26 Optimal Bounds for Johnson-Lindenstrauss
... simultaneously optimal in ε, n, and δ. For p ∈ (0, 2], this matches the upper bound of Kane et al. [2010a]. Indeed, in Kane et al. [2010a], it was shown how to achieve O(ε−2 log n) space and constant probability of error. To reduce this to error probability δ, run the algorithm O(log 1/δ) times in p ...
... simultaneously optimal in ε, n, and δ. For p ∈ (0, 2], this matches the upper bound of Kane et al. [2010a]. Indeed, in Kane et al. [2010a], it was shown how to achieve O(ε−2 log n) space and constant probability of error. To reduce this to error probability δ, run the algorithm O(log 1/δ) times in p ...
using standard syste - the Max Planck Institute for the Physics of
... self-consistent-field method shortly after the new quantum theory was established. They can be handled to such accuracy today that they are used for highprecision measurements and calculations to improve on the fundamental physical constants. Doubly excited resonant states could not, on the other ha ...
... self-consistent-field method shortly after the new quantum theory was established. They can be handled to such accuracy today that they are used for highprecision measurements and calculations to improve on the fundamental physical constants. Doubly excited resonant states could not, on the other ha ...
Quantum and Classical Magnetoresistance in Ambipolar Topological Insulator Transistors with
... the TSS in the BBG11,16–18,43,44 dominating the charge transport at low T (see Fig. S1). Our observations demonstrate a striking transition from the metallic to insulating behavior in the bulk of such films, driven by Ef (tuned by Vg). This transition can also be regarded as that from a ‘‘topologica ...
... the TSS in the BBG11,16–18,43,44 dominating the charge transport at low T (see Fig. S1). Our observations demonstrate a striking transition from the metallic to insulating behavior in the bulk of such films, driven by Ef (tuned by Vg). This transition can also be regarded as that from a ‘‘topologica ...
Public-key encryption
... – problems solvable with an algorithm that is non-deterministic and run in p-time on a non-deterministic machine – problems in NP have no known deterministic p-time algorithms • asymptotic worst case complexity of the most efficient algorithms known is often an exponential function of the input leng ...
... – problems solvable with an algorithm that is non-deterministic and run in p-time on a non-deterministic machine – problems in NP have no known deterministic p-time algorithms • asymptotic worst case complexity of the most efficient algorithms known is often an exponential function of the input leng ...
Atomic Physics Division Fachverband - DPG
... partners to be either in the separable, entangled, or Bell correlated regions. The symmetry of the scattering process allows for the construction of explicit examples applying methods of classical communication and local operations for illustrating the concepts of nonlocality versus separability. It ...
... partners to be either in the separable, entangled, or Bell correlated regions. The symmetry of the scattering process allows for the construction of explicit examples applying methods of classical communication and local operations for illustrating the concepts of nonlocality versus separability. It ...
The statistical interpretation according to Born and Heisenberg
... interpretation we shall find in Born and Heisenberg’s Solvay report. For instance, the requirement that the state of an isolated system be always a stationary state is unfamiliar, to say the least. (As we shall see, it is eventually relaxed in Born and Heisenberg’s report.) For now let us focus on ...
... interpretation we shall find in Born and Heisenberg’s Solvay report. For instance, the requirement that the state of an isolated system be always a stationary state is unfamiliar, to say the least. (As we shall see, it is eventually relaxed in Born and Heisenberg’s report.) For now let us focus on ...
Squeezed spin states
... 2[(S,)~ [3]. This definition implies that a coherent spin state (CSS) [4] is already squeezed if it is placed in an appropriate system of coordinates, and also that spin can be squeezed by just rotating the CSS. Squeezed light emission from an atomic system in a certain CSS [5] has been regarded as ...
... 2[(S,)~ [3]. This definition implies that a coherent spin state (CSS) [4] is already squeezed if it is placed in an appropriate system of coordinates, and also that spin can be squeezed by just rotating the CSS. Squeezed light emission from an atomic system in a certain CSS [5] has been regarded as ...
Ph.D. Thesis Chirag Dhara
... This is the outcome of the non-linear dynamics of such systems making them highly sensitive to initial conditions despite the dynamics being described by deterministic equations. Minor variations are amplified quickly resulting in their characteristic behaviour. In other words, the behaviour of such ...
