We investigate the decay of entanglement of generalized N-particle Greenberger-Horne-Zeilinger (GHZ) states interacting with independent reservoirs. Scaling laws for the decay of entanglement and for its finite-time extinction (sudden death) are derived for different types of reservoirs. The latter is found to increase with N. However, entanglement becomes arbitrarily small, and therefore useless as a resource, much before it completely disappears, around a time which is inversely proportional to the number of particles. We also show that the decay of multiparticle GHZ states can generate bound entangled states.

Parameter estimation is of fundamental importance in areas from atomic spectroscopy and atomic clocks to gravitational wave-detection. Entangled probes provide a significant precision gain over classical strategies in the absence of noise. However, recent results seem to indicate that any small amount of realistic noise restricts the advantage of quantum strategies to an improvement by at most a multiplicative constant. Here we identify a relevant scenario in which one can overcome this restriction and attain super-classical precision scaling even in the presence of uncorrelated noise. We show that precision can be significantly enhanced when the noise is concentrated along some spatial direction, while the Hamiltonian governing the evolution which depends on the parameter to be estimated can be engineered to point along a different direction. In the case of perpendicular orientation, we find super-classical scaling and identify a state which achieves the optimum.Estimation of an unknown parameter is essential across disciplines from atomic spectroscopy and clocks [1][2][3] to gravitational wave-detection [4]. It is typically achieved by letting a probe, e.g. light, interact with the system under investigation, picking up information about the desired parameter. As seen in Fig. 1, a metrology protocol can be understood in four main steps [5,6]: i) preparation of the probe, ii) interaction with the system, iii) readout of the probe, and iv) construction of an estimate of the unknown parameter from the results. Steps (i)-(iii) may be repeated many times before the final construction of the estimate. FIG. 1.General metrology protocol where a known probe state evolves according to a physical evolution depending on an unknown parameter ω. After sufficient amount of data is collected an estimate for the parameter is constructed.The estimate uncertainty will depend on the available resources, here the probe size N and the total time T available for the experiment (other choices are possible [7]). By the central limit theorem, for N uncorrelated particles, the best uncertainty scales as 1/ √ νN , where ν = T /t is the number of evolve-and-measure rounds. This bound is known as the shot-noise or standard quantum limit (SQL). By making use of quantum phenomena, a metrology protocol may surpass the SQL, reaching instead the limits imposed by the quantum uncertainty relations. For probes of non-interacting particles, the best possible scaling compatible with these relations is 1/( √ νN ), known as the Heisenberg limit. Without noise, the Heisenberg limit can be attained using entangled input states, e.g. Greenberger-HorneZeilinger (GHZ) states for atomic spectroscopy [8]. In the presence of noise however, the picture is much less clear, as the optimal strategy depends strongly on the model of decoherence considered. Nevertheless, the SQL has been significantly surpassed in experiments of optical magnetometry [9,10], which proved that some sources of noise can be effectively counterbalanced [11,12]. However, unless one can k...

In recent years, the use of information principles to understand quantum correlations has been very successful. Unfortunately, all principles considered so far have a bipartite formulation, but intrinsically multipartite principles, yet to be discovered, are necessary for reproducing quantum correlations. Here we introduce local orthogonality, an intrinsically multipartite principle stating that events involving different outcomes of the same local measurement must be exclusive or orthogonal. We prove that it is equivalent to no-signalling in the bipartite scenario but more restrictive for more than two parties. By exploiting this nonequivalence, it is then demonstrated that some bipartite supra-quantum correlations do violate the local orthogonality when distributed among several parties. Finally, we show how its multipartite character allows revealing the non-quantumness of correlations for which any bipartite principle fails. We believe that local orthogonality is a crucial ingredient for understanding no-signalling and quantum correlations.