State reconstruction of finite dimensional compound systems via local projective measurements and one-way classical communication

For a finite dimensional discrete bipartite system, we find the relation between local projections performed by Alice, and Bob post-selected state dependence on the global state submatrices. With this result the joint state reconstruction problem for a bipartite system can be solved with strict local projections and one-way classical communication. The generalization to multipartite systems is straightforward.Comment: 4 pages, 1 figur

Fourth post-Newtonian effective-one-body Hamiltonians with generic spins

In a compact binary coalescence, the spins of the compact objects can have a significant effect on the orbital motion and gravitational-wave (GW) emission. For generic spin orientations, the orbital plane precesses, leading to characteristic modulations of the GW signal. The observation of precession effects is crucial to discriminate among different binary formation scenarios, and to carry out precise tests of General Relativity. Here, we work toward an improved description of spin effects in binary inspirals, within the effective-one-body (EOB) formalism, which is commonly used to build waveform models for LIGO and Virgo data analysis. We derive EOB Hamiltonians including the complete fourth post-Newtonian (4PN) conservative dynamics, which is the current state of the art. We place no restrictions on the spin orientations or magnitudes, or on the type of compact object (e.g., black hole or neutron star), and we produce the first generic-spin EOB Hamiltonians complete at 4PN order. We consider multiple spinning EOB Hamiltonians, which are more or less direct extensions of the varieties found in previous literature, and we suggest another simplified variant. Finally, we compare the circular-orbit, aligned-spin binding-energy functions derived from the EOB Hamiltonians to numerical-relativity simulations of the late inspiral. While finding that all proposed Hamiltonians perform reasonably well, we point out some interesting differences, which could guide the selection of a simpler, and thus faster-to-evolve EOB Hamiltonian to be used in future LIGO and Virgo inference studies

Reduced Hamiltonian for next-to-leading order Spin-Squared Dynamics of General Compact Binaries

Within the post Newtonian framework the fully reduced Hamiltonian (i.e., with eliminated spin supplementary condition) for the next-to-leading order spin-squared dynamics of general compact binaries is presented. The Hamiltonian is applicable to the spin dynamics of all kinds of binaries with self-gravitating components like black holes and/or neutron stars taking into account spin-induced quadrupolar deformation effects in second post-Newtonian order perturbation theory of Einstein's field equations. The corresponding equations of motion for spin, position and momentum variables are given in terms of canonical Poisson brackets. Comparison with a nonreduced potential calculated within the Effective Field Theory approach is made.Comment: 11 pages, minor changes to match published version at CQ

An improved effective-one-body Hamiltonian for spinning black-hole binaries

Building on a recent paper in which we computed the canonical Hamiltonian of a spinning test particle in curved spacetime, at linear order in the particle's spin, we work out an improved effective-one-body (EOB) Hamiltonian for spinning black-hole binaries. As in previous descriptions, we endow the effective particle not only with a mass m, but also with a spin S*. Thus, the effective particle interacts with the effective Kerr background (having spin S_Kerr) through a geodesic-type interaction and an additional spin-dependent interaction proportional to S*. When expanded in post-Newtonian (PN) orders, the EOB Hamiltonian reproduces the leading order spin-spin coupling and the spin-orbit coupling through 2.5PN order, for any mass-ratio. Also, it reproduces all spin-orbit couplings in the test-particle limit. Similarly to the test-particle limit case, when we restrict the EOB dynamics to spins aligned or antialigned with the orbital angular momentum, for which circular orbits exist, the EOB dynamics has several interesting features, such as the existence of an innermost stable circular orbit, a photon circular orbit, and a maximum in the orbital frequency during the plunge subsequent to the inspiral. These properties are crucial for reproducing the dynamics and gravitational-wave emission of spinning black-hole binaries, as calculated in numerical relativity simulations.Comment: 22 pages, 9 figures. Minor changes to match version accepted for publication in PR

Entanglement and nonclassical properties of hypergraph states

Hypergraph states are multi-qubit states that form a subset of the locally maximally entangleable states and a generalization of the well--established notion of graph states. Mathematically, they can conveniently be described by a hypergraph that indicates a possible generation procedure of these states; alternatively, they can also be phrased in terms of a non-local stabilizer formalism. In this paper, we explore the entanglement properties and nonclassical features of hypergraph states. First, we identify the equivalence classes under local unitary transformations for up to four qubits, as well as important classes of five- and six-qubit states, and determine various entanglement properties of these classes. Second, we present general conditions under which the local unitary equivalence of hypergraph states can simply be decided by considering a finite set of transformations with a clear graph-theoretical interpretation. Finally, we consider the question whether hypergraph states and their correlations can be used to reveal contradictions with classical hidden variable theories. We demonstrate that various noncontextuality inequalities and Bell inequalities can be derived for hypergraph states.Comment: 29 pages, 5 figures, final versio

On the comparison of results regarding the post-Newtonian approximate treatment of the dynamics of extended spinning compact binaries

A brief review is given of all the Hamiltonians and effective potentials calculated hitherto covering the post-Newtonian (pN) dynamics of a two body system. A method is presented to compare (conservative) reduced Hamiltonians with nonreduced potentials directly at least up to the next-to-leading-pN order.Comment: Conference proceedings for the 7th International Conference on Gravitation and Cosmology (ICGC2011), 4 page

On Robust Discursive Equality

This paper explores the idea of robust discursive equality on which respect-based conceptions of justificatory reciprocity often draw. I distinguish between formal and substantive discursive equality and argue that if justificatory reciprocity requires that people be accorded formally equal discursive standing, robust discursive equality should not be construed as requiring standing that is equal substantively, or in terms of its discursive purchase. Still, robust discursive equality is purchase sensitive: it does not obtain when discursive standing is impermissibly unequal in purchase. I then showcase different candidate conceptions of purchase justice, and draw conclusions about the substantive commitments of justificatory reciprocity