Chapter 2 Theory of angular momentum
... • In classical mechanics, a rigid object admits two kinds of angular momentum: ~ = ~r × ~p), associated with the motion of the center of mass; – orbital (L ~ = Iω), associated with the motion about the center of mass. – spin (|S| F.i., the Earth has an orbital angular momentum attributable to its an ...
... • In classical mechanics, a rigid object admits two kinds of angular momentum: ~ = ~r × ~p), associated with the motion of the center of mass; – orbital (L ~ = Iω), associated with the motion about the center of mass. – spin (|S| F.i., the Earth has an orbital angular momentum attributable to its an ...
Quantum Computing: The Risk to Existing Encryption Methods
... of magnitude faster than classic computers and thousands of times faster than modern supercomputers.2 While there is a endless list of positive and innovative applications for quantum computing, there is a concern that its sheer power could be used for more a malicious intent. Many existing security ...
... of magnitude faster than classic computers and thousands of times faster than modern supercomputers.2 While there is a endless list of positive and innovative applications for quantum computing, there is a concern that its sheer power could be used for more a malicious intent. Many existing security ...
Chapter 3 Foundations II: Measurement and Evolution 3.1
... that can be realized on system A by performing orthogonal measurements on a larger system that contains A. But first we will briefly consider how (orthogonal) measurements of an arbitrary observable can be achieved in principle, following the classic treatment of Von Neumann. To measure an observabl ...
... that can be realized on system A by performing orthogonal measurements on a larger system that contains A. But first we will briefly consider how (orthogonal) measurements of an arbitrary observable can be achieved in principle, following the classic treatment of Von Neumann. To measure an observabl ...
Quantum supergroups and canonical bases Sean Clark University of Virginia Dissertation Defense
... U̇ admits a π-signed canonical basis generalizing the basis for U− . For π = 1, this specializes to Lusztig’s canonical basis for U̇|π=1 . Idea of proof (generalizing Lusztig): Consider modules N(λ, λ0 ) → U̇1λ−λ0 as λ, λ0 → ∞. Define epimorphisms t : N(λ + λ00 , λ00 + λ0 ) → N(λ, λ0 ). ({N(λ, λ0 )} ...
... U̇ admits a π-signed canonical basis generalizing the basis for U− . For π = 1, this specializes to Lusztig’s canonical basis for U̇|π=1 . Idea of proof (generalizing Lusztig): Consider modules N(λ, λ0 ) → U̇1λ−λ0 as λ, λ0 → ∞. Define epimorphisms t : N(λ + λ00 , λ00 + λ0 ) → N(λ, λ0 ). ({N(λ, λ0 )} ...
1.01
... There is a common expression of information, strings of bits, regardless of the object/entity/process it describes. Bits are independent of their physical embodiment. Information is transformed using logic operations. Gates implement logic operations and allow for automatic processing of information ...
... There is a common expression of information, strings of bits, regardless of the object/entity/process it describes. Bits are independent of their physical embodiment. Information is transformed using logic operations. Gates implement logic operations and allow for automatic processing of information ...
How “Quantum” is the D-Wave Machine?
... in the introduction, this schedule is different from the one reported in [7], which was based on an error by D-Wave [24], although this did not change their conclusions. Our paper is based entirely on the new corrected schedule [8]. We note that our conclusions also hold equally well for both schedu ...
... in the introduction, this schedule is different from the one reported in [7], which was based on an error by D-Wave [24], although this did not change their conclusions. Our paper is based entirely on the new corrected schedule [8]. We note that our conclusions also hold equally well for both schedu ...
The Physical World as a Virtual Reality
... Quantum mechanics and relativity theory are the crown jewels of modern physics because they have quite simply never been proved wrong. It all began with Maxwell's wave equations in the 1860s, followed by Planck's constant in 1900, Einstein's special relativity in 1905, general relativity in 1915, an ...
... Quantum mechanics and relativity theory are the crown jewels of modern physics because they have quite simply never been proved wrong. It all began with Maxwell's wave equations in the 1860s, followed by Planck's constant in 1900, Einstein's special relativity in 1905, general relativity in 1915, an ...
