Continuous-variable quantum key distribution exploits coherent measurements of the electromagnetic field, i.e., homodyne or heterodyne detection. The most advanced security analyses developed so far relied on idealised mathematical models for such me
asurements, which assume that the measurement outcomes are continuous and unbounded variables. As any physical measurement device has finite range and precision, these mathematical models only serve as an approximation. It is expected that, under suitable conditions, the predictions obtained using these simplified models are in good agreement with the actual experimental implementations. However, a quantitative analysis of the error introduced by this approximation, and of its impact on composable security, have been lacking so far. Here we present a theory to rigorously account for the experimental limitations of realistic heterodyne detection. We focus on asymptotic security against collective attacks, and indicate a route to include finite-size effects.
Detecting the faint emission of a secondary source in the proximity of the much brighter source has been the most severe obstacle for using direct imaging in searching for exoplanets. Using quantum state discrimination and quantum imaging techniques,
we show that one can significantly reduce the probability of error for detecting the presence of a weak secondary source, even when the two sources have small angular separations. If the weak source has relative intensity $epsilon ll 1 $ to the bright source, we find that the error exponent can be improved by a factor of $1/epsilon$. We also find the linear-optical measurements that are optimal in this regime. Our result serves as a complementary method in the toolbox of optical imaging, from astronomy to microscopy.
Symmetry plays a fundamental role in the security analysis of quantum key distribution (QKD). Here we review how symmetry is exploited in continuous-variable (CV) QKD to prove the optimality of Gaussian attacks in the finite-size regime. We then appl
y these results to improve the efficiency, and thus the key rate, of these protocols. First we show how to improve the efficiency of the energy test, which is one important routine in a CV QKD protocol aimed at establishing an upper bound on the effective dimensions of the otherwise infinite-dimensional Hilbert space of CV systems. Second, we show how the routine of parameter estimation can be made resource efficient in measurement-device independent (MDI) QKD. These results show that all the raw data can be used both for key extraction and for the routines of energy test and parameter estimation.
The energy-time uncertainty relation puts a fundamental limit on the precision of radars and lidars for the estimation of range and velocity. The precision in the estimation of the range (through the time of arrival) and the velocity (through Doppler
frequency shifts) of a target are inversely related to each other, and dictated by the bandwidth of the signal. Here we use the theoretical toolbox of multi-parameter quantum metrology to determine the ultimate precision of the simultaneous estimation of range and velocity. We consider the case of a single target as well as a pair of closely separated targets. In the latter case, we focus on the relative position and velocity. We show that the trade-off between the estimation precision of position and velocity is relaxed for entangled probe states, and is completely lifted in the limit of infinite entanglement. In the regime where the two targets are close to each other, the relative position and velocity can be estimated nearly optimally and jointly, even without entanglement, using the measurements determined by the symmetric logarithmic derivatives.
We consider discrete-alphabet encoding schemes for coherent-state quantum key distribution. The sender encodes the letters of a finite-size alphabet into coherent states whose amplitudes are symmetrically distributed on a circle centered in the origi
n of the phase space. We study the asymptotic performance of this phase-encoded coherent-state protocol in direct and reverse reconciliation assuming both loss and thermal noise in the communication channel. In particular, we show that using just four phase-shifted coherent states is sufficient for generating secret key rates of the order of $4 times 10^{-3}$ bits per channel use at about 15 dB loss in the presence of realistic excess noise.
One crucial step in any quantum key distribution (QKD) scheme is parameter estimation. In a typical QKD protocol the users have to sacrifice part of their raw data to estimate the parameters of the communication channel as, for example, the error rat
e. This introduces a tradeoff between the secret key rate and the accuracy of parameter estimation in the finite-size regime. Here we show that continuous-variable (CV) QKD is not subject to this constraint as the whole raw keys can be used for both parameter estimation and secret key generation, without compromising the security. First we show that this property holds for measurement-device independent (MDI) protocols, as a consequence of the fact that in an MDI protocol the correlations between Alice and Bob are post-selected by the measurement performed by an untrusted relay. This result is then extended beyond the MDI framework by exploiting the fact that MDI protocols can simulate device-dependent one-way QKD with arbitrarily high precision.
The set of quantum Gaussian channels acting on one bosonic mode can be classified according to the action of the group of Gaussian unitaries. We look for bounds on the classical capacity for channels belonging to such a classification. Lower bounds c
an be efficiently calculated by restricting to Gaussian encodings, for which we provide analytical expressions.
We investigate the quantum state transfer in a chain of particles satisfying q-deformed oscillators algebra. This general algebraic setting includes the spin chain and the bosonic chain as limiting cases. We study conditions for perfect state transfe
r depending on the number of sites and excitations on the chain. They are formulated by means of irreducible representations of a quantum algebra realized through Jordan-Schwinger maps. Playing with deformation parameters, we can study the effects of nonlinear perturbations or interpolate between the spin and bosonic chain.
We study the robustness of geometric phase in the presence of parametric noise. For that purpose we consider a simple case study, namely a semiclassical particle which moves adiabatically along a closed loop in a static magnetic field acquiring the D
irac phase. Parametric noise comes from the interaction with a classical environment which adds a Brownian component to the path followed by the particle. After defining a gauge invariant Dirac phase, we discuss the first and second moments of the distribution of the Dirac phase angle coming from the noisy trajectory.
We consider the Schmidt decomposition of a bipartite density operator induced by the Hilbert-Schmidt scalar product, and we study the relation between the Schmidt coefficients and entanglement. First, we define the Schmidt equivalence classes of bipa
rtite states. Each class consists of all the density operators (in a given bipartite Hilbert space) sharing the same set of Schmidt coefficients. Next, we review the role played by the Schmidt coefficients with respect to the separability criterion known as the `realignment or `computable cross norm criterion; in particular, we highlight the fact that this criterion relies only on the Schmidt equivalence class of a state. Then, the relevance -- with regard to the characterization of entanglement -- of the `symmetric polynomials in the Schmidt coefficients and a new family of separability criteria that generalize the realignment criterion are discussed. Various interesting open problems are proposed.
