Witnessing random unitary and projective quantum channels: Complementarity between separable and maximally entangled states
arXiv:1601.04817 · doi:10.1103/PhysRevA.93.032132
Abstract
Modern applications in quantum computation and quantum communication require the precise characterization of quantum states and quantum channels. In practice, this means that one has to determine the quantum capacity of a physical system in terms of measurable quantities. Witnesses, if properly constructed, succeed in performing this task. We derive a method that is capable to compute witnesses for identifying deterministic evolutions and measurement-induced collapse processes. At the same time, applying the Choi-Jamiolkowski isomorphism, it uncovers the entanglement characteristics of bipartite quantum states. Remarkably, a statistical mixture of unitary evolutions is mapped onto mixtures of maximally entangled states, and classical separable states originate from genuine quantum-state reduction maps. Based on our treatment we are able to witness these opposing attributes at once and, furthermore, obtain an insight into their different geometric structures. The complementarity is further underpinned by formulating a complementary Schmidt decomposition of a state in terms of maximally entangled states and discrete Fourier-transformed Schmidt coefficients.
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References in corpus (10)
- Quantum Process Tomography: Resource Analysis of Different Strategies
- Quantum channels and memory effects
- Necessary and sufficient conditions for bipartite entanglement
- Quantum Decoherence of Two Qubits
- Determination of the Schmidt number
- Dynamics of correlations due to a phase noisy laser
- Quantum channel detection
- Strongly entangled light from planar microcavities
- Geometric representation of two-qubit entanglement witnesses
- Visualizing extremal positive maps in unital and trace preserving form