for quantum key distribution. These fundamental entropic uncertainty relations will be a valuable tool in quantum information and will, for example, find application in security proofs of quantum key distribution protocols in the asymptotic regime and in entanglement witnessing in quantum optics

Long-term effects of a mandatory multistage program: the New Deal for young people in the UK

The New Deal For Young People is the major welfare-to-work program in the UK. It is a mandatory multistage policy targeted at the 18-24 year old unemployed. This paper investigates the effectiveness of the program in terms of enhancing the (re)employment probability of participant males. I exploit the eligibility rule to identify a suitable counterfactual relying upon a simple regression discontinuity design. By exploiting such a discontinuity I am able to non parametrically identify (Hahn et al., 2001) a local average treatment effect (LATE). While relying upon the non parametric local linear regression method I am able to push forward such a parameter to a "global" dimension, implicitly adding parametric structure. No evidence of possible general equilibrium as well as substitution effects is found by a co- hort specific approach (before and after the program). The main result is that the program enhances employability by about 6-7%.Labour market policy evaluation, regression discontinuity, non parametric

Strategic Registration of Voters: The Chilean Case

In this paper we investigate how the employment relationship, if it implies transfer of rents, may allow employers to control the voting behavior of their workers and lead to strategic registration of voters. This is feasible when individual voting behavior is observable, as in open ballot elections. More easily controlled voters are more likely registered providing an even larger impact of vote controlling on election results. Making individual vote truly secret (for instance with the adoption of a secret ballot) significantly reduces this control. Moreover, we show that as long as electoral districts are heterogeneous enough, i.e., contain also free voters, any attempt to control votes on the basis of district aggregate results is bound to fail. We test the predictions of the model by examining in detail the effects of the introduction of thesecret ballot in Chile in 1958.

The conditional entropy power inequality for quantum additive noise channels

We prove the quantum conditional Entropy Power Inequality for quantum additive noise channels. This inequality lower bounds the quantum conditional entropy of the output of an additive noise channel in terms of the quantum conditional entropies of the input state and the noise when they are conditionally independent given the memory. We also show that this conditional Entropy Power Inequality is optimal in the sense that we can achieve equality asymptotically by choosing a suitable sequence of Gaussian input states. We apply the conditional Entropy Power Inequality to find an array of information-theoretic inequalities for conditional entropies which are the analogues of inequalities which have already been established in the unconditioned setting. Furthermore, we give a simple proof of the convergence rate of the quantum Ornstein-Uhlenbeck semigroup based on Entropy Power Inequalities.Comment: 26 pages; updated to match published versio