Einstein`s Unknown Insight and the Problem of Quantizing Chaos
... complexity or the number of degrees of freedom of the system that matters. The dynamics of systems with fewer constants of motion than degrees of freedom are fundamentally different from those of systems with at least as many constants as degrees of freedom. In modern terminology, the former type of ...
... complexity or the number of degrees of freedom of the system that matters. The dynamics of systems with fewer constants of motion than degrees of freedom are fundamentally different from those of systems with at least as many constants as degrees of freedom. In modern terminology, the former type of ...
The Light of Existence
... Currently, light is seen as vibrating electrical and magnetic fields, where according to Feynman: “A real field is a mathematical function we use for avoiding the idea of action at a distance.” (Feynman, Leighton, & Sands, 1977) Vol. II, p15-7 Fields are today so common in physics that we forget the ...
... Currently, light is seen as vibrating electrical and magnetic fields, where according to Feynman: “A real field is a mathematical function we use for avoiding the idea of action at a distance.” (Feynman, Leighton, & Sands, 1977) Vol. II, p15-7 Fields are today so common in physics that we forget the ...
Pairing in a system of a few attractive fermions in a harmonic trap
... pair which can be compared to the size of the whole manybody system. The latter is not the single particle extension determined by the characteristic length of the ground state of the external trap [35], in particular for attractive systems. The size of the system can be determined from a correlated ...
... pair which can be compared to the size of the whole manybody system. The latter is not the single particle extension determined by the characteristic length of the ground state of the external trap [35], in particular for attractive systems. The size of the system can be determined from a correlated ...
Comment on “Non-representative Quantum Mechanical Weak Values”
... the weak value of S is problematic when in|S|in = 0. In the nested interferometer in| B |in = 0 and in|C |in = 0, where B = |BB| is the projection operator on path B, and similarly for C . Thus, the weak values ( B )w and (C )w are not supposed to be problematic, but their nonvanish ...
... the weak value of S is problematic when in|S|in = 0. In the nested interferometer in| B |in = 0 and in|C |in = 0, where B = |BB| is the projection operator on path B, and similarly for C . Thus, the weak values ( B )w and (C )w are not supposed to be problematic, but their nonvanish ...
M10/17
... representation for D and α ∈ C with |α| = 1, then (H, E, αψ) is an equivalent operator representation for D. In this case, the unitary operator is U = αI. We shall show that a decoherence functional on a finite measurable space possesses an operator representation. It is an open problem whether this ...
... representation for D and α ∈ C with |α| = 1, then (H, E, αψ) is an equivalent operator representation for D. In this case, the unitary operator is U = αI. We shall show that a decoherence functional on a finite measurable space possesses an operator representation. It is an open problem whether this ...
Document
... Electromagnetically trapped atomic ions are qubit standards, with unsurpassed levels of quantum coherence and near-perfect measurement. When qubit state-dependent laser or microwave forces are applied to ions in a crystal, their Coulomb interaction is modulated in a way that forms entangling quantum ...
... Electromagnetically trapped atomic ions are qubit standards, with unsurpassed levels of quantum coherence and near-perfect measurement. When qubit state-dependent laser or microwave forces are applied to ions in a crystal, their Coulomb interaction is modulated in a way that forms entangling quantum ...
Bell's theorem
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Bell's theorem is a ‘no-go theorem’ that draws an important distinction between quantum mechanics (QM) and the world as described by classical mechanics. This theorem is named after John Stewart Bell.In its simplest form, Bell's theorem states:Cornell solid-state physicist David Mermin has described the appraisals of the importance of Bell's theorem in the physics community as ranging from ""indifference"" to ""wild extravagance"". Lawrence Berkeley particle physicist Henry Stapp declared: ""Bell's theorem is the most profound discovery of science.""Bell's theorem rules out local hidden variables as a viable explanation of quantum mechanics (though it still leaves the door open for non-local hidden variables). Bell concluded:Bell summarized one of the least popular ways to address the theorem, superdeterminism, in a 1985 BBC Radio interview: