Quantum computing and mathematical research
... How to control the (initial) quantum states? How to create the appropriate environment for the quantum mechanical system to evolve without observing? How to “fight” decoherence (the interaction of the system and the external environment)? How to use the phenomena of superposition and entanglement ef ...
... How to control the (initial) quantum states? How to create the appropriate environment for the quantum mechanical system to evolve without observing? How to “fight” decoherence (the interaction of the system and the external environment)? How to use the phenomena of superposition and entanglement ef ...
Probabilistic interpretation of resonant states
... where Ω ≡ [−L, L] is a large region whose edges x = ±L are far away from the support of the scattering potential V (x); that is, V (L) = V (−L) = 0. We may take the limit L → ∞ in the end if we can, but for the moment we keep L to be finite. (Note here and hereafter that the bra vector is given by t ...
... where Ω ≡ [−L, L] is a large region whose edges x = ±L are far away from the support of the scattering potential V (x); that is, V (L) = V (−L) = 0. We may take the limit L → ∞ in the end if we can, but for the moment we keep L to be finite. (Note here and hereafter that the bra vector is given by t ...
Comparisons between classical and quantum mechanical
... Satyendra Nath Bose (whom they are named after) and Albert Einstein in 19241925 [20, 37, 38]. It was Einstein who realized that a macroscopic fraction of noninteracting massive bosons will accumulate in the lowest single particle quantum state for sufficiently low temperatures. This new phase of mat ...
... Satyendra Nath Bose (whom they are named after) and Albert Einstein in 19241925 [20, 37, 38]. It was Einstein who realized that a macroscopic fraction of noninteracting massive bosons will accumulate in the lowest single particle quantum state for sufficiently low temperatures. This new phase of mat ...
Lecture Notes in Quantum Mechanics Doron Cohen
... oscillators are in the ground state) is called the ”vacuum state”. If a specific oscillator is excited to level n, we say that there are n photons with frequency ω in the system. A similar formalism is used to describe a many particle system. A vacuum state and occupation states are defined. This fo ...
... oscillators are in the ground state) is called the ”vacuum state”. If a specific oscillator is excited to level n, we say that there are n photons with frequency ω in the system. A similar formalism is used to describe a many particle system. A vacuum state and occupation states are defined. This fo ...
Does Geometric Algebra provide a loophole to Bell`s Theorem?
... In 2007, Joy Christian surprised the world with his announcement that Bell’s theorem was incorrect, because, according to Christian, Bell had unnecessarily restricted the co-domain of the measurement outcomes to be the traditional real numbers. Christian’s first publication on arXiv spawned a host o ...
... In 2007, Joy Christian surprised the world with his announcement that Bell’s theorem was incorrect, because, according to Christian, Bell had unnecessarily restricted the co-domain of the measurement outcomes to be the traditional real numbers. Christian’s first publication on arXiv spawned a host o ...
Dynamics of Quantum Many Body Systems Far From Thermal
... do not change with time (stationarity) • no currents of charges associated to conserved quantities (particles, energy, ...) flow through it Needless to say, such a concept is more an exception than a rule in every day life. Indeed, non equilibrium effects are extremely common in many different physi ...
... do not change with time (stationarity) • no currents of charges associated to conserved quantities (particles, energy, ...) flow through it Needless to say, such a concept is more an exception than a rule in every day life. Indeed, non equilibrium effects are extremely common in many different physi ...
Distances in Probability Space and the Statistical Complexity
... In this review we discuss the role that distances in probability space, as ingredients of statistical complexity measures, play in describing the dynamics of the quantum-classical (QC) transition. We choose an exceedingly well-known model, whose physics has received detailed attention over the years ...
... In this review we discuss the role that distances in probability space, as ingredients of statistical complexity measures, play in describing the dynamics of the quantum-classical (QC) transition. We choose an exceedingly well-known model, whose physics has received detailed attention over the years ...
Property calculation I
... • Ensemble average, obtained by integral over all microscopic states • Proper weight ...
... • Ensemble average, obtained by integral over all microscopic states • Proper weight ...
Superconducting Circuits and Quantum Computation
... coherence between states. This requires a coherent two-state system (a qubit) along with a method for control and measurement. Superconducting quantum computing could accomplish this in a manner that can be scaled to a large numbers of qubits. We are studying the properties of a two-state system mad ...
... coherence between states. This requires a coherent two-state system (a qubit) along with a method for control and measurement. Superconducting quantum computing could accomplish this in a manner that can be scaled to a large numbers of qubits. We are studying the properties of a two-state system mad ...
Braid Topologies for Quantum Computation
... which one quasiparticle is woven around two static quasiparticles and returns to its original position (left), and yields approximately the same transition matrix as braiding the two stationary quasiparticles around each other twice (right). The corresponding matrix equation is also shown. To charac ...
... which one quasiparticle is woven around two static quasiparticles and returns to its original position (left), and yields approximately the same transition matrix as braiding the two stationary quasiparticles around each other twice (right). The corresponding matrix equation is also shown. To charac ...
Document
... (and why must we detect) highly-entangled qubit states? • What is quantum entanglement? • How to detect it? the complete way: quantum state tomography the scalable way: entanglement witnesses ...
... (and why must we detect) highly-entangled qubit states? • What is quantum entanglement? • How to detect it? the complete way: quantum state tomography the scalable way: entanglement witnesses ...
Matematiska institutionen Department of Mathematics Covering the sphere with noncontextuality inequalities
... instead of spin 1/2 particles. In this sense Bell’s theorem is much simpler. For all the details see the original paper Kochen and Specker [1968]. Interestingly enough, this paper was published before the CHSH paper, though all details were first understood after they were both published. The theore ...
... instead of spin 1/2 particles. In this sense Bell’s theorem is much simpler. For all the details see the original paper Kochen and Specker [1968]. Interestingly enough, this paper was published before the CHSH paper, though all details were first understood after they were both published. The theore ...
Probability amplitude
In quantum mechanics, a probability amplitude is a complex number used in describing the behaviour of systems. The modulus squared of this quantity represents a probability or probability density.Probability amplitudes provide a relationship between the wave function (or, more generally, of a quantum state vector) of a system and the results of observations of that system, a link first proposed by Max Born. Interpretation of values of a wave function as the probability amplitude is a pillar of the Copenhagen interpretation of quantum mechanics. In fact, the properties of the space of wave functions were being used to make physical predictions (such as emissions from atoms being at certain discrete energies) before any physical interpretation of a particular function was offered. Born was awarded half of the 1954 Nobel Prize in Physics for this understanding (see #References), and the probability thus calculated is sometimes called the ""Born probability"". These probabilistic concepts, namely the probability density and quantum measurements, were vigorously contested at the time by the original physicists working on the theory, such as Schrödinger and Einstein. It is the source of the mysterious consequences and philosophical difficulties in the interpretations of quantum mechanics—topics that continue to be debated even today.