Potential output purity of completely positive maps

The notion of potential output purity of a completely positive map is introduced as a generalization of the regularized output purity. An upper bound is derived for this quantity, and for several classes of maps (including CQ, QC and Hadamard channels) it is shown that potential purity does not exceed the standard output purity. As an application the potential purity is used to bound the logarithmic Sobolev constant of a product of depolarizing channel semigroups.Comment: 18 page

F-purity of hypersurfaces

In this note, we study F-purity of pairs, and show (as is the case with log canonicity) that F-purity is preserved at the F-pure threshold. We also characterize when F-purity is equivalent to sharp F-purity, an alternate notion of purity for pairs introduced in [Sch08]. These results on purity at the threshold generalize results appearing in [Har06, Sch08], and were expected to hold by many experts in the field. We conclude by extending results in [BMS09] on the set of all F-pure thresholds to the most general setting.Comment: Version 1: 12 pages, 1 figure. Comments welcome! Version 2: Minor revisions (as suggested by the referee) and updated references. To appear in Mathematical Research Letter

Two-qubit mixed states and teleportation fidelity: Purity, concurrence, and beyond

To explore the properties of a two-qubit mixed state, we consider quantum teleportation. The fidelity of a teleported state depends on the resource state purity and entanglement, as characterized by concurrence. Concurrence and purity are functions of state parameters. However, it turns out that a state with larger purity and concurrence, may have comparatively smaller fidelity. By computing teleportation fidelity, concurrence and purity for two-qubit X-states, we show it explicitly. We further show that fidelity changes monotonically with respect to functions of parameters - other than concurrence and purity. A state with smaller concurrence and purity, but larger value of one of these functions has larger fidelity. These functions, thus characterize nonlocal classical and/or quantum properties of the state that are not captured by purity and concurrence alone. In particular, concurrence is not enough to characterize the entanglement properties of a two-qubit mixed state

Purity and impurity in nondualistic Śaiva Tantrism

Indian civilisation has been strongly characterised by the work of containment erected by the Brahmanical elite over the almost two thousand years of its grandiose attempt at culturally and so- cially dominating the Indian world as a whole. Lacking any direct power, the Brahmans have re- placed it by successfully imposing, as an alternative, an opposition between purity and impurity that has marked every aspect of Indian culture: purity of spirit, purity of philosophy, purity of rites, purity of language, purity of social and religious conduct, etc. Nondualistic Śaiva Tantrism’s re- sponse starts by questioning the legitimacy and very basis of the division between pure and impure, destined to crumble progressively beneath the thrust of deliberate “non-dual” behaviour (advaitācāra). Purity or impurity are not properties of things. They are quali cations pertaining to the knower depending on whether he perceives the object as united with consciousness or not. “Impure is what has fallen away from consciousness: therefore everything is pure if it has achieved identity with consciousness.” Moreover, if Śiva “is” the universe, there may be no impu- rity. In the Tantric texts special emphasis is laid on the necessity to overcome śaṅkā (“hesitation, inhibition”), viewed as the ultimate purpose of the Brahmanical rules concerning purity/impurity, acting as a subtle and effective instrumentum regni

Is Purity Eternal?

Phenomenological and formal restrictions on the evolution of pure into mixed states are discussed. In particular, it is argued that, if energy is conserved, loss of purity is incompatible with the weakest possible form of Lorentz covariance.Comment: 12 pages, in Plain Tex; section 3 on Lorentz covariance expanded and improved in response to year-long correspondence with the referee, but the conclusions are unchanged; UCSBTH-92-2

Purity of Gaussian states: measurement schemes and time-evolution in noisy channels

We present a systematic study of the purity for Gaussian states of single-mode continuous variable systems. We prove the connection of purity to observable quantities for these states, and show that the joint measurement of two conjugate quadratures is necessary and sufficient to determine the purity at any time. The statistical reliability and the range of applicability of the proposed measurement scheme is tested by means of Monte Carlo simulated experiments. We then consider the dynamics of purity in noisy channels. We derive an evolution equation for the purity of general Gaussian states both in thermal and squeezed thermal baths. We show that purity is maximized at any given time for an initial coherent state evolving in a thermal bath, or for an initial squeezed state evolving in a squeezed thermal bath whose asymptotic squeezing is orthogonal to that of the input state.Comment: 9 Pages, 6 Figures; minor errors correcte