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Articles 1 - 12 of 12
Full-Text Articles in Physics
Optimizing Measurement Strengths For Qubit Quasiprobabilities Behind Out-Of-Time-Ordered Correlators, Razieh Mohseninia, José Raúl González Alonso, Justin Dressel
Optimizing Measurement Strengths For Qubit Quasiprobabilities Behind Out-Of-Time-Ordered Correlators, Razieh Mohseninia, José Raúl González Alonso, Justin Dressel
Mathematics, Physics, and Computer Science Faculty Articles and Research
Out-of-time-ordered correlators (OTOCs) have been proposed as a tool to witness quantum information scrambling in many-body system dynamics. These correlators can be understood as averages over nonclassical multitime quasiprobability distributions (QPDs). These QPDs have more information and their nonclassical features witness quantum information scrambling in a more nuanced way. However, their high dimensionality and nonclassicality make QPDs challenging to measure experimentally. We focus on the topical case of a many-qubit system and show how to obtain such a QPD in the laboratory using circuits with three and four sequential measurements. Averaging distinct values over the same measured distribution reveals either …
Schrödinger Evolution Of Superoscillations With Δ - And Δ′ -Potentials, Yakir Aharonov, Jussi Behrndt, Fabrizio Colombo, Peter Schlosser
Schrödinger Evolution Of Superoscillations With Δ - And Δ′ -Potentials, Yakir Aharonov, Jussi Behrndt, Fabrizio Colombo, Peter Schlosser
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper, we study the time persistence of superoscillations as the initial data of the time-dependent Schrödinger equation with δ- and δ′-potentials. It is shown that the sequence of solutions converges uniformly on compact sets, whenever the initial data converge in the topology of the entire function space A1(C). Convolution operators acting in this space are our main tool. In particular, a general result about the existence of such operators is proven. Moreover, we provide an explicit formula as well as the large time asymptotics for the time evolution of a plane wave under δ- and δ′-potentials.
Topological Bound States For Quantum Charges, Yakir Aharonov, Ismael L. Paiva, Jeff Tollaksen, Mordecai Waegell
Topological Bound States For Quantum Charges, Yakir Aharonov, Ismael L. Paiva, Jeff Tollaksen, Mordecai Waegell
Mathematics, Physics, and Computer Science Faculty Articles and Research
We discuss how, in appropriately designed configurations, solenoids carrying a semifluxon can be used as topological energy barriers for charged quantum systems. We interpret this phenomenon as a consequence of the fact that such solenoids induce nodal lines in the wave function describing the charge, which on itself is a consequence of the Aharonov-Bohm effect. Moreover, we present a thought experiment with a cavity where two solenoids are sufficient to create bound states.
Diffraction-Based Interaction-Free Measurements, Spencer Rogers, Yakir Aharonov, Cyril Elouard, Andrew N. Jordan
Diffraction-Based Interaction-Free Measurements, Spencer Rogers, Yakir Aharonov, Cyril Elouard, Andrew N. Jordan
Mathematics, Physics, and Computer Science Faculty Articles and Research
We introduce diffraction-based interaction-free measurements. In contrast with previous work where a set of discrete paths is engaged, good-quality interaction-free measurements can be realized with a continuous set of paths, as is typical of optical propagation. If a bomb is present in a given spatial region—so sensitive that a single photon will set it off—its presence can still be detected without exploding it. This is possible because, by not absorbing the photon, the bomb causes the single photon to diffract around it. The resulting diffraction pattern can then be statistically distinguished from the bomb-free case. We work out the case …
Benchmarks Of Nonclassicality For Qubit Arrays, Mordecai Waegell, Justin Dressel
Benchmarks Of Nonclassicality For Qubit Arrays, Mordecai Waegell, Justin Dressel
Mathematics, Physics, and Computer Science Faculty Articles and Research
We present a set of practical benchmarks for N-qubit arrays that economically test the fidelity of achieving multi-qubit nonclassicality. The benchmarks are measurable correlators similar to two-qubit Bell correlators, and are derived from a particular set of geometric structures from the N-qubit Pauli group. These structures prove the Greenberger–Horne–Zeilinger (GHZ) theorem, while the derived correlators witness genuine N-partite entanglement and establish a tight lower bound on the fidelity of particular stabilizer state preparations. The correlators need only M ≤ N + 1 distinct measurement settings, as opposed to the 22N − 1 settings that would normally be …
A Panorama On Superoscillations, Fabrizio Colombo, Irene Sabadini, Daniele Carlo Struppa
A Panorama On Superoscillations, Fabrizio Colombo, Irene Sabadini, Daniele Carlo Struppa
Mathematics, Physics, and Computer Science Faculty Articles and Research
Purpose of this note is to give an overview on superoscillating sequences and some of their properties. We discuss their persistence in time under Schrödinger equation, we propose various classes of superoscillating functions and we also briefly mention how they can be used to approximate some generalized functions.
