Approach to ergodicity in quantum wave functions
... e.g. billiards, or systems with a suitable scaling of parameters, such as hydrogen in a magnetic eld. Then it is possible to absorb Planck's constant into some power of the energy and so to map the semiclassical limit h ! 0 into the more familiar one of increasing energy or increasing quantum numbe ...
... e.g. billiards, or systems with a suitable scaling of parameters, such as hydrogen in a magnetic eld. Then it is possible to absorb Planck's constant into some power of the energy and so to map the semiclassical limit h ! 0 into the more familiar one of increasing energy or increasing quantum numbe ...
Toposes and categories in quantum theory and gravity
... In any category, an object T is called a terminal (resp. initial) object if for every object A there is exactly one arrow f : A → T (resp. f : T → A). Any two terminal (resp. initial) objects are isomorphic (two objects A and B in a category are said to be isomorphic if there exists arrows f : A → B ...
... In any category, an object T is called a terminal (resp. initial) object if for every object A there is exactly one arrow f : A → T (resp. f : T → A). Any two terminal (resp. initial) objects are isomorphic (two objects A and B in a category are said to be isomorphic if there exists arrows f : A → B ...
Orbital angular momentum
... R1 (φ1 )R2 (φ2 ) − R2 (φ2 )R1 (φ1 ), in the configuration where the body fixed and space fixed axes coincide before the rotations are made. The first rotation can then be replaced by a space fixed rotation. So, for example, the first term above can be written as R1 (φ1 )Ry (φ2 ) = Rx ′ (φ1 )Ry (φ2 ) ...
... R1 (φ1 )R2 (φ2 ) − R2 (φ2 )R1 (φ1 ), in the configuration where the body fixed and space fixed axes coincide before the rotations are made. The first rotation can then be replaced by a space fixed rotation. So, for example, the first term above can be written as R1 (φ1 )Ry (φ2 ) = Rx ′ (φ1 )Ry (φ2 ) ...
Structure, Individuality and Quantum Gravity
... between the essential and non-essential properties of any thing,5 For II to hold (i.e. things are primary and their relation is secondary), no essential property of the relata can depend on the particular relation under consideration; while for III to hold( i.e. the relation is primary and the rela ...
... between the essential and non-essential properties of any thing,5 For II to hold (i.e. things are primary and their relation is secondary), no essential property of the relata can depend on the particular relation under consideration; while for III to hold( i.e. the relation is primary and the rela ...
A Classical-Light Attack on Energy-Time Entangled Quantum Key Distribution, and Countermeasures
... Up until the early 1970’s, all cryptographic protocols used symmetric algorithms which means that the two keys are identical. The discovery of asymmetric cryptography, or public-key cryptography, revolutionized the field of cryptology by instead using two different keys; one key for encryption and o ...
... Up until the early 1970’s, all cryptographic protocols used symmetric algorithms which means that the two keys are identical. The discovery of asymmetric cryptography, or public-key cryptography, revolutionized the field of cryptology by instead using two different keys; one key for encryption and o ...
- Philsci
... It is an open question whether this interpretation can be applied to proper mixtures; typically that may only be decided on a case by case basis. The following decisive argument shows that the ignorance interpretation is never available for improper mixtures.3 Consider a composite system S1+2 in a p ...
... It is an open question whether this interpretation can be applied to proper mixtures; typically that may only be decided on a case by case basis. The following decisive argument shows that the ignorance interpretation is never available for improper mixtures.3 Consider a composite system S1+2 in a p ...
Quantum Error Correction (QEC) - ETH E
... a quantum system of n spin-1/2 particles is represented in a 2ndimensional space due to entanglement and not in a 2n-dimensional space as in the classical n bit problem. This fact led him to conjecture that a computer based on quantum mechanics might be much more power full than a classical one. ...
... a quantum system of n spin-1/2 particles is represented in a 2ndimensional space due to entanglement and not in a 2n-dimensional space as in the classical n bit problem. This fact led him to conjecture that a computer based on quantum mechanics might be much more power full than a classical one. ...
Quantum Theory: a Pragmatist Approach
... ensemble of systems, then its main job is simply to yield these probabilities. But what kind of probabilities are these, and what, exactly, are they probabilities of? If one clear conclusion has been established by foundational work, it is that not every probability derivable by applying the Born ru ...
... ensemble of systems, then its main job is simply to yield these probabilities. But what kind of probabilities are these, and what, exactly, are they probabilities of? If one clear conclusion has been established by foundational work, it is that not every probability derivable by applying the Born ru ...
Maximal Newton polygons via the quantum Bruhat graph
... tool. We begin with a brief historical survey of each of these two geometric contexts and the relevant combinatorial questions, and then we informally state our main result. In the 1950s, Dieudonné introduced the notion of isocrystals over perfect fields of characteristic p > 0 (see [Man63]), which ...
... tool. We begin with a brief historical survey of each of these two geometric contexts and the relevant combinatorial questions, and then we informally state our main result. In the 1950s, Dieudonné introduced the notion of isocrystals over perfect fields of characteristic p > 0 (see [Man63]), which ...
Quantum Money from Hidden Subspaces
... • A notion of mini-schemes, and a proof that (together with standard cryptographic assumptions) these objects imply full-fledged quantum money schemes. • A method to amplify weak counterfeiters into strong ones, so that one only needs to rule out the latter to show security. • A new connection betwe ...
... • A notion of mini-schemes, and a proof that (together with standard cryptographic assumptions) these objects imply full-fledged quantum money schemes. • A method to amplify weak counterfeiters into strong ones, so that one only needs to rule out the latter to show security. • A new connection betwe ...
Wave-Particle Duality and Uncertainty Principle: Phenomenographic
... Although this is known, many introductory quantum physics students still face significant challenges when they first learn about the probabilistic features and non-local theory of quantum mechanics, which disallows any classical interpretation [12-13]. Students’ problems in learning quantum mechanic ...
... Although this is known, many introductory quantum physics students still face significant challenges when they first learn about the probabilistic features and non-local theory of quantum mechanics, which disallows any classical interpretation [12-13]. Students’ problems in learning quantum mechanic ...
Quantum computing
Quantum computing studies theoretical computation systems (quantum computers) that make direct use of quantum-mechanical phenomena, such as superposition and entanglement, to perform operations on data. Quantum computers are different from digital computers based on transistors. Whereas digital computers require data to be encoded into binary digits (bits), each of which is always in one of two definite states (0 or 1), quantum computation uses quantum bits (qubits), which can be in superpositions of states. A quantum Turing machine is a theoretical model of such a computer, and is also known as the universal quantum computer. Quantum computers share theoretical similarities with non-deterministic and probabilistic computers. The field of quantum computing was initiated by the work of Yuri Manin in 1980, Richard Feynman in 1982, and David Deutsch in 1985. A quantum computer with spins as quantum bits was also formulated for use as a quantum space–time in 1968.As of 2015, the development of actual quantum computers is still in its infancy, but experiments have been carried out in which quantum computational operations were executed on a very small number of quantum bits. Both practical and theoretical research continues, and many national governments and military agencies are funding quantum computing research in an effort to develop quantum computers for civilian, business, trade, and national security purposes, such as cryptanalysis.Large-scale quantum computers will be able to solve certain problems much more quickly than any classical computers that use even the best currently known algorithms, like integer factorization using Shor's algorithm or the simulation of quantum many-body systems. There exist quantum algorithms, such as Simon's algorithm, that run faster than any possible probabilistic classical algorithm.Given sufficient computational resources, however, a classical computer could be made to simulate any quantum algorithm, as quantum computation does not violate the Church–Turing thesis.