Related papers: Relation Between Quantum Speed Limits And Metrics …
Using the frame formalism we determine some possible metrics and metric-compatible connections on the noncommutative differential geometry of the real quantum plane. By definition a metric maps the tensor product of two 1-forms into a…
A discrete-time quantum walk (QW) is essentially a unitary operator driving the evolution of a single particle on the lattice. Some QWs have familiar physics PDEs as their continuum limit. Some slight generalization of them (allowing for…
We consider mappings satisfying an upper bound for the distortion of families of curves. We establish lower bounds for the distortion of distances under such mappings. As applications, we obtain theorems on the discreteness of the limit…
In this contribution I review rigorous formulations of a variety of limitations of measurability in quantum mechanics. To this end I begin with a brief presentation of the conceptual tools of modern measurement theory. I will make precise…
Quantum speed limit (QSL) is a fundamental concept in quantum mechanics and provides a lower bound on the evolution time. The attainability of QSL, greatly depending on the understanding of QSL, is a long-standing open problem especially…
The speed limits on entanglement are defined as the maximal rate at which entanglement can be generated or degraded in a physical process. We derive the speed limits on entanglement, using the relative entropy of entanglement and…
A one-to-one correspondence is established between linearized space-time metrics of general relativity and the wave equations of quantum mechanics. Also, the key role of boundary conditions in distinguishing quantum mechanics from classical…
Bounds to the speed of evolution of a quantum system are of fundamental interest in quantum metrology, quantum chemical dynamics and quantum computation. We derive a time-energy uncertainty relation for open quantum systems undergoing a…
Recent progress in quantum information has led to the start of several large national and industrial efforts to build a quantum computer. Researchers are now working to overcome many scientific and technological challenges. The program's…
We probe the quantum speed limit (QSL) of an electron when it is trapped in a non-uniform magnetic field. We show that the QSL increases to a large value, but within the regime of causality, by choosing a proper variation in magnetic…
Efficient measures to determine similarity of quantum states, such as the fidelity metric, have been widely studied. In this paper, we address the problem of defining a similarity measure for quantum operations that can be…
Speed of state transitions in macroscopic systems is a crucial concept for foundations of nonequilibrium statistical mechanics as well as various applications in quantum technology represented by optimal quantum control. While extensive…
One-way measurement based quantum computations (1WQC) may describe unitary transformations, via a composition of CPTP maps which are not all unitary themselves. This motivates the following decision problems: Is it possible to determine…
A finite-dimensional pseudo-unitary framework is set up for describing the dynamics of free elementary particles in a purely relativistic quantum mechanical way. States of any individual particles or antiparticles are defined as suitably…
Quantum metrology is an auspicious discipline of quantum information which is currently witnessing a surge of experimental breakthroughs and theoretical developments. The main goal of quantum metrology is to estimate unknown parameters as…
Quantum mechanics sets limits on how fast quantum processes can run given some system energy through time-energy uncertainty relations, and they imply that time and energy are tradeoff against each other. Thus, we propose to measure the…
We define the entropic bounds, i.e minimal uncertainty for pairs of unitary testers in distinguishing between unitary transformations not unlike the well known entropic bounds for observables. We show that in the case of specific sets of…
This paper defines a new pseudometric for binary relations between finite sets that measures consensus among subsets. The main results are (1) a concise restatement of this pseudometric with an intuitively appealing interpretation via a…
We briefly discuss recent experiments on quantum information processing using trapped ions at NIST. A central theme of this work has been to increase our capabilities in terms of quantum computing protocols, but we have also applied the…
Quantum error correction (QEC) is a key concept in quantum computation as well as many areas of physics. There are fundamental tensions between continuous symmetries and QEC. One vital situation is unfolded by the Eastin--Knill theorem,…