Raffaele Romano

An optimal entropic uncertainty relation in a two-dimensional Hilbert space ☆

We derive an optimal entropic uncertainty relation for an arbitrary pair of observables in a two-dimensional Hilbert space. Such a result, for the simple case we are considering, definitively improves all the entropic uncertainty relations which have appeared in the literature.

Complete positivity and entangled degrees of freedom

We study how some recently proposed noncontextuality tests based on quantum interferometry are affected if the test particles propagate as open systems in the presence of a Gaussian stochastic background. We show that physical consistency requires the resulting Markovian dissipative time evolution to be completely positive.

Complete positivity and dissipative factorized dynamics

We show that any Hermiticity and trace-preserving continuous semigroup {γt}t≥0 in d dimensions is completely positive if and only if the semigroup {γt ⊗ γt}t≥0 is positivity-preserving.

On a proposal of superluminal communication

Recently, various new proposals of superluminal transmission of information have been suggested in the literature. Since the proposals make systematic use of recent formal and practical improvements in quantum mechanics, the old theorems proving the impossibility of such a performance must be adapted to the new scenario. In this communication, we consider some of the most challenging proposals of this kind and we show why they cannot work.

A method for exact simulation of quantum dynamics

We propose a method to simulate exactly quantum dynamics for finite-dimensional quantum systems and analyze its complexity. We apply this method to the exact simulation of any unitary using the dynamics of a time-varying discrete quantum walk on a graph. For this example, in the special case where the graph is a cycle, we show that the complexity grows like Nlogu2009N, N being the number of vertices of the graph.

Analysis and design of parallel concatenated channel codes for Quantum Key Distribution (QKD) applications

Objective of this paper is the study of Quantum Key Distribution (QKD) protocols based on classical error-correcting codes. The Quantum Key Distribution (QKD) systems and related protocols, in particular conditions, can use the classic channel coding techniques, instead of quantum error-correcting codes, both for correcting errors that occurred during the exchange of a cryptographic key between two authorized users, and to allow privacy amplification, in order to make completely vain a possible intruder attempt. The secret key is transmitted over a quantum, and thus safe, channel, characterized by very low transmission rates and high error rates. This channel is safe for the properties of a quantum system, where each measurement on the system perturbs the system itself, allowing the authorized users to “feel” if there is any intruder listening. Moreover, as shown by accurate experimental studies, the communication channel used for quantum key exchange is not able to reach high levels of reliability (the Quantum Bit Error Rate (QBER) takes values between 0.05 and 0.11), both because of the inherent characteristics of the system, and of the presence of a possible attacker. Thus, in order to obtain acceptable residual error rates, it is necessary to use a parallel classical and public channel, conversely characterized by high transmission rates and low error rates, on which to transmit only the redundancy bits of systematic channel codes with performance possibly close to the capacity limit.

Optimal generation of entanglement under local control

We study the optimal generation of entanglement between two qubits subject to local unitary control. With the only assumptions of linear control and unitary dynamics, by means of a numerical protocol based on the variational approach (Pontryagins Minimum Principle), we evaluate the optimal control strategy leading to the maximal achievable entanglement in an arbitrary interaction time, taking into account the energy cost associated to the controls. In our model we can arbitrarily choose the relative weight between a large entanglement and a small energy cost.

Indirect controllability and indirect observability of quantum mechanical systems

In many experiments, a target quantum mechanical system is controlled and-or measured indirectly using an auxiliary quantum system. In the case of control, this means that the control action only affects the auxiliary system while the evolution of the target system is affected indirectly through the interaction with the auxiliary system. In the case of measurement, only the state of the auxiliary system can be measured, providing information on the initial state of the target system. Indirect controllability is the property of the target system of being driven between two arbitrary states while indirect observability refers to the possibility of extracting all the information on the state of the target system by measuring the auxiliary system. This paper has three main goals. First, we summarize recent notions and results introduced by us on the study of indirect controllability. Then, we present some new technical results on indirect controllability. In particular, we present a counterexample to the converse of a criterion for indirect controllability, which shows that the Lie algebraic condition introduced in this criterion is necessary but not sufficient for indirect controllability. This gives an open problem which is how to strengthen this condition to obtain a necessary and sufficient condition for indirect controllability. Lastly, we present a parallel treatment of indirect observability, give the relevant notions and definitions and relate the properties of indirect controllability and observability. Our final result says that strong notions of indirect controllability and observability are equivalent properties to complete controllability of the system. We discuss examples of physical systems which are controlled and-or measured indirectly. The research is motivated by experimental schemes of current interest

Turbo codes for quantum key distribution (QKD) applications

This paper investigates further on Quantum Key Distribution (QKD) protocols based on classical error-correcting codes, previously proposed by the authors. In [1], the classic channel coding techniques were shown to be suitable, in particular conditions, instead of quantum error-correcting codes, for correcting errors that occur during the exchange of a cryptographic key between two authorized users. To this end, systematic parallel concatenated codes, also known as turbo codes, were proposed in [1]. In this paper we address the properties that the systematic parallel concatenated codes must have in order to be successfully used in a QKD protocol. In particular, we address the problem, not considered in [1], that the constituent codes used in the parallel concatenation scheme must be such that the information sequence cannot be easily recovered from the encoder output sequences. In fact, the parallel classical channel on which to transmit only the redundancy bits is highly reliable but also public, i.e., very vulnerable as far as the attack attempts of a possible attacker are concerned.

An Open Quantum System Approach to the B-Mesons System

AbstractIn this paper we consider a nonstandard evolution for the B0-n