Ordering states with various coherence measures

Quantum coherence is one of the most significant theories in quantum physics. Ordering states with various coherence measures is an intriguing task in quantification theory of coherence. In this paper, we study this problem by use of four important coherence measures -- the $l_1$ norm of coherence, the relative entropy of coherence, the geometric measure of coherence and the modified trace distance measure of coherence. We show that each pair of these measures give a different ordering of qudit states when $d\geq 3$. However, for single-qubit states, the $l_1$ norm of coherence and the geometric coherence provide the same ordering. We also show that the relative entropy of coherence and the geometric coherence give a different ordering for single-qubit states. Then we partially answer the open question proposed in [Quantum Inf. Process. 15, 4189 (2016)] whether all the coherence measures give a different ordering of states.Comment: 12 page

Dynamics of coherence-induced state ordering under Markovian channels

We study the dynamics of coherence-induced state ordering under incoherent channels, particularly four specific Markovian channels: $-$ amplitude damping channel, phase damping channel, depolarizing channel and bit flit channel for single-qubit states. We show that the amplitude damping channel, phase damping channel, and depolarizing channel do not change the coherence-induced state ordering by $l_1$ norm of coherence, relative entropy of coherence, geometric measure of coherence, and Tsallis relative $\alpha$-entropies, while the bit flit channel does change for some special cases.Comment: 7 pages, 21 figure

Information-entropic measures for non-zero l states of confined hydrogen-like ions

Relative Fisher information (IR), which is a measure of correlative fluctuation between two probability densities, has been pursued for a number of quantum systems, such as, 1D quantum harmonic oscillator (QHO) and a few central potentials namely, 3D isotropic QHO, hydrogen atom and pseudoharmonic potential (PHP) in both position ($r$) and momentum ($p$) spaces. In the 1D case, the $n=0$ state is chosen as reference, whereas for a central potential, the respective circular or node-less (corresponding to lowest radial quantum number $n_{r}$) state of a given $l$ quantum number, is selected. Starting from their exact wave functions, expressions of IR in both $r$ and $p$ spaces are obtained in closed analytical forms in all these systems. A careful analysis reveals that, for the 1D QHO, IR in both coordinate spaces increase linearly with quantum number $n$. Likewise, for 3D QHO and PHP, it varies with single power of radial quantum number $n_{r}$ in both spaces. But, in H atom they depend on both principal ($n$) and azimuthal ($l$) quantum numbers. However, at a fixed $l$, IR (in conjugate spaces) initially advance with rise of $n$ and then falls off; also for a given $n$, it always decreases with $l$

Thermodynamic semirings

The Witt construction describes a functor from the category of Rings to the category of characteristic 0 rings. It is uniquely determined by a few associativity constraints which do not depend on the types of the variables considered, in other words, by integer polynomials. This universality allowed Alain Connes and Caterina Consani to devise an analogue of the Witt ring for characteristic one, an attractive endeavour since we know very little about the arithmetic in this exotic characteristic and its corresponding field with one element. Interestingly, they found that in characteristic one, the Witt construction depends critically on the Shannon entropy. In the current work, we examine this surprising occurrence, defining a Witt operad for an arbitrary information measure and a corresponding algebra we call a thermodynamic semiring. This object exhibits algebraically many of the familiar properties of information measures, and we examine in particular the Tsallis and Renyi entropy functions and applications to nonextensive thermodynamics and multifractals. We find that the arithmetic of the thermodynamic semiring is exactly that of a certain guessing game played using the given information measure

Self-organization in dissipative optical lattices

We show that the transition from Gaussian to the q-Gaussian distributions occurring in atomic transport in dissipative optical lattices can be interpreted as self-organization by recourse to a modified version of Klimontovich's S-theorem. As a result, we find that self-organization is possible in the transition regime, only where the second moment is finite. Therefore, the nonadditivity parameter q is confined within the range 1<q<5/3, although whole spectrum of q values i.e., 1<q<3, is considered theoretically possible. The range of q values obtained from the modified S-theorem is also confirmed by the experiments carried out by Douglas et al. [Phys. Rev. Lett. 96, 110601 (2006)].Comment: 9 pages, 1 fi