to be completed. LECTURE NOTES 1
... If no ambiguity occurs, we will write the symbol map as σ. Homework Show that σm here is linear. But σ is not. When M is a manifold, one can choose a coordinate atlas {Uα }. Then on each coordinate patch Uα , σ(D) will be a function on the cotangent bundle T ∗ (Uα ) with local coordinate (x, ξ). So ...
... If no ambiguity occurs, we will write the symbol map as σ. Homework Show that σm here is linear. But σ is not. When M is a manifold, one can choose a coordinate atlas {Uα }. Then on each coordinate patch Uα , σ(D) will be a function on the cotangent bundle T ∗ (Uα ) with local coordinate (x, ξ). So ...
Square-root measurement for quantum
... the suboptimum quantum receiver [1]. In the Helstrom’s iterative procedure of the Bayes-cost reduction [8] and the other numerical calculation methods [21]–[23], the SRM is used to give the initial measurement process. After the paper of Helstrom’s iterative algorithm, the SRM has been investigated ...
... the suboptimum quantum receiver [1]. In the Helstrom’s iterative procedure of the Bayes-cost reduction [8] and the other numerical calculation methods [21]–[23], the SRM is used to give the initial measurement process. After the paper of Helstrom’s iterative algorithm, the SRM has been investigated ...
Representation of Quantum Field Theory by Elementary Quantum
... quantum information to states referring to space-time. More exactly the states in the tensor space have to be represented in space-time. The method to achieve a transition from tensor space to space-time as it is considered in this paper consists in the definition of four pairs of position and momen ...
... quantum information to states referring to space-time. More exactly the states in the tensor space have to be represented in space-time. The method to achieve a transition from tensor space to space-time as it is considered in this paper consists in the definition of four pairs of position and momen ...
Majorana and the path-integral approach to Quantum Mechanics
... that of the sufficiently wide integration region in Eq. (5) for quantum systems. In this respect, such a mathematical point is intimately related to a fundamental physical principle. The crucial point in the Feynman formulation of Quantum Mechanics is, as seen above, to consider not only the paths c ...
... that of the sufficiently wide integration region in Eq. (5) for quantum systems. In this respect, such a mathematical point is intimately related to a fundamental physical principle. The crucial point in the Feynman formulation of Quantum Mechanics is, as seen above, to consider not only the paths c ...
Lecture 12
... Partial trace (I) Two quantum registers (e.g. two qubits) in states and (respectively) are independent if then the combined system is in state = ...
... Partial trace (I) Two quantum registers (e.g. two qubits) in states and (respectively) are independent if then the combined system is in state = ...
Remarks on quantum gravity models and supersymplectic structures
... The Fisher's information metric is introduced in order to find the real meaning of the probability distribution in classical and quantum systems described by Riemaniann non-degenerated superspaces. In particular, the physical rôle played by the coefficients a and a∗ of the pure fermionic part of a g ...
... The Fisher's information metric is introduced in order to find the real meaning of the probability distribution in classical and quantum systems described by Riemaniann non-degenerated superspaces. In particular, the physical rôle played by the coefficients a and a∗ of the pure fermionic part of a g ...
Heisenberg`s original derivation of the uncertainty principle and its
... The repeatability hypothesis applies only to a restricted class of measurements and does not generally characterize the state changes caused by quantum measurements. In fact, there exist commonly used measurements of discrete observables, such as photon counting, that do not satisfy the repeatabilit ...
... The repeatability hypothesis applies only to a restricted class of measurements and does not generally characterize the state changes caused by quantum measurements. In fact, there exist commonly used measurements of discrete observables, such as photon counting, that do not satisfy the repeatabilit ...
Quantum Szilard Engine - Physics (APS)
... fermionic SZE over the entire range of temperature. [See [18] for detailed discussions of the Wtot ðTÞ.] While details of Wtot ðTÞ depend on the confinement potential, its lowtemperature limits given in Table I are universal and have a deep physical meaning associated with the information content of ...
... fermionic SZE over the entire range of temperature. [See [18] for detailed discussions of the Wtot ðTÞ.] While details of Wtot ðTÞ depend on the confinement potential, its lowtemperature limits given in Table I are universal and have a deep physical meaning associated with the information content of ...
