A classical linear code
C of length
n is said to have symbol locality
(r,δ) if for any index
j there exists a repair group
Jj⊆{1,…,n} with
j∈Jj and
∣Jj∣≤r+δ−1 such that any
δ−1 or fewer erasures in
Jj can be corrected by using codeword symbols only in
Jj. Later it turned out that this way of defining
r overestimates the number of necessary codeword symbols for multiple-erasure correction, and information locality was proposed to define
r as the dimension of the punctured code of
C onto
Jj. Recently locality
(r,δ) was proposed for quantum error-correcting codes by following the original definition of symbol locality
(r,δ). We propose a quantum counterpart of the information locality for quantum stabilizer codes constructed by Hermitian orthogonality, and a linear algebraic procedure computing a smaller repair group predicted by the proposed information locality and simultaneously reducing the number of measured observables in decoding to its minimum possible value. Then we demonstrate that the previously proposed definition of quantum locality
(r,δ) has the same drawback of overestimating the number of necessary codeword symbols for erasure correction by providing an explicit example of a quantum stabilizer code. Finally, we will give another example of a quantum stabilizer code constructed by Euclidean orthogonality and two different linear codes, with which a natural translation of the classical information locality into the quantum setting underestimates the number of necessary codeword symbols for erasure correction.
If one defines a conditional probability P(p/x) = a(p) exp(ipx) / W(x) where W(x)=wavefunction then Sum over p P(p/x) = 1, but P(p/x) is complex and its real and imaginary parts may have positive and negative values at different x points. Nevertheless one may establish an average energy conservation equation with the same En (energy of the nth level) at each x which mimics classical mechanics for all n values. This equation is identical to the time-independent Schrodinger equation. If one treats P(p/x) as a distribution and obtains an average En that holds at each x point like temperature holds at each x for a statistical mechanical gas, one should be able to calculate the variance at x as well i.e. Sum over p P(p/x) [ pp/2m + V(x) -En] [ pp/2m +V(x) -En] = Var(E(x)). We examine this value for a particle in a box with infinite potential walls and for a harmonic oscillator. One may then average Var(En(x). We also consider implications on entropy.
It presents the evolution of the quantum observables from their classical counterpart and distinctly analyses the meaning of observable in context to both the classical and the quantum realms, with an emphasis on W. Heisenberg's realization of observable and unobservable [1925]. It is stated that quantum observables are, in the first place, indeed distinctive to classical observables since each appears unobservable to the other; however, to associate physical essence as possessed by the latter, the expectation value of the former is determined. Further, the possibility of mapping quantum information to the classical ones through the action of the operator may be realized after re-interpreting analogies between the quantum commutator and Poisson brackets.
The Jaynes-Cummings model is one of the most basic systems in quantum optics. It is exactly soluble but the quantities of interest are given by infinite oscillating series which cannot be summed. This leads to problems if one wants to learn about the long-time behavior of the system. On the other hand, the time averages of those quantities can be computed exactly. Infinite time averages give information about behavior which persists for all time. We examine the time averages of the squeezing and the variance of the photon number of the field. We also use time averages to gain information about the inversion. For example, one finds that the fraction of time which the inversion spends far from its mean value decreases as the amplitude of the initial field increases. The importance of periodic behavior in the inversion also decreases as the initial amplitude increases. Finally we examine how long the system must be observed for time averages of quantities to approach their infinite time limits.
We present a resolution of the Wigner's Friend paradox within a framework of quantum mechanics (QM) on the hybrid space RxQ_{p}, where Q_{p} denotes the field of p-adic numbers, regarded as a model of discrete microscopic space at the Planck-Bronstein scale. In this framework, wavefunction collapse is not an independent postulate but a dynamical consequence of the Schrödinger equation with non-local Hamiltonians: wavefunctions localize onto compact supports during measurement interactions, producing definite pointer readings without the intervention of observers or the exchange of information between subsystems. We model both Wigner and his Friend as classical apparatuses and show that each produces a definite reading through independent applications of the collapse mechanism, thereby eliminating the conflict between their descriptions of reality. The framework is consistent with the principal no-go theorems in finite- and infinite-dimensional Hilbert spaces associated with extended Wigner's Friend scenarios -- including those of Frauchiger-Renner, Brukner, Bong et al., and Guérin et al. -- since it requires no agents capable of recording or reasoning about outcomes, thereby vacating the observer-dependent assumptions that drive those theorems. We illustrate the collapse mechanism explicitly through a toy model of a particle in a box, comparing the standard description with the new one. The non-locality intrinsic to QM on L2(RxQ_{p}) permits realism at the cost of locality, and the Absoluteness of Observed Events holds in our framework without requiring observer independence.