arXiv subjects

Yu-Chun Yin

Publications and source records attributed to Yu-Chun Yin.

3 recordsLinked to original sources

arXiv2024

Nonlocality of Quantum States can be Transitive

As a striking manifestation of quantum entanglement, nonlocality has long played a pivotal role in shaping our understanding of the quantum world. When considering a Bell test involving three parties, we may even find a remarkable situation where the nonlocality in two bipartite subsystems {\em forces} the remaining bipartite subsystem to exhibit nonlocality. This intriguing effect, dubbed nonlocality transitivity, was first identified in the non-quantum non-signaling world in 2011. However, whether such transitivity could manifest within quantum theory has remained unresolved -- until now. Here, we provide the first affirmative answer to this open problem at the level of quantum states, thereby showing that there exists a quantum-realizable notion of nonlocality transitivity. Specifically, by leveraging the possibility of Bell-inequality violation by tensoring, we analytically construct a pair of nonlocal bipartite states such that simultaneously realizing them in a tripartite system induces nonlocality in the remaining bipartite subsystem. En route to showing this, we also prove that multiple copies of the $W$-state marginals uniquely determine the global compatible state, thus establishing another instance when the parts determine the whole. Surprisingly, the nonlocality transitivity of quantum states also occurs among the reduced states of Haar-random three-qutrit pure states. We further show that the transitivity of quantum steering can already be demonstrated with the marginals of a three-qubit $W$ state, showing again another noteworthy difference between the two forms of quantum correlations. Finally, we present a simple method to construct quantum states and correlations that are nonlocal in all their non-unipartite marginals, which may be of independent interest.

quant-ph↗

arXiv2024

Resource Marginal Problems

We introduce the resource marginal problems, which concern the possibility of having a resource-free target subsystem compatible with a given collection of marginal density matrices. By identifying an appropriate choice of resource R and target subsystem T, our problems reduce, respectively, to the well-known marginal problems for quantum states and the problem of determining if a given quantum system is a resource. More generally, we say that a set of marginal states is resource-free incompatible with a target subsystem T if all global states compatible with this set must result in a resourceful state in T of type R. We show that this incompatibility induces a resource theory that can be quantified by a monotone and obtain necessary and sufficient conditions for this monotone to be computable as a conic program with finite optimum. We further show, via the corresponding witnesses, that (1) resource-free incompatibility is equivalent to an operational advantage in some channel-discrimination tasks, and (2) some specific cases of such tasks fully characterize the convertibility between marginal density matrices exhibiting resource-free incompatibility. Through our framework, one sees a clear connection between any marginal problem -- which implicitly involves some notion of incompatibility -- for quantum states and a resource theory for quantum states. We also establish a close connection between the physical relevance of resource marginal problems and the ground state properties of certain many-body Hamiltonians. In terms of application, the universality of our framework leads, for example, to a further quantitative understanding of the incompatibility associated with the recently-proposed entanglement marginal problems and entanglement transitivity problems.

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arXiv2022

Entanglement transitivity problems

One of the goals of science is to understand the relation between a whole and its parts, as exemplified by the problem of certifying the entanglement of a system from the knowledge of its reduced states. Here, we focus on a different but related question: can a collection of marginal information reveal new marginal information? We answer this affirmatively and show that (non-) entangled marginal states may exhibit (meta)transitivity of entanglement, i.e., implying that a different target marginal must be entangled. By showing that the global $n$-qubit state compatible with certain two-qubit marginals in a tree form is unique, we prove that transitivity exists for a system involving an arbitrarily large number of qubits. We also completely characterize -- in the sense of providing both the necessary and sufficient conditions -- when (meta)transitivity can occur in a tripartite scenario when the two-qudit marginals given are either the Werner states or the isotropic states. Our numerical results suggest that in the tripartite scenario, entanglement transitivity is generic among the marginals derived from pure states.

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