A theorem of Davies states that for symmetric quantum states there exists a symmetric POVM maximizing the mutual information. To apply this theorem the representation of the symmetry group has to be irreducible. We obtain a similar yet weaker result for reducible representations.
Multi-party local quantum operations with shared quantum entanglement or shared classical randomness are studied. The following facts are established:
Quantum error correction deals with correcting errors introduced via quantum channels, modelled by trace-preserving completely positive maps. Correctable subsystems are roughly subsystems of the overlying Hilbert space on which the channel has a left inverse. Given a unital completely positive map, the multiplicative domain of that map is the largest subalgebra on which the map acts as a homomorphism. We show that for a unital quantum channel, the correctable subsystems that are correctable via conjugation by a unitary (called unitarily correctable subsystems) are exactly what are captured by that map's multiplicative domain. We also show that if we remove the requirement that the map be unital, a weaker relationship between the two notions still holds.
This is joint work with Man-Duen Choi and David Kribs.
Hastings has recently shown that the conjectured additivity of minimal output entropy is false. Put in a more positive light, this implies that entangled inputs can enhance the capacity of memoryless quantum channels for transmitting classical information. We consider the new issues and challenges that emerge from this breakthrough.
A quantum channel models a physical process in which noise is added to a quantum system via interaction with its environment. Protecting quantum systems from such noise can be viewed as an extension of the classical communication problem introduced by Shannon sixty years ago. A fundamental quantity of interest is the quantum capacity of a given channel, which measures the amount of quantum information which can be protected, in the limit of many transmissions over the channel. In this talk, I will show that certain pairs of channels, each with a capacity of zero, can have a strictly positive capacity when used together, implying that the quantum capacity does not completely characterize a channel's ability to transmit quantum information.
This is joint work with Graeme Smith (IBM) published in Science on Sept. 26, 2008.