An Introduction to the Mathematical Aspects of Quantum Mechanics:
... where xk is an arbitrary point of Ik . We desire that this sum converge to a limit as the maximum length goes to zero, and furthermore the convergence is independent of our choices of intervals Ik and point xk . If all this holds, we call the limit x̄ the mathematical expectation of x. If x is not r ...
... where xk is an arbitrary point of Ik . We desire that this sum converge to a limit as the maximum length goes to zero, and furthermore the convergence is independent of our choices of intervals Ik and point xk . If all this holds, we call the limit x̄ the mathematical expectation of x. If x is not r ...
Microscopic quantum coherence in a photosynthetic-light
... (3.4) [52]. Following these lines of thought, the appearance of a classical world in quantum theory has been explored [51,52,55,56]. On the other hand, an example of fake decoherence is to interpret the result of an ensemble average over different noisy realizations of a system as the description of ...
... (3.4) [52]. Following these lines of thought, the appearance of a classical world in quantum theory has been explored [51,52,55,56]. On the other hand, an example of fake decoherence is to interpret the result of an ensemble average over different noisy realizations of a system as the description of ...
Quantum Computational Complexity - Cheriton School of Computer
... be polynomial-time computable if there exists a polynomial-time deterministic Turing machine that outputs f ( x) for every input x ∈ Σ∗ . Two related points on the terminology used throughout this article are as follows. 1. A function of the form p : N → N (where N = {0, 1, 2, . . . }) is said to be ...
... be polynomial-time computable if there exists a polynomial-time deterministic Turing machine that outputs f ( x) for every input x ∈ Σ∗ . Two related points on the terminology used throughout this article are as follows. 1. A function of the form p : N → N (where N = {0, 1, 2, . . . }) is said to be ...
Measurement and assignment of the size-dependent
... presence of the unresolved states, modeled by the cubic background. In addition, since PLE represents a combination of absorption and emission behavior, a detailed knowledge of the emission quantum yield for each transition would be required to quantify the absorption strength of the states observed ...
... presence of the unresolved states, modeled by the cubic background. In addition, since PLE represents a combination of absorption and emission behavior, a detailed knowledge of the emission quantum yield for each transition would be required to quantify the absorption strength of the states observed ...
Quantum Annealing with Markov Chain Monte Carlo Simulations
... computation and processing information. It intends to develop quantum computing devices for solving certain tough computational problems faster and/or more efficient than classical computers. Any computers must utilize some states of physical systems to store digits. Classical computers use voltage ...
... computation and processing information. It intends to develop quantum computing devices for solving certain tough computational problems faster and/or more efficient than classical computers. Any computers must utilize some states of physical systems to store digits. Classical computers use voltage ...
A mechanistic classical laboratory situation violating the Bell
... two material point particles moving in space and having total momentum zero. A coincidence measurement of the momenta of the individual particles gives us correlated results. These correlations were however already present before the coincidence measurement. The measurement only detects the correlat ...
... two material point particles moving in space and having total momentum zero. A coincidence measurement of the momenta of the individual particles gives us correlated results. These correlations were however already present before the coincidence measurement. The measurement only detects the correlat ...
23 - Electronic Colloquium on Computational Complexity
... about the original state is vanished (or exists in parallel universes depending on your interpretation of quantum mechanics). A more general version of the measurement rule allows us to measure a given state |ψi in any orthonormal basis {|v1 i, |v2 i, . . . , |vN i}. In this case, the probability th ...
... about the original state is vanished (or exists in parallel universes depending on your interpretation of quantum mechanics). A more general version of the measurement rule allows us to measure a given state |ψi in any orthonormal basis {|v1 i, |v2 i, . . . , |vN i}. In this case, the probability th ...
UNRAVELING OPEN QUANTUM SYSTEMS: CLASSICAL
... A Quantum Markov Semigroup (QMS) arises as the natural noncommutative extension of the well-known concept of Markov semigroup defined on a classical probability space. The motivation for studying a noncommutative theory of Markov semigroups came firstly from Physics. The challenge was to produce a mat ...
... A Quantum Markov Semigroup (QMS) arises as the natural noncommutative extension of the well-known concept of Markov semigroup defined on a classical probability space. The motivation for studying a noncommutative theory of Markov semigroups came firstly from Physics. The challenge was to produce a mat ...
Random numbers, coin tossing
... million RSA keys, in 2012 Lenstra et al. [LHA+ 12] were able to crack 2 out of every 1000 RSA keys via a simple pairwise GCD algorithm! Something similar was done independently by Heninger et al. at the same time [HDWH12]. If all the keys were generated from truly random primes p, q then the probabi ...
