ua nt - p h / 05 06 19 6 v 2 2 3 Ja n 20 06 Multiplicativity of completely bounded p - norms implies a new additivity result

ua nt - p h / 05 06 19 6 v 1 2 3 Ju n 20 05 Multiplicativity of completely bounded p - norms implies a new additivity result Igor

We prove additivity of the minimal conditional entropy associated with a quantum channel Φ, represented by a completely positive (CP), trace-preserving map, when the infimum of S(γ12)−S(γ1) is restricted to states of the form (I⊗Φ) ( |ψ〉〈ψ| ) . We show that this follows from multiplicativity of the completely bounded norm of Φ considered as a map from L1 → Lp for Lp spaces defined by the Schatt...

ar X iv : q ua nt - p h / 06 06 17 6 v 1 2 1 Ju n 20 06 On quantum positive dynamical maps

The new arguments indicating that non-completely positive maps can describe open quantum evolution are given. This work was partially supported by KBN grant PB/1490/PO3/2003/25 and SCALA (IST-2004-015714) 1

ua nt - p h / 03 06 19 6 v 1 2 9 Ju n 20 03 On Shor ’ s channel extension and constrained channels

ua nt - p h / 06 05 18 5 v 3 3 1 Ja n 20 09 Single qubit , two qubit gates and no signalling principle

In this work we investigate that whether one can construct single and two qubit gates for arbitrary quantum states from the principle of no signalling. We considered the problem for Pauli gates, Hadamard gate, C-Not gate.

ua nt - p h / 05 09 12 6 v 3 2 6 M ar 2 00 6 Properties of Conjugate Channels with Applications to Additivity and Multiplicativity

Quantum channels can be described via a unitary coupling of system and environment, followed by a trace over the environment state space. Taking the trace instead over the system state space produces a different mapping which we call the conjugate channel. We explore the properties of conjugate channels and describe several different methods of construction. In general, conjugate channels map M...