Partitioned trace distances

Xifan Zheng, Reihaneh Safavi–Naini, Hadi Ahmadi

Alexey E. Rastegin

Basic properties of Uhlmann's partial fidelities are discussed. Statistical interpretation in terms of POVM measurements is established. Multiplicativity properties are considered. The relationship between partial fidelities and partitioned trace distances is derived. As it is shown, the partial fidelities cannot decrease under unistochastic quantum operations. Thus, the partial fidelities have good properties in the sense of their use as distinguishability measures.

Walter Dittrich, Martin Reuter

Alexey E. Rastegin

Basic properties of Uhlmann's partial fidelities are discussed. Statistical interpretation in terms of POVM measurements is established. Multiplicativity properties are considered. The relationship between partial fidelities and partitioned trace distances is derived. As it is shown, the partial fidelities cannot decrease under unistochastic quantum operations. Thus, the partial fidelities have good properties in the sense of their use as distinguishability measures.

Seyed Mohammad Hashemi Rafsanjani, Curtis J. Broadbent, Joseph H. Eberly

We introduce a measure for the genuinely N-partite (all-party) entanglement of N-qubit states using the trace distance metric and find an algebraic formula for the Greenberger-Horne-Zeilinger (GHZ)-diagonal states. We then use this formula to show how the all-party entanglement of experimentally produced GHZ states of an arbitrary number of qubits may be bounded with only four measurements.

Walter Dittrich, Martin Reuter