March 2002 Vol - Basarab Nicolescu
... Obviously, there is coherence between the different levels of Reality, at least in the natural world. In fact, a vast selfconsistence seems to rule the evolution of the Universe, from the infinitely small to the infinitely large,, from the infinitely short to the infinitely long. For example, a very ...
... Obviously, there is coherence between the different levels of Reality, at least in the natural world. In fact, a vast selfconsistence seems to rule the evolution of the Universe, from the infinitely small to the infinitely large,, from the infinitely short to the infinitely long. For example, a very ...
The solution of the “constant term problem” and the ζ
... corresponding approximating metric graph with non-standard boundary conditions being not necessarily of the δ-type or δ 0 -type. The analysis of the Laplacian as the prime example and generic model system for a Schrödinger operator is very wide-reaching in the field of quantum chaos such as the anal ...
... corresponding approximating metric graph with non-standard boundary conditions being not necessarily of the δ-type or δ 0 -type. The analysis of the Laplacian as the prime example and generic model system for a Schrödinger operator is very wide-reaching in the field of quantum chaos such as the anal ...
On Lattices, Learning with Errors, Random Linear Codes, and
... answer to the important open question of understanding the hardness of decoding from random linear codes. It turns out that certain problems, which are seemingly easier than the LWE problem, are in fact equivalent to the LWE problem. We establish these equivalences in Section 4 using elementary red ...
... answer to the important open question of understanding the hardness of decoding from random linear codes. It turns out that certain problems, which are seemingly easier than the LWE problem, are in fact equivalent to the LWE problem. We establish these equivalences in Section 4 using elementary red ...
Tensor Product Methods and Entanglement
... In quantum systems, correlations having no counterpart in classical physics arise. Pure states showing these strange kinds of correlations are called entangled ones,[26–30,154–156] and the existence of these states has so deep and important consequences[157–159] €dinger has identified entanglement t ...
... In quantum systems, correlations having no counterpart in classical physics arise. Pure states showing these strange kinds of correlations are called entangled ones,[26–30,154–156] and the existence of these states has so deep and important consequences[157–159] €dinger has identified entanglement t ...
Many Body Quantum Mechanics
... (Hint: Use Jensen’s inequality and the fact that t 7→ t log t is strictly convex. The problem is easier if one assumes that exp(−H/T ) is trace class, otherwise some version of the spectral Theorem is needed4 . ) ...
... (Hint: Use Jensen’s inequality and the fact that t 7→ t log t is strictly convex. The problem is easier if one assumes that exp(−H/T ) is trace class, otherwise some version of the spectral Theorem is needed4 . ) ...
Quantum Information with Fermionic Gaussian States - Max
... In this Thesis we study finite-dimensional fermionic Gaussian states and channels. In physics, Gaussian approximation is a frequently used tool for solving many-body problems. Gaussian approximation relies on describing system fully in terms of two-point correlation functions. This means that all th ...
... In this Thesis we study finite-dimensional fermionic Gaussian states and channels. In physics, Gaussian approximation is a frequently used tool for solving many-body problems. Gaussian approximation relies on describing system fully in terms of two-point correlation functions. This means that all th ...
Entanglement Witnesses
... • State acts as teleportation channel fidelity exceeds classical value (e.g., 2/3 in 2-d) ...
... • State acts as teleportation channel fidelity exceeds classical value (e.g., 2/3 in 2-d) ...
Biological Autonomy
... back into the river, nature’s command is short: survive! This command does not inform the fish in terms of physical details and spatial coordinates what to do, such as to turn left or right. Organisms commonly have alternative means of performing the same function (Beckner 1969), therefore, they mus ...
... back into the river, nature’s command is short: survive! This command does not inform the fish in terms of physical details and spatial coordinates what to do, such as to turn left or right. Organisms commonly have alternative means of performing the same function (Beckner 1969), therefore, they mus ...
Interplay of driving, nonlinearity and dissipation in nanoscale and ultracold atom systems
... classical Duffing oscillator. An anharmonic statically monostable potential can be driven into a dynamically bistable regime showing various interesting features of non-linear response [2–4], such as hysteresis, period doubling, and thermal activation when finite temperatures are considered. The ext ...
... classical Duffing oscillator. An anharmonic statically monostable potential can be driven into a dynamically bistable regime showing various interesting features of non-linear response [2–4], such as hysteresis, period doubling, and thermal activation when finite temperatures are considered. The ext ...
The University of Sydney
... simply putting numbers into formulae without explanation. Model solutions to all the questions or problems will be posted on the unit WebCT pages when the marked assignments are returned. ...
... simply putting numbers into formulae without explanation. Model solutions to all the questions or problems will be posted on the unit WebCT pages when the marked assignments are returned. ...
Quantum key distribution
Quantum key distribution (QKD) uses quantum mechanics to guarantee secure communication. It enables two parties to produce a shared random secret key known only to them, which can then be used to encrypt and decrypt messages. It is often incorrectly called quantum cryptography, as it is the most well known example of the group of quantum cryptographic tasks.An important and unique property of quantum key distribution is the ability of the two communicating users to detect the presence of any third party trying to gain knowledge of the key. This results from a fundamental aspect of quantum mechanics: the process of measuring a quantum system in general disturbs the system. A third party trying to eavesdrop on the key must in some way measure it, thus introducing detectable anomalies. By using quantum superpositions or quantum entanglement and transmitting information in quantum states, a communication system can be implemented which detects eavesdropping. If the level of eavesdropping is below a certain threshold, a key can be produced that is guaranteed to be secure (i.e. the eavesdropper has no information about it), otherwise no secure key is possible and communication is aborted.The security of encryption that uses quantum key distribution relies on the foundations of quantum mechanics, in contrast to traditional public key cryptography which relies on the computational difficulty of certain mathematical functions, and cannot provide any indication of eavesdropping at any point in the communication process, or any mathematical proof as to the actual complexity of reversing the one-way functions used. QKD has provable security based on information theory, and forward secrecy.Quantum key distribution is only used to produce and distribute a key, not to transmit any message data. This key can then be used with any chosen encryption algorithm to encrypt (and decrypt) a message, which can then be transmitted over a standard communication channel. The algorithm most commonly associated with QKD is the one-time pad, as it is provably secure when used with a secret, random key. In real world situations, it is often also used with encryption using symmetric key algorithms like the Advanced Encryption Standard algorithm. In the case of QKD this comparison is based on the assumption of perfect single-photon sources and detectors, that cannot be easily implemented.