On the analytical convergence of the QPA procedure

We present an analytical proof of the convergence of the ``quantum privacy amplification'' procedure proposed by D. Deutsch et al. [Phys. Rev. Lett. 77, 2818 (1996)]. The proof specifies the range of states which can be purified by this method.Comment: 3 pages (revtex), 1 figure, to appear in Phys. Lett.

Detection of properties and capacities of quantum channels

We review in a unified way a recently proposed method to detect properties of unknown quantum channels and lower bounds to quantum capacities, without resorting to full quantum process tomography. The method is based on the preparation of a fixed bipartite entangled state at the channel input or, equivalently, an ensemble of an overcomplete set of single-system states, along with few local measurements at the channel output.Comment: 8 pages, 1 figure. arXiv admin note: text overlap with arXiv:1510.0021

Entanglement enhanced information transmission over a quantum channel with correlated noise

We show that entanglement is a useful resource to enhance the mutual information of the depolarizing channel when the noise on consecutive uses of the channel has some partial correlations. We obtain a threshold in the degree of memory, depending on the shrinking factor of the channel, above which a higher amount of classical information is transmitted with entangled signals

Mixed-state certification of quantum capacities for noisy communication channels

We extend a recent method to detect lower bounds to the quantum capacity of quantum communication channels by considering realistic scenarios with general input probe states and arbitrary detection procedures at the output. Realistic certification relies on a new bound for the coherent information of a quantum channel that can be applied with arbitrary bipartite mixed input states and generalized output measurements.Comment: 7 pages, 2 figure

Complementarity and correlations

We provide an interpretation of entanglement based on classical correlations between measurement outcomes of complementary properties: states that have correlations beyond a certain threshold are entangled. The reverse is not true, however. We also show that, surprisingly, all separable nonclassical states exhibit smaller correlations for complementary observables than some strictly classical states. We use mutual information as a measure of classical correlations, but we conjecture that the first result holds also for other measures (e.g. the Pearson correlation coefficient or the sum of conditional probabilities).Comment: Published version (+1 reference

Tight entropic uncertainty relations for systems with dimension three to five

We consider two (natural) families of observables $O_k$ for systems with dimension $d=3,4,5$: the spin observables $S_x$, $S_y$ and $S_z$, and the observables that have mutually unbiased bases as eigenstates. We derive tight entropic uncertainty relations for these families, in the form $\sum_kH(O_k)\geqslant\alpha_d$, where $H(O_k)$ is the Shannon entropy of the measurement outcomes of $O_k$ and $\alpha_d$ is a constant. We show that most of our bounds are stronger than previously known ones. We also give the form of the states that attain these inequalities

Entanglement-assisted quantum metrology

Entanglement-assisted quantum communication employs pre-shared entanglement between sender and receiver as a resource. We apply the same framework to quantum metrology, introducing shared entanglement between the preparation and the measurement stage, namely using some entangled ancillary system that does not interact with the system to be sampled. This is known to be useless in the noiseless case, but was recently shown to be useful in the presence of noise. Here we detail how and when it can be of use. For example, surprisingly it is useful when randomly time sharing two channels where ancillas do not help (depolarizing). We show that it is useful for all levels of noise for many noise models and propose a simple experiment to test these results.Comment: 5 pages, 5 figure

Digital Quantum Estimation

Quantum Metrology calculates the ultimate precision of all estimation strategies, measuring what is their root mean-square error (RMSE) and their Fisher information. Here, instead, we ask how many bits of the parameter we can recover, namely we derive an information-theoretic quantum metrology. In this setting we redefine "Heisenberg bound" and "standard quantum limit" (the usual benchmarks in quantum estimation theory), and show that the former can be attained only by sequential strategies or parallel strategies that employ entanglement among probes, whereas parallel-separable strategies are limited by the latter. We highlight the differences between this setting and the RMSE-based one.Comment: 5 pages+5 supplementary informatio

Multipartite steering inequalities based on entropic uncertainty relations

We investigate quantum steering for multipartite systems by using entropic uncertainty relations. We introduce entropic steering inequalities whose violation certifies the presence of different classes of multipartite steering. These inequalities witness both steerable states and genuine multipartite steerable states. Furthermore, we study their detection power for several classes of states of a three-qubit system.Comment: 3 figure

Economical Phase-Covariant Cloning of Qudits

We derive the optimal N to M phase-covariant quantum cloning for equatorial states in dimension d with M=kd+N, k integer. The cloning maps are optimal for both global and single-qudit fidelity. The map is achieved by an ``economical'' cloning machine, which works without ancilla.Comment: 10 pages revtex4, 7 figures, replaced with modified versio