Yeong Cherng Liang

Quantum non-locality based on finite-speed causal influences leads to superluminal signalling

Non-local quantum correlations between distant particles cannot be explained by signals propagating slower than the speed of light. It is now shown that they cannot be explained by hidden influences propagating faster than the speed of light either, because that would permit faster-than-light communication.

Device-independent witnesses of genuine multipartite entanglement

We consider the problem of determining whether genuine multipartite entanglement was produced in an experiment, without relying on a characterization of the systems observed or of the measurements performed. We present an n-partite inequality that is satisfied by all correlations produced by measurements on biseparable quantum states, but which can be violated by n-partite entangled states, such as Greenberger-Horne-Zeilinger states. In contrast to traditional entanglement witnesses, the violation of this inequality implies that the state is not biseparable independently of the Hilbert space dimension and of the measured operators. Violation of this inequality does not imply, however, genuine multipartite nonlocality. We show more generically how the problem of identifying genuine tripartite entanglement in a device-independent way can be addressed through semidefinite programming.

Detecting genuine multipartite quantum nonlocality: A simple approach and generalization to arbitrary dimensions

The structure of Bell-type inequalities detecting genuine multipartite nonlocality, and hence detecting genuine multipartite entanglement, is investigated. We first present a simple and intuitive approach to Svetlichnys original inequality, which provides a clear understanding of its structure and of its violation in quantum mechanics. Based on this approach, we then derive a family of Bell-type inequalities for detecting genuine multipartite nonlocality in scenarios involving an arbitrary number of parties and systems of arbitrary dimension. Finally, we discuss the tightness and quantum mechanical violations of these inequalities.

Alternative fidelity measure between quantum states

We propose an alternative fidelity measure (namely, a measure of the degree of similarity) between quantum states and benchmark it against a number of properties of the standard Uhlmann-Jozsa fidelity. This measure is a simple function of the linear entropy and the Hilbert-Schmidt inner product between the given states and is thus, in comparison, not as computationally demanding. It also features several remarkable properties such as being jointly concave and satisfying all of Jozsas axioms. The trade-off, however, is that it is supermultiplicative and does not behave monotonically under quantum operations. In addition, metrics for the space of density matrices are identified and the joint concavity of the Uhlmann-Jozsa fidelity for qubit states is established.

All bipartite entangled states display some hidden nonlocality

One of the most significant and well-known properties of entangled states is that they may lead to violations of Bell inequalities and are thus inconsistent with any local-realistic theory. However, there are entangled states that cannot violate any Bell inequality, and in general the precise relationship between entanglement and observable nonlocality is not well understood. We demonstrate that a violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality can be demonstrated in a certain kind of Bell experiment for all entangled states. Our proof of the result consists of two main steps. We first provide a simple characterization of the set of states that do not violate the CHSH inequality even after general local operations and classical communication. Second, we prove that for each entangled state sigma, there exists another state rho not violating the CHSH inequality, such that rhomultiply sign in circlesigma violates the CHSH inequality.

Measurement-Device-Independent Entanglement Witnesses for All Entangled Quantum States

The problem of demonstrating entanglement is central to quantum information processing applications. Resorting to standard entanglement witnesses requires one to perfectly trust the implementation of the measurements to be performed on the entangled state, which may be an unjustified assumption. Inspired by the recent work of F. Buscemi [Phys. Rev. Lett. 108, 200401 (2012)], we introduce the concept of measurement-device-independent entanglement witnesses (MDI-EWs), which allow one to demonstrate entanglement of all entangled quantum states with untrusted measurement apparatuses. We show how to systematically obtain such MDI-EWs from standard entanglement witnesses. Our construction leads to MDI-EWs that are loss tolerant and can be implemented with current technology.

Device-independent entanglement quantification and related applications.

We present a general method to quantify both bipartite and multipartite entanglement in a device-independent manner, meaning that we put a lower bound on the amount of entanglement present in a system based on the observed data only but independent of any quantum description of the employed devices. Some of the bounds we obtain, such as for the Clauser-Horne-Shimony-Holt Bell inequality or the Svetlichny inequality, are shown to be tight. Besides, device-independent entanglement quantification can serve as a basis for numerous tasks. We show in particular that our method provides a rigorous way to construct dimension witnesses, gives new insights into the question whether bound entangled states can violate a Bell inequality, and can be used to construct device-independent entanglement witnesses involving an arbitrary number of parties.

Imperfect measurement settings: Implications for quantum state tomography and entanglement witnesses

Reliable and well-characterized quantum resources are indispensable ingredients in quantum information processing. Typically, in a realistic characterization of these resources, apparatuses come with intrinsic uncertainties that can manifest themselves in the form of systematic errors. While systematic errors are generally accounted for through careful calibration, the effect of remaining imperfections on the characterization of quantum resources has been largely overlooked in the literature. In this paper, we investigate the effect of systematic errors that arise from imperfect alignment of measurement bases—an error that can conceivably take place due to the limited controllability of measurement devices. We show that characterization of quantum resources using quantum state tomography or entanglement witnesses can be undermined with an amount of such imprecision that is not uncommon in laboratories. Curiously, for quantum state tomography, we find that having entanglement can help to reduce the susceptibility to this kind of error. We also briefly discuss how a given entanglement witness can be modified to incorporate the effect of such errors.

Guaranteed violation of a Bell inequality without aligned reference frames or calibrated devices

Bell tests — the experimental demonstration of a Bell inequality violation — are central to understanding the foundations of quantum mechanics, and are a powerful diagnostic tool for the development of quantum technologies. To date, Bell tests have relied on careful calibration of measurement devices and alignment of a shared reference frame between two parties — both technically demanding tasks. We show that neither of these operations are necessary, violating Bell inequalities (i) with certainty using unaligned, but calibrated, measurement devices, and (ii) with near-certainty using uncalibrated and unaligned devices. We demonstrate generic quantum nonlocality with randomly chosen measurements on a singlet state of two photons, implemented using a reconfigurable integrated optical waveguide circuit. The observed results demonstrate the robustness of our schemes to imperfections and statistical noise. This approach is likely to have important applications both in fundamental science and quantum technologies, including device-independent quantum key distribution.

Arbitrarily small amount of measurement independence is sufficient to manifest quantum nonlocality

The use of Bells theorem in any application or experiment relies on the assumption of free choice or, more precisely, measurement independence, meaning that the measurements can be chosen freely. Here, we prove that even in the simplest Bell test-one involving 2 parties each performing 2 binary-outcome measurements-an arbitrarily small amount of measurement independence is sufficient to manifest quantum nonlocality. To this end, we introduce the notion of measurement dependent locality and show that the corresponding correlations form a convex polytope. These correlations can thus be characterized efficiently, e.g., using a finite set of Bell-like inequalities-an observation that enables the systematic study of quantum nonlocality and related applications under limited measurement independence.