Two types of potential functions and their use in the
... Note that E is the expectation operator. This paper has mentioned in its introduction that we consider two types of potentials. But what are they? The real potential is the first type, wellknown from elementary classical mechanics. The real potential formalizes potential energy. The second type, is ...
... Note that E is the expectation operator. This paper has mentioned in its introduction that we consider two types of potentials. But what are they? The real potential is the first type, wellknown from elementary classical mechanics. The real potential formalizes potential energy. The second type, is ...
Quantum strategies
... f (y) if and only if y = x ⊕ s for some s ∈ {0, 1}n (⊕ denotes componentwise addition, mod 2), correspond to Picard’s pure strategies; we may imagine the oracle choosing a mixed strategy intended to minimize our chances of efficiently determining s probabilistically. Simon’s algorithm is a quantum s ...
... f (y) if and only if y = x ⊕ s for some s ∈ {0, 1}n (⊕ denotes componentwise addition, mod 2), correspond to Picard’s pure strategies; we may imagine the oracle choosing a mixed strategy intended to minimize our chances of efficiently determining s probabilistically. Simon’s algorithm is a quantum s ...
Anharmonic Oscillator Potentials: Exact and Perturbation Results
... time to reach convergence. Yet when reaching the zeroes of the determinant, Eq. (7) is purely real and we find that the roots correspond to the eigenvalues of Eq. (2). In this work, we only compute the first four eigenvalues and use them to plot the wave functions. Results with various γ, such as en ...
... time to reach convergence. Yet when reaching the zeroes of the determinant, Eq. (7) is purely real and we find that the roots correspond to the eigenvalues of Eq. (2). In this work, we only compute the first four eigenvalues and use them to plot the wave functions. Results with various γ, such as en ...
gaussian wavepackets
... My purpose here is simply to collect together, for the convenience of future reference, material pertaining to the “Gaussian quantum mechanics” which will be central to any effort to put meat on the bare bones of my present intuition. The rudiments of this subject are, of course, treated in every int ...
... My purpose here is simply to collect together, for the convenience of future reference, material pertaining to the “Gaussian quantum mechanics” which will be central to any effort to put meat on the bare bones of my present intuition. The rudiments of this subject are, of course, treated in every int ...
Luttinger-Liquid Behavior in Tunneling through a Quantum Dot at Zero... Paula Rojt, Yigal Meir, and Assa Auerbach
... two-dimensional vector r, and r is in units p of h =m!0 . Thus the spectrum consists of equally spaced shells. The energy of the nth shell is nh!0 , and its degeneracy is n. Within a given shell the states are characterized by a single quantum number, e.g., the angular momentum ‘. ...
... two-dimensional vector r, and r is in units p of h =m!0 . Thus the spectrum consists of equally spaced shells. The energy of the nth shell is nh!0 , and its degeneracy is n. Within a given shell the states are characterized by a single quantum number, e.g., the angular momentum ‘. ...
10 Quantum Complexity Theory I - Department of Computer Science
... get inherently new kinds of (discrete) computing devices based on quantum physics? The first indication that such a device might potentially be more powerful than a probabilistic Turing machine appeared in a paper by Feynman about two decades ago. In that paper, Feynman pointed out a very curious pr ...
... get inherently new kinds of (discrete) computing devices based on quantum physics? The first indication that such a device might potentially be more powerful than a probabilistic Turing machine appeared in a paper by Feynman about two decades ago. In that paper, Feynman pointed out a very curious pr ...
Zero-point energy in the Johnson noise of resistors: Is it there? [
... radiation field (it is easy to shield the resistor to make that sure) a "zero-point energy flow" with fluctuating direction and value of the short-time average were observable between the antenna's input and its radiation field. This is not the case and it is a hard experimental fact that neither ze ...
... radiation field (it is easy to shield the resistor to make that sure) a "zero-point energy flow" with fluctuating direction and value of the short-time average were observable between the antenna's input and its radiation field. This is not the case and it is a hard experimental fact that neither ze ...