... This is the outcome of the non-linear dynamics of such systems making them highly sensitive to initial conditions despite the dynamics being described by deterministic equations. Minor variations are amplified quickly resulting in their characteristic behaviour. In other words, the behaviour of such ...
Chapter 7 Quantum Error Correction
... from errors. As we have already noted in Chapter 1, there are several aspects to this challenge. A quantum computer will inevitably interact with its surroundings, resulting in decoherence and hence in the decay of the quantum information stored in the device. Unless we can successfully combat decoh ...
... from errors. As we have already noted in Chapter 1, there are several aspects to this challenge. A quantum computer will inevitably interact with its surroundings, resulting in decoherence and hence in the decay of the quantum information stored in the device. Unless we can successfully combat decoh ...
Introduction
... can warrant the claim that structural explanation applies to special relativity and quantum mechanics but not, say, to the kinetic theory of gases. I argue that Hughes finds such a warrant in Einstein’s distinction between principle and constructive theories and in the claim that quantum mechanics b ...
... can warrant the claim that structural explanation applies to special relativity and quantum mechanics but not, say, to the kinetic theory of gases. I argue that Hughes finds such a warrant in Einstein’s distinction between principle and constructive theories and in the claim that quantum mechanics b ...
Aalborg Universitet Quantum Organizational World-Making through Material Emobided Storytelling Practices
... The performative agency of materials and bodies opposes not only the old materialism of traditional scientific realism but also the social construction approaches. In these approaches the materiality of the world is made passive and immutable, a static entity waiting for significance and to be comp ...
... The performative agency of materials and bodies opposes not only the old materialism of traditional scientific realism but also the social construction approaches. In these approaches the materiality of the world is made passive and immutable, a static entity waiting for significance and to be comp ...
Interacting Fock spaces: central limit theorems and quantum
... ii) we are able to construct the approximating sequence of random variables. The main technical tool used to reach such a theorem is given by a special class of interacting Fock spaces (IFS), namely the 1-mode type Free interacting Fock spaces. More precisely, after introducing a new basic operator ...
... ii) we are able to construct the approximating sequence of random variables. The main technical tool used to reach such a theorem is given by a special class of interacting Fock spaces (IFS), namely the 1-mode type Free interacting Fock spaces. More precisely, after introducing a new basic operator ...
Q ua nt um
... as predicted by the Tavis-Cummings model. To our knowledge this is the first observation of this nonlinearity in a system in which the atom number can be changed one by one in a discrete fashion. In addition, the energies of both bright and dark coupled multi-qubit photon states are well explained b ...
... as predicted by the Tavis-Cummings model. To our knowledge this is the first observation of this nonlinearity in a system in which the atom number can be changed one by one in a discrete fashion. In addition, the energies of both bright and dark coupled multi-qubit photon states are well explained b ...
- Philsci-Archive
... Now let’s continue in more or less chronological order. It is only in retrospect, by meeting many people from universities over the world, that I recognize how much my own thinking is influenced by the education I received at the Radboud University Nijmegen. But in particular I want to mention Klaas ...
... Now let’s continue in more or less chronological order. It is only in retrospect, by meeting many people from universities over the world, that I recognize how much my own thinking is influenced by the education I received at the Radboud University Nijmegen. But in particular I want to mention Klaas ...
Transport study on two-dimensional electrons with controlled short-range alloy disorder
... mentor when I joined the Tsui group. Actually almost all my knowledge of cryogenics was learned from Gabor. He helped me from the very first stage to engage my thesis projects, and kept on discussing with me when I grew more experienced. A big part of my thesis work was done at ultra-low temperature ...
... mentor when I joined the Tsui group. Actually almost all my knowledge of cryogenics was learned from Gabor. He helped me from the very first stage to engage my thesis projects, and kept on discussing with me when I grew more experienced. A big part of my thesis work was done at ultra-low temperature ...
Photodissociation of ozone in the Hartley band: Potential energy
... Hay et al.13 these three 共diabatic兲 states will be termed B, A, and R, respectively. Both B and A correlate with channel 共2兲 while R correlates with channel 共1兲. Transitions to and dissociation via the X state are in principle also possible. With increasing photon energy the dissociating molecule wi ...
... Hay et al.13 these three 共diabatic兲 states will be termed B, A, and R, respectively. Both B and A correlate with channel 共2兲 while R correlates with channel 共1兲. Transitions to and dissociation via the X state are in principle also possible. With increasing photon energy the dissociating molecule wi ...
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.