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26
On Factorization of MChannel Paraunitary Filterbanks
, 2001
"... We systematically investigate the factorization of causal finite impulse response (FIR) paraunitary filterbanks with given filter length. Based on the singular value decomposition of the coefficient matrices of the polyphase representation, a fundamental orderone factorization form is first propose ..."
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We systematically investigate the factorization of causal finite impulse response (FIR) paraunitary filterbanks with given filter length. Based on the singular value decomposition of the coefficient matrices of the polyphase representation, a fundamental orderone factorization form is first proposed for general paraunitary systems. Then, we develop a new structure for the design and implementation of paraunitary system based on the decomposition of Hermitian unitary matrices. Within this framework, the linearphase filterbank and pairwise mirrorimage symmetry filterbank are revisited. Their structures are special cases of the proposed general structures. Compared with the existing structures, more efficient ones that only use approximately half the number of free parameters are derived. The proposed structures are complete and minimal. Although the factorization theory with or without constraints is discussed in the framework ofchannel filterbanks, the results can be applied to wavelets and multiwavelet systems and could serve as a general theory for paraunitary systems.
On Generalized Probabilities: Correlation Polytopes for Automaton Logic and Generalized Urn Models, Extensions of Quantum Mechanics and Parameter Cheats
, 2001
"... Three extensions and reinterpretations of nonclassical probabilities are reviewed. ..."
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Three extensions and reinterpretations of nonclassical probabilities are reviewed.
On the Brightness of the Thomson Lamp. A Prolegomenon to Quantum Recursion Theory
, 2009
"... Some physical aspects related to the limit operations of the Thomson lamp are discussed. Regardless of the formally unbounded and even infinite number of “steps” involved, the physical limit has an operational meaning in agreement with the Abel sums of infinite series. The formal analogies to accele ..."
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Cited by 1 (1 self)
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Some physical aspects related to the limit operations of the Thomson lamp are discussed. Regardless of the formally unbounded and even infinite number of “steps” involved, the physical limit has an operational meaning in agreement with the Abel sums of infinite series. The formal analogies to accelerated (hyper) computers and the recursion theoretic diagonal methods are discussed. As quantum information is not bound by the mutually exclusive states of classical bits, it allows a consistent representation of fixed point states of the diagonal operator. In an effort to reconstruct the selfcontradictory feature of diagonalization, a generalized diagonal method allowing no quantum fixed points is proposed.
Use of WeiNorman formul and parameter differentiation in quantum computing
"... For the unitary operator, solution of the Schrödinger equation corresponding to a timevarying Hamiltonian, the relation between the Magnus and the product of exponentials expansions can be expressed in terms of a system of first order differential equations in the parameters of the two expansions, ..."
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For the unitary operator, solution of the Schrödinger equation corresponding to a timevarying Hamiltonian, the relation between the Magnus and the product of exponentials expansions can be expressed in terms of a system of first order differential equations in the parameters of the two expansions, often referred to as WeiNorman formula. It is shown how to use WeiNorman formul for the purposes of quantum computing.
Quantum information: the new frontier
, 2000
"... Quantum information and computation is the new hype in physics. It is promising, mindboggling and even already applicable in cryptography, with good prospects ahead. A brief, rather subjective outline is presented. ..."
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Quantum information and computation is the new hype in physics. It is promising, mindboggling and even already applicable in cryptography, with good prospects ahead. A brief, rather subjective outline is presented.
The diagonalization method in quantum recursion theory
, 2009
"... As quantum parallelism allows the effective corepresentation of classical mutually exclusive states, the diagonalization method of classical recursion theory has to be modified. Quantum diagonalization involves unitary operators whose eigenvalues are different from one. ..."
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As quantum parallelism allows the effective corepresentation of classical mutually exclusive states, the diagonalization method of classical recursion theory has to be modified. Quantum diagonalization involves unitary operators whose eigenvalues are different from one.
Testing quantum contextuality
, 1999
"... Two entangled particles in threedimensional Hilbert space (per particle) are considered in an EPRtype arrangement. On each side the KochenSpecker observables {J 2 1,J 2 2,J 2 3} and { ¯ J 2 1, ¯ J 2 2,J 2 3} with [J 2 1, ¯ J 2 1] ̸= 0 are measured. The outcomes of measurements of J 2 3 (via J 2 ..."
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Two entangled particles in threedimensional Hilbert space (per particle) are considered in an EPRtype arrangement. On each side the KochenSpecker observables {J 2 1,J 2 2,J 2 3} and { ¯ J 2 1, ¯ J 2 2,J 2 3} with [J 2 1, ¯ J 2 1] ̸= 0 are measured. The outcomes of measurements of J 2 3 (via J 2 1,J 2 2) and J 2 3 (via ¯ J 2 1, ¯ J 2 2) are compared. Although formally J 2 3 is associated with the same projection operator, quantum contextuality requires that the outcome depends on the complete disposition of the measurement apparatus, in particular whether J 2 1 or ¯ J 2 1 is measured alongside. Besides complementarity, contextuality [1, 2, 3, 4, 5] is another, more subtle nonclassical feature of quantum mechanics. That is, one and the same physical observable may appear different, depending on the context of measurement; i.e., depending on the particular way it was inferred. Stated differently, the outcome of a physical measurement may depend also on other physical measurements which are coperformed. In Bell’s own words [1, section 5], “The result of an