Properties of Conjugate Channels with Applications to Additivity and Multiplicativity
| dc.creator | King, Christopher | |
| dc.creator | Matsumoto, Keiji | |
| dc.creator | Nathanson, Michael | |
| dc.creator | Ruskai, Mary Beth | |
| dc.date | 2005-09-19 | |
| dc.date | 2006-03-26 | |
| dc.date.accessioned | 2026-07-07T12:29:20Z | |
| dc.date.available | 2026-07-07T12:29:20Z | |
| dc.description | 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_d to M_d' with d < d', and different constructions may differ by conjugation with a partial isometry. We show that a channel and its conjugate have the same minimal output entropy and maximal output p-norm. It then follows that the additivity and multiplicativity conjectures for these measures of optimal output purity hold for a product of channels if and only if they also hold for the product of their conjugates. This allows us to reduce these conjectures to the special case of maps taking M_d to M_d' with a minimal representation of dimension at most d. We find explicit expressions for the conjugates for a number of well-known examples, including entanglement-breaking channels, unital qubit channels, the depolarizing channel, and a subclass of random unitary channels. For the entanglement-breaking channels, channels this yields a new class of channels for which additivity and multiplicativity of optimal output purity can be established. For random unitary channels using the generalized Pauli matrices, we obtain a new formulation of the multiplicativity conjecture. The conjugate of the completely noisy channel plays a special role and suggests a mechanism for using noise to transmit information. | |
| dc.description | Final version to appear in Markov Processes and Related Fields special issue in memory of John T. Lewis | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0509126 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0509126 | |
| dc.identifier | Markov Process and Related Fields 13, 391-423 (2007) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/215839 | |
| dc.subject | Quantum Physics | |
| dc.title | Properties of Conjugate Channels with Applications to Additivity and Multiplicativity | |
| dc.type | text |