On Locality of Schmidt-Correlated States

We review some results on the equivalence of quantum states under local unitary transformations (LUT). In particular, the classification of two-qubit Schmidt correlated (SC) states under LUT is investigated. By presenting the standard form of quantum states under LUT, the sufficient and necessary conditions of whether two different SC states are local unitary equivalent are provided. The correlations of SC states are also discussed.Comment: 14 page

A Note on State Decomposition Independent Local Invariants

We derive a set of invariants under local unitary transformations for arbitrary dimensional quantum systems. These invariants are given by hyperdeterminants and independent from the detailed pure state decompositions of a given quantum state. They also give rise to necessary conditions for the equivalence of quantum states under local unitary transformations

Necessity for quantum coherence of nondegeneracy in energy flow

In this work, we show that the quantum coherence among non-degenerate energy subspaces (CANES) is essential for the energy flow in any quantum system. CANES satisfies almost all of the requirements as a coherence measure, except that the coherence within degenerate subspaces is explicitly eliminated.We show that the energy of a system becomes frozen if and only if the corresponding CANES vanishes, which is true regardless of the form of interaction with the environment. However, CANES can remain zero even if the entanglement changes over time. Furthermore, we show how the power of energy flow is bounded by the value of CANES. An explicit relation connecting the variation of energy and CANES is also presented. These results allow us to bound the generation of system-environment correlation through the local measurement of the system's energy flow