Saddlepoint approximation for Student's t-statistic with no moment conditions

A saddlepoint approximation of the Student's t-statistic was derived by Daniels and Young [Biometrika 78 (1991) 169-179] under the very stringent exponential moment condition that requires that the underlying density function go down at least as fast as a Normal density in the tails. This is a severe restriction on the approximation's applicability. In this paper we show that this strong exponential moment restriction can be completely dispensed with, that is, saddlepoint approximation of the Student's t-statistic remains valid without any moment condition. This confirms the folklore that the Student's t-statistic is robust against outliers. The saddlepoint approximation not only provides a very accurate approximation for the Student's t-statistic, but it also can be applied much more widely in statistical inference. As a result, saddlepoint approximations should always be used whenever possible. Some numerical work will be given to illustrate these points.Comment: Published at http://dx.doi.org/10.1214/009053604000000742 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Necessity for quantum coherence of nondegeneracy in energy flow

In this work, we show that the quantum coherence among non-degenerate energy subspaces (CANES) is essential for the energy flow in any quantum system. CANES satisfies almost all of the requirements as a coherence measure, except that the coherence within degenerate subspaces is explicitly eliminated.We show that the energy of a system becomes frozen if and only if the corresponding CANES vanishes, which is true regardless of the form of interaction with the environment. However, CANES can remain zero even if the entanglement changes over time. Furthermore, we show how the power of energy flow is bounded by the value of CANES. An explicit relation connecting the variation of energy and CANES is also presented. These results allow us to bound the generation of system-environment correlation through the local measurement of the system's energy flow

Incompatibility of Observables as State-Independent Bound of Uncertainty Relations

For a pair of observables, they are called "incompatible", if and only if the commutator between them does not vanish, which represents one of the key features in quantum mechanics. The question is, how can we characterize the incompatibility among three or more observables? Here we explore one possible route towards this goal through Heisenberg's uncertainty relations, which impose fundamental constraints on the measurement precisions for incompatible observables. Specifically, we quantify the incompatibility by the optimal state-independent bounds of additive variance-based uncertainty relations. In this way, the degree of incompatibility becomes an intrinsic property among the operators, but not on the quantum state. To justify our case, we focus on the incompatibility of spin systems. For an arbitrary setting of two or three linearly-independent Pauli-spin operators, the incompatibility is analytically solved, the spins are maximally incompatible if and only if they are orthogonal to each other. On the other hand, the measure of incompatibility represents a versatile tool for applications such as testing entanglement of bipartite states, and EPR-steering criteria.Comment: Comments are welcom

A Comet Active Beyond the Crystallization Zone

We present observations showing in-bound long-period comet C/2017 K2 (PANSTARRS) to be active at record heliocentric distance. Nucleus temperatures are too low (60 K to 70 K) either for water ice to sublimate or for amorphous ice to crystallize, requiring another source for the observed activity. Using the Hubble Space Telescope we find a sharply-bounded, circularly symmetric dust coma 10$^5$ km in radius, with a total scattering cross section of $\sim$10$^5$ km$^2$. The coma has a logarithmic surface brightness gradient -1 over much of its surface, indicating sustained, steady-state dust production. A lack of clear evidence for the action of solar radiation pressure suggests that the dust particles are large, with a mean size $\gtrsim$ 0.1 mm. Using a coma convolution model, we find a limit to the apparent magnitude of the nucleus $V >$ 25.2 (absolute magnitude $H >$ 12.9). With assumed geometric albedo $p_V$ = 0.04, the limit to the nucleus circular equivalent radius is $<$ 9 km. Pre-discovery observations from 2013 show that the comet was also active at 23.7 AU heliocentric distance. While neither water ice sublimation nor exothermic crystallization can account for the observed distant activity, the measured properties are consistent with activity driven by sublimating supervolatile ices such as CO$_2$, CO, O$_2$ and N$_2$. Survival of supervolatiles at the nucleus surface is likely a result of the comet's recent arrival from the frigid Oort cloud.Comment: 20 pages, 3 figures, 2 tables, published on Astrophysical Journal Letters, 847:L19 (5pp), 2017 October