Some Bipartite States do not Arise from Channels
arXiv:quant-ph/0303141
Abstract
It is well-known that the action of a quantum channel on a state can be represented, using an auxiliary space, as the partial trace of an associated bipartite state. Recently, it was observed that for the bipartite state associated with the optimal average input of the channel, the entanglement of formation is simply the entropy of the reduced density matrix minus the Holevo capacity. It is natural to ask if every bipartite state can be associated with some channel in this way. We show that the answer is negative.
7 pages; minor typos corrected. To appear in special issue of the IBM Journal of Research and Development for Charles Bennett's 60th birthday
References in corpus (5)
- Entanglement of Formation of an Arbitrary State of Two Qubits
- Remarks on additivity of the Holevo channel capacity and of the entanglement of formation
- Simulating quantum operations with mixed environments
- Qubit Channels Can Require More Than Two Inputs to Achieve Capacity
- Quantum operations that cannot be implemented using a small mixed environment