Trade-off relations for operation entropy of complementary quantum channels

The entropy of a quantum operation, defined as the von Neumann entropy of the corresponding Choi–Jamiołkowski state, characterizes the coupling of the principal system with the environment. For any quantum channel acting on a state of a given size, one defines the complementary channel, which sends the input state into the state of the environment after the operation. Making use of subadditivity of entropy, we show that for any dimension the sum of both entropies is bounded from below. This result characterizes the trade-off between the information on the initial quantum state accessible to the principal system and the information leaking to the environment. For one qubit maps we describe the interpolating family of depolarizing maps, for which the sum of both entropies gives the lower boundary of the region allowed in the space spanned by both entropies.

On the complementary quantum capacity of the depolarizing channel

The qubit depolarizing channel with noise parameter η transmits an input qubit perfectly with probability 1−η, and outputs the completely mixed state with probability η. We show that its complementary channel has positive quantum capacity for all η>0. Thus, we find that there exists a single parameter family of channels having the peculiar property of having positive quantum capacity even when the outputs of these channels approach a fixed state independent of the input. Comparisons with other related channels, and implications on the difficulty of studying the quantum capacity of the depolarizing channel are discussed.

The extreme points of SU(2)-irreducibly covariant channels

In this paper, we introduce EPOSIC channels, a class of SU(2)-covariant quantum channels. For each of them, we give a Kraus representation, its Choi matrix, a complementary channel, and its dual map. We show that they are the extreme points of all SU(2)-irreducibly covariant channels. As an application of these channels, we get an example of a positive map that is not completely positive.

Tracing the Many Translations of a Web-Based IT Artefact

This chapter adopts an interpretive, case based research strategy to discuss the centrality of meaning in implementing an Internet-based self-service technology. Actor-Network theory (ANT) is used to describe the complex evolution of a Web-based service at a healthcare insurance firm. Using processes of inscribing, translating and framing, this chapter explores the emergence of the technology from 1999 – 2005 using three technological frames, ‘channel of choice’, ‘dazzle the customer’, and ‘complementary channel’ as episodes of translation. ANT demonstrates that the Internet-based self-service technology at this particular healthcare context emerged out of many unplanned negotiations and mediations with both human and non human actors. Finally, this chapter argues that ANT’s socio-technical lens provides a richer understanding of the meaning of Internet-based self-service technology within a multi-channel context.

Tracing the Many Translations of a Web-Based IT Artefact

This chapter adopts an interpretive, case based research strategy to discuss the centrality of meaning in implementing an Internet-based self-service technology. Actor-Network theory (ANT) is used to describe the complex evolution of a Web-based service at a healthcare insurance firm. Using processes of inscribing, translating and framing, this chapter explores the emergence of the technology from 1999 – 2005 using three technological frames, ‘channel of choice’, ‘dazzle the customer’, and ‘complementary channel’ as episodes of translation. ANT demonstrates that the Internet-based self-service technology at this particular healthcare context emerged out of many unplanned negotiations and mediations with both human and non human actors. Finally, this chapter argues that ANT’s socio-technical lens provides a richer understanding of the meaning of Internet-based self-service technology within a multi-channel context.