Related papers: Interference of macroscopic superpositions
Macrorealism is a classical world view asserting that the properties of macro-objects exist independently and irrespective of observation. One practical approach to test this view in quantum theory is to observe the quantum coherence for…
The 2-sets convex feasibility problem aims at finding a point in the nonempty intersection of two closed convex sets $A$ and $B$ in a Hilbert space $X$. The method of alternating projections is the simplest iterative procedure for finding a…
For any persistence module $M$ over a finite poset $\mathbf{P}$, and any interval $I$ of $\mathbf{P}$, we give a formula for the multiplicity $d_M(V_I)$ of the interval module $V_I$ in the indecomposable decomposition of $M$ in terms of the…
Classical wisdom of wave-particle duality says that it is impossible to observe simultaneously the wave and particle nature of microscopic object. Mathematically the principle requests that the interference visibility V and which-path…
We propose an experimental scheme to implement a second-order nonlocal superposition operation and its variants by way of Hong-Ou-Mandel interference. The second-order coherent operations enable us to generate a NOON state with high…
We are interested in developing a numerical method for capturing stationary sheaths, that a plasma forms in contact with a metallic wall. This work is based on a bi-species (ion/electron) Vlasov-Amp{\`e}re model proposed in [3]. The main…
In attempting to derive irreversible macroscopic thermodynamics from reversible microscopic dynamics, Boltzmann inadvertently smuggled in a premise that assumed the very irreversibility he was trying to prove: 'molecular chaos.' The program…
The double-slit experiment strikingly demonstrates the wave-particle duality of quantum objects. In this famous experiment, particles pass one-by-one through a pair of slits and are detected on a distant screen. A distinct wave-like pattern…
We present a unified deterministic approach for experimental design problems using the method of interlacing polynomials. Our framework recovers the best-known approximation guarantees for the well-studied D/A/E-design problems with simple…
Given two arbitrary closed sets in Euclidean space, a simple transversality condition guarantees that the method of alternating projections converges locally, at linear rate, to a point in the intersection. Exact projection onto nonconvex…
We assess the most macroscopic matter-wave experiments to date as to the extent to which they probe the quantum-classical boundary by demonstrating interference of heavy molecules and cold atomic ensembles. To this end, we consider a…
Sufficient conditions for the design of a simple class of interval observers for linear impulsive systems subject to minimum and range dwell-time constraints are obtained and formulated in terms of infinite-dimensional linear programs. The…
We develop a formalism for the calculation of the macroscopic dielectric response of composite systems made of particles of one material embedded periodically within a matrix of another material, each of which is characterized by a well…
While persistent homology has taken strides towards becoming a wide-spread tool for data analysis, multidimensional persistence has proven more difficult to apply. One reason is the serious drawback of no longer having a concise and…
We study variational obstacle avoidance problems on complete Riemannian manifolds and apply the results to the construction of piecewise smooth curves interpolating a set of knot points in systems with impulse effects. We derive the…
We consider shifts of a set $A\subseteq\mathbb{N}$ by elements from another set $B\subseteq\mathbb{N}$, and prove intersection properties according to the relative asymptotic size of $A$ and $B$. A consequence of our main theorem is the…
This paper considers the problem of testing whether there exists a non-negative solution to a possibly under-determined system of linear equations with known coefficients. This hypothesis testing problem arises naturally in a number of…
For an even set of points in the plane, choose a max-sum matching, that is, a perfect matching maximizing the sum of Euclidean distances of its edges. For each edge of the max-sum matching, consider the ellipse with foci at the edge's…
Given a complex structure, we investigate diverging sequences of projective structures on the fixed complex structure in terms of Thurston's parametrization. In particular, we will give a geometric proof to the theorem by Kapovich stating…
Inserting a lossy dielectric into one arm of an interference experiment acts in many ways like a measurement. If two entangled photons are passed through the interferometer, a certain amount of information is gained about which path they…