Related papers: Diffraction limit of the sub-Planck structures
In quantum phase estimation, the Heisenberg limit provides the ultimate accuracy over quasi-classical estimation procedures. However, realizing this limit hinges upon both the detection strategy employed for output measurements and the…
Quantization dimension has been computed for many invariant measures of dynamically defined fractals having well separated cylinders, that is, in the cases when the so-called Open Set Condition (OSC) holds. To attack the same problem in…
The recent paper of Lieu and Hillman [1] that a possible, (birefringence like) phase difference ambiguity coming from Planck effects would alter stellar images of distant sources is questioned. Instead for {\em division of wavefront}…
We describe the interplay of quantum and thermal fluctuations in the infinite-range Heisenberg spin glass. This model is generalized to SU(N) symmetry, and we describe the phase diagram as a function of the spin S and the temperature T. The…
Adaptive techniques make practical many quantum measurements that would otherwise be beyond current laboratory capabilities. For example: they allow discrimination of nonorthogonal states with a probability of error equal to the Helstrom…
We consider discrete spectra of bound states for non-relativistic motion in attractive potentials V_{\sigma}(x) = -|V_{0}| |x|^{-\sigma}, 0 < \sigma \leq 2. For these potentials the quasiclassical approximation for n -> \infty predicts…
The state of a microscopic system encodes its complete quantum description, from which the probabilities of all measurement outcomes are inferred. Being a statistical concept, the state cannot be obtained from a single system realization.…
In a seminal paper [8] it was shown that Heisenberg-limited measurements could be achieved without using entangled states by coupling the quantum resources to a common environment that could be measured, at least, in part. The authors also…
The entangled Schrodinger cat state obtained immediately upon measurement of a superposed two-state quantum system is often considered paradoxical because it appears to predict two macroscopically different outcomes, such as an alive and…
We study optimal design problems where the design corresponds to a coefficient in the principal part of the state equation. The state equation, in addition, is parameter dependent, and we allow it to change type in the limit of this…
Much of the discussion of decoherence has been in terms of a particle moving in one dimension that is placed in an initial superposition state (a Schr\"{o}dinger "cat" state) corresponding to two widely separated wave packets. Decoherence…
Spin cat states are promising candidates for quantum-enhanced measurement. Here, we analytically show that the ultimate measurement precision of spin cat states approaches the Heisenberg limit, where the uncertainty is inversely…
We propose a method to perform precision measurements of the interaction parameters in systems of N ultra-cold spin 1/2 atoms. The spectroscopy is realized by first creating a coherent spin superposition of the two relevant internal states…
Information recycling has been shown to improve the sensitivity of atom interferometers by exploiting atom-light entanglement. In this paper, we apply information recycling to an interferometer where the input quantum state has been…
We examine the results of the paper "Precision metrology using weak measurements", [Zhang, Datta, and Walmsley, arXiv:1310.5302] from a quantum state discrimination point of view. The Heisenberg scaling of the photon number for the…
Linear superpositions of macroscopically distinct quantum states (sometimes also called Schr\"odinger cat states) are usually almost immediately reduced to a statistical mixture if exposed to the dephasing influence of a dissipative…
Quantum coherence of electrons interacting via the magnetostatic coupling and confined to a mesoscopic cylinder is discussed. The electromagnetic response of a system is studied. It is shown that the electromagnetic kernel has finite low…
We prove strictly that one dimension spin 1/2 Heisenberg model has a symmetry of energy spectrum between its subspace $n$ and the subspace $L-n$ of the Fock space. Our proof is completed by introducing two general quantum operations. One is…
Despite nearly a century of study of the $S=1/2$ Heisenberg model on the square lattice, there is still disagreement on the nature of its high-energy excitations. By tuning toward the Heisenberg model from the exactly soluble Ising limit,…
The overlap measurement scheme accomplishes to evaluate the overlap of two input quantum states by only measuring an introduced auxiliary qubit, irrespective of the complexity of the two input states. We find a counterintuitive phenomenon…