We present a permutation-symmetric supporting relation between the pairwise concurrences and the three-tangle in three-qubit system, whose extrema are attained only by the symmetric $W$ and GHZ local-unitary classes. Furthermore, by introducing the concept of a four-dimensional compatibility body, we show that our proposed global relation and the previous CKW relation can be uniformly viewed as different supporting directions of the same achievable set. Subsequently, we provide a necessary-and-sufficient semi-algebraic characterization of the complete four-dimensional compatibility of a three-qubit pure state. Based on this, we can conversely describe the compatibility between entangled components: given the remaining entangled components, the missing two-body entangled component can only take values within a precise parameter-free interval. We demonstrate that the above construction also applies to arbitrary concurrence-generated entanglement measures.
For the three-qubit Shifts unextendible product basis (UPB), the minimum product-state expectation value $\lambda_{\mathrm{Shifts}}=1-3\sqrt6/8$ of the UPB projector is known, and four attaining product states were exhibited previously. We determine the complete equality set over all complex product states and prove th...
Bargmann invariants constructed from a bipartite density operator and its two lifted marginals are polynomial invariants of local-unitary conjugation. We determine the precise information encoded in these invariants. Whenever one subsystem is a qubit, the ordinary marginal-word family determines the full spectrum of th...
We introduce the unitary-accessible coherence-erasure distance, which measures the minimum unitary-control cost required to transform a quantum state into an incoherent state without changing its spectrum. The target states are restricted to incoherent states on the same unitary orbit, leading to a geometry different f...
Dong-Ping Xuan, Hua Nan, Zhi-Xi Wang et al.· 0 citations
Basis-independent coherence of a quantum multistate is fixed by whether its constituent states commute, and for qubits it is detected by pairwise state overlaps alone. What governs its deterministic transformation has been open. We give the exact resource-conversion theory of quantum multistates under common commutativ...
Yuan-Hong Tao, Yu-Xin Wu, Bing Xie et al.· 0 citations
Local unitary (LU) equivalent states are crucial for understanding the structure of quantum entanglement. We investigate the LU equivalence based on the LU Bargmann invariants (LUBIs). We consider for which states the LUBIs are sufficient to ensure the LU equivalence. We focus on a class of multipartite states with com...
In this work, we study asymmetric $(1\to2)$ quantum cloning for pure states belonging to orbits generated by the orthogonal group. For every dimension $(d\geq3)$, we determine the full region of achievable pairs of average single-copy fidelities. Using orthogonal covariance and the Brauer algebra, we reduce the optimiz...
Piotr Ćwikliński, M. Studziński· 0 citations
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