Weak Value Amplification For Nonunitary Evolution, Wei-Tao Liu, Julián Martínez-Rincón, John C. Howell
Weak Value Amplification For Nonunitary Evolution, Wei-Tao Liu, Julián Martínez-Rincón, John C. Howell
Mathematics, Physics, and Computer Science Faculty Articles and Research
We discuss interferometric parameter estimation of the amplitude, instead of the phase, via weak value amplification. The considered weak interaction introduces modulation on the amplitude of the wave function; therefore, the two-party state experiences a nonunitary evolution. With the same pre- and postselection states as those of original weak value amplification, a much larger anomalous amplification factor can be attained. The shift in the intensity profile at the dark port and the signal-to-noise ratio for the parameter of interest get further amplified by the weak value, compared to phase-based weak value amplification. Although the nonunitary evolution introduces loss, more information …
The Nature Of The Heisenberg-Von Neumann Cut: Enhanced Orthodox Interpretation Of Quantum Mechanics, Ashok Narasimhan, Deepak Chopra, Menas Kafatos
The Nature Of The Heisenberg-Von Neumann Cut: Enhanced Orthodox Interpretation Of Quantum Mechanics, Ashok Narasimhan, Deepak Chopra, Menas Kafatos
Mathematics, Physics, and Computer Science Faculty Articles and Research
We examine the issue of the Heisenberg-von Neumann cut in light of recent interpretations of quantum eraser experiments which indicate the possibility of a universal Observer outside space-time at an information level of existence. The delayed-choice aspects of observation, measurement, the role of the observer, and information in the quantum framework of the universe are discussed. While traditional double-slit experiments are usually interpreted as indicating that the collapse of the wave function involves choices by an individual observer in space-time, the extension to quantum eraser experiments brings in some additional subtle aspects relating to the role of observation and what …
Roadmap On Superoscillations, Michael Berry, Nicolay Zheludev, Yakir Aharonov, Fabrizio Colombo, Irene Sabadini, Daniele C. Struppa, Jeff Tollaksen, Edward T. F. Rogers, Fei Qin, Minghui Hong, Xiangang Luo, Roei Remez, Ady Arie, Jörg B. Götte, Mark R. Dennis, Alex M. H. Wong, George V. Eleftheriades, Yaniv Eliezer, Alon Bahabad, Gang Chen, Zhongquan Wen, Gaofeng Liang, Chenglong Hao, C-W Qiu, Achim Kempf, Eytan Katzav, Moshe Schwartz
Roadmap On Superoscillations, Michael Berry, Nicolay Zheludev, Yakir Aharonov, Fabrizio Colombo, Irene Sabadini, Daniele C. Struppa, Jeff Tollaksen, Edward T. F. Rogers, Fei Qin, Minghui Hong, Xiangang Luo, Roei Remez, Ady Arie, Jörg B. Götte, Mark R. Dennis, Alex M. H. Wong, George V. Eleftheriades, Yaniv Eliezer, Alon Bahabad, Gang Chen, Zhongquan Wen, Gaofeng Liang, Chenglong Hao, C-W Qiu, Achim Kempf, Eytan Katzav, Moshe Schwartz
Mathematics, Physics, and Computer Science Faculty Articles and Research
Superoscillations are band-limited functions with the counterintuitive property that they can vary arbitrarily faster than their fastest Fourier component, over arbitrarily long intervals. Modern studies originated in quantum theory, but there were anticipations in radar and optics. The mathematical understanding—still being explored—recognises that functions are extremely small where they superoscillate; this has implications for information theory. Applications to optical vortices, sub-wavelength microscopy and related areas of nanoscience are now moving from the theoretical and the demonstrative to the practical. This Roadmap surveys all these areas, providing background, current research, and anticipating future developments.
Realization Of Tensor Product And Of Tensor Factorization Of Rational Functions, Daniel Alpay, Izchak Lewkowicz
Realization Of Tensor Product And Of Tensor Factorization Of Rational Functions, Daniel Alpay, Izchak Lewkowicz
Mathematics, Physics, and Computer Science Faculty Articles and Research
We study the state space realization of a tensor product of a pair of rational functions. At the expense of “inflating” the dimensions, we recover the classical expressions for realization of a regular product of rational functions. Under an additional assumption that the limit at infinity of a given rational function exists and is equal to identity, we introduce an explicit formula for a tensor factorization of this function.
Out-Of-Time-Ordered-Correlator Quasiprobabilities Robustly Witness Scrambling, José Raúl González Alonso, Nicole Yunger Halpern, Justin Dressel
Out-Of-Time-Ordered-Correlator Quasiprobabilities Robustly Witness Scrambling, José Raúl González Alonso, Nicole Yunger Halpern, Justin Dressel
Mathematics, Physics, and Computer Science Faculty Articles and Research
Out-of-time-ordered correlators (OTOCs) have received considerable recent attention as qualitative witnesses of information scrambling in many-body quantum systems. Theoretical discussions of OTOCs typically focus on closed systems, raising the question of their suitability as scrambling witnesses in realistic open systems. We demonstrate empirically that the nonclassical negativity of the quasiprobability distribution (QPD) behind the OTOC is a more sensitive witness for scrambling than the OTOC itself. Nonclassical features of the QPD evolve with timescales that are robust with respect to decoherence and are immune to false positives caused by decoherence. To reach this conclusion, we numerically simulate spinchain dynamics and …
Why Physical Understanding Should Precede The Mathematical Formalism—Conditional Quantum Probabilities As A Case-Study, Yakir Aharonov, Eliahu Cohen, David H. Oaknin
Why Physical Understanding Should Precede The Mathematical Formalism—Conditional Quantum Probabilities As A Case-Study, Yakir Aharonov, Eliahu Cohen, David H. Oaknin
Mathematics, Physics, and Computer Science Faculty Articles and Research
Conditional probabilities in quantum systems which have both initial and final boundary conditions are commonly evaluated using the Aharonov–Bergmann–Lebowitz rule. In this short note, we present a seemingly disturbing paradox that appears when applying the rule to systems with slightly broken degeneracies. In these cases, we encounter a singular limit—the probability “jumps” when going from perfect degeneracy to negligibly broken one. We trace the origin of the paradox and solve it from both traditional and modern perspectives in order to highlight the physics behind it: the necessity to take into account the finite resolution of the measuring device. As a …