Relative phase change during quantum operation

Quantum operations represented by completely positive maps encompass many of the physical processes and have been very powerful in describing quantum computation and information processing tasks. We introduce the notion of relative phase change for a quantum system undergoing quantum operation. We find that the relative phase shift of a system not only depends on the state of the system, but also depends on the initial state of the ancilla with which it might have interacted in the past. The relative phase change during a sequence of quantum operations is shown to be non-additive in nature. This property can attribute a `memory' to a quantum channel. Also the notion of relative phase shift helps us to define what we call `in-phase quantum channels'. We will present the relative phase shift for a qubit undergoing depolarizing channel and complete randomization and discuss their implications.Comment: Latex file, article style, 15 pages, no figures. Invited talk presented at First Feynman Festival on Quantum Computation at University of Maryland, College Park from August 23-28th, 2002 under the title ``Quantum phase during quantum operation'

Replication and Evolution of Quantum Species

We dwell upon the physicist's conception of `life' since Schroedinger and Wigner through to the modern-day language of living systems in the light of quantum information. We discuss some basic features of a living system such as ordinary replication and evolution in terms of quantum bio-information. We also discuss the principle of no-culling of living replicas. We show that in a collection of identical species there can be no entanglement between one of the mutated copies and the rest of the species in a closed universe. Even though these discussions revolve around `artificial life' they may still be applicable in real biological systems under suitable conditions.Comment: Latex, 12 pages, no figure

Stronger uncertainty relations for the sum of variances

Heisenberg-Robertson's uncertainty relation expresses a limitation in the possible preparations of the system by giving a lower bound to the product of the variances of two observables in terms of their commutator. Notably, it does not capture the concept of incompatible observables because it can be trivial, i.e., the lower bound can be null even for two non-compatible observables. Here we give two stronger uncertainty relations, relating to the sum of variances, whose lower bound is guaranteed to be nontrivial whenever the two observables are incompatible on the state of the system.Comment: Version accepted for publication on Phys. Rev. Let

Perfect Teleportation and Superdense Coding With W-States

True tripartite entanglement of the state of a system of three qubits can be classified on the basis of stochastic local operations and classical communications (SLOCC). Such states can be classified in two categories: GHZ states and W-states. It is known that GHZ states can be used for teleportation and superdense coding, but the prototype W-state cannot be. However, we show that there is a class of W-states that can be used for perfect teleportation and superdense coding.Comment: 9 pages, no figur