... million RSA keys, in 2012 Lenstra et al. [LHA+ 12] were able to crack 2 out of every 1000 RSA keys via a simple pairwise GCD algorithm! Something similar was done independently by Heninger et al. at the same time [HDWH12]. If all the keys were generated from truly random primes p, q then the probabi ...
Matter-Wave Interferometer for Large Molecules
... in the range from 50 to 450 s21 at central velocities of 80 and 160 m兾s, respectively [17]. The phase of the peak FFT component gives the spatial position of the fringe pattern. Comparison of subsequent scans gives the lateral drift of the three-grating setup, which is of the order of 2 nm兾min. Tilt ...
... in the range from 50 to 450 s21 at central velocities of 80 and 160 m兾s, respectively [17]. The phase of the peak FFT component gives the spatial position of the fringe pattern. Comparison of subsequent scans gives the lateral drift of the three-grating setup, which is of the order of 2 nm兾min. Tilt ...
Pauline Oliveros and Quantum Sound
... the whole of space” (233). For undivided wholeness quantum physicists, such as Bohm, the implicate order is “…not to be understood solely in terms of a regular arrangement of objects (e.g., in rows) or as a regular arrangement of events (e.g., in a series). Rather, a total order is contained, in som ...
... the whole of space” (233). For undivided wholeness quantum physicists, such as Bohm, the implicate order is “…not to be understood solely in terms of a regular arrangement of objects (e.g., in rows) or as a regular arrangement of events (e.g., in a series). Rather, a total order is contained, in som ...
Edge states and integer quantum Hall effect in topological insulator
... approaching one edge: one branch goes upward (called electron-like) and the other goes downward (called hole-like), as shown in Fig. 2e. The position y 0 = 2B k x is the guiding center of the wave packages of surface LLs and is proportional to the wave vector kx, where the magnetic length B = ...
... approaching one edge: one branch goes upward (called electron-like) and the other goes downward (called hole-like), as shown in Fig. 2e. The position y 0 = 2B k x is the guiding center of the wave packages of surface LLs and is proportional to the wave vector kx, where the magnetic length B = ...
An information-theoretic perspective on the foundations of
... theory; as Feynman points out. At the heart of this confusion is the paradigm about which QM has been constructed. Unlike other fundamental theories like special relativity, the postulates of QM are purely mathematical, involving complex vectors in a Hilbert space [29,25]. In special relativity, phy ...
... theory; as Feynman points out. At the heart of this confusion is the paradigm about which QM has been constructed. Unlike other fundamental theories like special relativity, the postulates of QM are purely mathematical, involving complex vectors in a Hilbert space [29,25]. In special relativity, phy ...
“Formal” vs. “Empirical” Approaches to Quantum
... show one theory to subsume the domain of another without showing that the mathematical formalism of the latter constitutes a special or limiting case of the former. In particular, it is possible for the mathematical structures of two theories to dovetail approximately over some restricted domain (na ...
... show one theory to subsume the domain of another without showing that the mathematical formalism of the latter constitutes a special or limiting case of the former. In particular, it is possible for the mathematical structures of two theories to dovetail approximately over some restricted domain (na ...
Quantum computing
Quantum computing studies theoretical computation systems (quantum computers) that make direct use of quantum-mechanical phenomena, such as superposition and entanglement, to perform operations on data. Quantum computers are different from digital computers based on transistors. Whereas digital computers require data to be encoded into binary digits (bits), each of which is always in one of two definite states (0 or 1), quantum computation uses quantum bits (qubits), which can be in superpositions of states. A quantum Turing machine is a theoretical model of such a computer, and is also known as the universal quantum computer. Quantum computers share theoretical similarities with non-deterministic and probabilistic computers. The field of quantum computing was initiated by the work of Yuri Manin in 1980, Richard Feynman in 1982, and David Deutsch in 1985. A quantum computer with spins as quantum bits was also formulated for use as a quantum space–time in 1968.As of 2015, the development of actual quantum computers is still in its infancy, but experiments have been carried out in which quantum computational operations were executed on a very small number of quantum bits. Both practical and theoretical research continues, and many national governments and military agencies are funding quantum computing research in an effort to develop quantum computers for civilian, business, trade, and national security purposes, such as cryptanalysis.Large-scale quantum computers will be able to solve certain problems much more quickly than any classical computers that use even the best currently known algorithms, like integer factorization using Shor's algorithm or the simulation of quantum many-body systems. There exist quantum algorithms, such as Simon's algorithm, that run faster than any possible probabilistic classical algorithm.Given sufficient computational resources, however, a classical computer could be made to simulate any quantum algorithm, as quantum computation does not violate the Church–Turing thesis.