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Register a new userNonlinear Improvement of Qubit-qudit Entanglement Witnesses
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The entanglement witness is an important and experimentally applicable tool for entanglement detection. In this paper, we provide a nonlinear improvement of any entanglement witness for $2otimes d$ quantum systems. Compared with any existing entanglement witness, the improved separability criterion only needs two more measurements on local observables. Detailed examples are employed to illustrate the efficiency of the nonlinear improvement for general, optimal and non-decomposable entanglement witnesses.
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Entanglement witnesses (EWs) are a fundamental tool for the detection of entanglement. We study the inertias of EWs, i.e., the triplet of the numbers of negative, zero, and positive eigenvalues respectively. We focus on the EWs constructed by the partial transposition of states with non-positive partial transposes. We provide a method to generate more inertias from a given inertia by the relevance between inertias. Based on that we exhaust all the inertias for EWs in each qubit-qudit system. We apply our results to propose a separability criterion in terms of the rank of the partial transpose of state. We also connect our results to tripartite genuinely entangled states and the classification of states with non-positive partial transposes. Additionally, the inertias of EWs constructed by X-states are clarified.
The ultrafine entanglement witness, introduced in [F. Shahandeh, M. Ringbauer, J.C. Loredo, and T.C. Ralph, Phys. Rev. Lett. textbf{118}, 110502 (2017)], can seamlessly and easily improve any standard entanglement witness. In this paper, by combining the constraint and the test operators, we rotate the hyperplane determined by the test operator and improve further the original ultrafine entanglement witness. In particular, we present a series of new ultrafine entanglement witnesses, which not only can detect entangled states that the original ultrafine entanglement witnesses cannot detect, but also have the merits that the original ultrafine entanglement witnesses have.
The generation and control of quantum correlations in high-dimensional systems is a major challenge in the present landscape of quantum technologies. Achieving such non-classical high-dimensional resources will potentially unlock enhanced capabilities for quantum cryptography, communication and computation. We propose a protocol that is able to attain entangled states of $d$-dimensional systems through a quantum-walk-based {it transfer & accumulate} mechanism involving coin and walker degrees of freedom. The choice of investigating quantum walks is motivated by their generality and versatility, complemented by their successful implementation in several physical systems. Hence, given the cross-cutting role of quantum walks across quantum information, our protocol potentially represents a versatile general tool to control high-dimensional entanglement generation in various experimental platforms. In particular, we illustrate a possible photonic implementation where the information is encoded in the orbital angular momentum and polarization degrees of freedom of single photons.
An entanglement witness is an observable detecting entanglement for a subset of states. We present a framework that makes an entanglement witness twice as powerful due to the general existence of a second (lower) bound, in addition to the (upper) bound of the very definition. This second bound, if non-trivial, is violated by another subset of entangled states. Differently stated, we prove via the structural physical approximation that two witnesses can be compressed into a single one. Consequently, our framework shows that any entanglement witness can be upgraded to a witness $2.0$. The generality and its power are demonstrate by applications to bipartite and multipartite qubit/qudit systems.
We show that each entanglement witness detecting given bipartite entangled state provides an estimation of its concurrence. We illustrate our result with several well known examples of entanglement witnesses and compare the corresponding estimation of concurrence with other estimations provided by the trace norm of partial transposition and realignment.
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