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Quantum coherence, incompatibility, and quantum correlations are fundamental features of quantum physics. A unified view of those features is crucial for revealing quantitatively their intrinsic connections. We define the relative quantum coherence of two states as the coherence of one state in the reference basis spanned by the eigenvectors of another one and establish its quantitative connections with the extent of mutual incompatibility of two states. We also show that the proposed relative quantum coherence, which can take any form of measures such as l1 norm and relative entropy, can be interpreted as or connected to various quantum correlations such as quantum discord, symmetric discord, entanglement of formation, and quantum deficits. Our results reveal conceptual implications and basic connections of quantum coherence, mutual incompatibility, and quantum correlations.

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Nonlocality is one unique property of quantum mechanics differing from classical world. One of its quantifications can be properly described as the maximum global effect caused by locally invariant measurements, termed as measurement-induced nonlocality (MIN) (2011 Phys. Rev. Lett. 106 120401). Here, we propose to quantify the MIN by the trace norm. We show explicitly that this measure is monotonically decreasing under the action of completely positive trace-preserving map, which is the general local quantum operation, on the unmeasured party for the bipartite state. This property avoids the undesirable characteristic appearing in the known measure of MIN defined by the Hilbert-Schmidt norm that may be increased or decreased by trivial local reversible operations on the unmeasured party. We obtain analytical formulas of the trace-norm MIN for any 2 × n dimensional pure state, two-qubit state, and certain high-dimensional states. As other quantum correlation measures, the new defined MIN can be directly applied to various models for physical interpretations.

As the [2Fe] H subsite models of [FeFe]-hydrogenases, a series of PNP-chelated and -bridged diiron dithiolate complexes 1a−f and 2a−f together with the three related monophosphine complexes 3a−c were prepared by the selective substitutions of the all-carbonyl complex Fe 2 (μpdt)(CO) 6 (A, pdt = SCH 2 CH 2 CH 2 S) with aminodiphosphines (Ph 2 P) 2 NR (denoted as PNP) under different reaction conditions. The first UV irradiation of the toluene solutions of A with different PNP ligands (PNP = (Ph 2 P) 2 NR; R = (CH 2 ) 3 Me, (CH 2 ) 3 NMe 2 , (CH 2 ) 3 Si(OEt) 3 , C 6 H 5 , C 6 H 4 OMe-p, C 6 H 4 CO 2 Me-p) readily afforded the target PNP-chelated complexes Fe 2 (μ-pdt)(CO) 4 {(κ 2 -Ph 2 P) 2 NR} (1a−f), while the reflux of xylene solutions of A with the aforementioned PNP ligands produced the PNP-bridged complexes Fe 2 (μ-pdt)(CO) 4 {(μ-Ph 2 P) 2 NR} (2a−f). Comparatively, treatments of A and one type of PNP ligand with N-aryl substituents R (R = C 6 H 5 , C 6 H 4 OMe-p, C 6 H 4 CO 2 Me-p) in MeCN at room temperature in the presence of the decarbonylating agent Me 3 NO•2H 2 O formed the unexpected monophosphine complexes Fe 2 (μ-pdt)(CO) 5 {κ 1 -Ph 2 P(NHR)} (3a−c) and the minor chelated complexes 1d−f. All of the complexes 1a−f, 2a−f, and 3a−c have been characterized by elemental analysis, FT-IR, NMR spectroscopy, and particularly for 1a,b,d−f, 2b,d−f, and 3b by X-ray crystallography. Additionally, the electrochemical and electrocatalytic properties of complexes 1a and 2a as a pair of representative isomers have been evaluated and compared by cyclic voltammetry in MeCN as solvent in the absence and presence of HOAc as a proton source.

By local measurements on party A of a system AB and classical communication between its two parties, one can achieve a nonlocal advantage of quantum coherence (NAQC) on party B. For the l 1 norm of coherence and the relative entropy of coherence, we generalized the framework of NAQC for two qubits and derived the criteria which capture NAQC in the (d × d)-dimensional states when d is a power of a prime. We also presented a new framework for formulating NAQC, and showed through explicit examples its capacity on capturing the NAQC states. Moreover, we proved that any bipartite state with NAQC is quantum entangled, thus the obtained criteria can also be used as an entanglement witness.

The estimation of the decoherence process of an open quantum system is of both theoretical significance and experimental appealing. Practically, the decoherence can be easily estimated if the coherence evolution satisfies some simple relations. We introduce a framework for studying evolution equation of coherence. Based on this framework, we prove a simple factorization relation (FR) for the l1 norm of coherence, and identified the sets of quantum channels for which this FR holds. By using this FR, we further determine condition on the transformation matrix of the quantum channel which can support permanently freezing of the l1 norm of coherence. We finally reveal the universality of this FR by showing that it holds for many other related coherence and quantum correlation measures.

We relate the principle of quantum-memory-assisted entropic uncertainty to quantum teleportation and show geometrically that any two-qubit state which lowers the upper bound of this uncertainty relation is useful for teleportation. We also explore the efficiency of this entropic uncertainty principle on witnessing entanglement in a general class of bosonic structured reservoirs. The entanglement regions witnessed by different estimates are determined, which may have no relation with the explicit form of the spectral density of the reservoir for certain special chosen sets of the initial states. DOI: null PACS number(s): 03.67.Mn, 03.65.Ta, 03.65.Yz