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Physical Review Letters

Experimental Estimate of a Classicality Witness via a Single Measurement

G. H. Aguilar, O. Jiménez Farías, Jonas Maziero, Roberto M. Serra, P. H. Souto Ribeiro, Stephen Patrick Walborn

Published Feb 8, 2012• 31 citations
Publisher

Abstract

The perception that quantum correlations can still appear in separable states has opened exciting new possibilities regarding their use as a resource in quantum information science. Quantifying such quantum correlations involves the complete knowledge of the system's state and numerical optimization procedures. Thus, it is natural to seek methods involving fewer measurements that indicate the nature of the correlations in a system. Here we propose a classicality witness that can be accurately estimated via statistics from a single measurement and perform an experiment to explore the utility of this witness for quantum states with different types of correlations.

DOI
10.1103/physrevlett.108.063601

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The perception that quantum correlations can still appear in separable states has opened exciting new possibilities regarding their use as a resource in quantum information science. Quantifying such quantum correlations involves the complete knowledge of the system's state and numerical optimization procedures. Thus, it is natural to seek methods involving fewer measurements that indicate the nature of the correlations in a system. Here we propose a classicality witness that can be accurately estimated via statistics from a single measurement and perform an experiment to explore the utility of this witness for quantum states with different types of correlations.
The quantification of quantum correlations (other than entanglement) usually entails labored numerical optimization procedures also demanding quantum state tomographic methods. Thus it is interesting to have a laboratory friendly witness for the nature of correlations. In this Letter we report a direct experimental implementation of such a witness in a room temperature nuclear magnetic resonance system. In our experiment the nature of correlations is revealed by performing only few local magnetization measurements. We also compared the witness results with those for the symmetric quantum discord and we obtained a fairly good agreement.
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We introduce new methods and tools to study and characterise classical and quantum correlations emerging from prepare-and-measure experiments with informationally restricted communication. We consider the most general kind of informationally restricted correlations, namely the ones formed when the sender is allowed to prepare statistical mixtures of mixed states, showing that contrary to what happens in Bell nonlocality, mixed states can outperform pure ones. We then leverage these tools to derive device-independent witnesses of the information content of quantum communication, witnesses for different quantum information resources, and demonstrate that these methods can be used to develop a new avenue for semi-device independent random number generators.
Quantifying non-Markovianity is a fundamental problem in the theory of open quantum systems, as it is essential for exploiting environmental memory as a resource in quantum technologies. Existing resource-theoretic and operational quantifiers, however, generally require complete knowledge of the intermediate dynamical map and are therefore experimentally demanding. Here, we develop a witness-based framework for the quantification of non-Markovianity that bypasses complete reconstruction of the Choi state associated with the intermediate dynamical map. We first show that every non-Markovianity witness provides a certifiable lower bound on the geometric resource measure of non-Markovianity and identify the necessary and sufficient conditions under which this bound is tight. Motivated by the fact that non-positive-semidefinite witnesses are generally difficult to measure in real experimental scenario, we then focus on positive-semidefinite witnesses, which admit a natural implementation as positive operator valued measure (POVM) elements. We prove that every positive witness yields a certified lower bound on the Rivas--Huelga--Plenio (RHP) measure, thereby establishing a complete hierarchy connecting witness-based quantification, the RHP measure, and the geometric distance measure. Applying our framework to amplitude-damping and general Pauli dynamics, we find that the optimal positive witnesses reduce to simple Bell-parity projectors. Furthermore, we show that the resulting witness values can be obtained directly from a small number of experimentally accessible correlation measurements, thereby eliminating the need for complete Choi-state reconstruction and providing an efficient and experimentally feasible approach for the quantification of non-Markovianity in open quantum systems.
Entanglement is an essential resource in quantum information science [1] and its presence in any quantum system can be experimentally detected through entanglement witness operators [2]. In particular, measuring a negative expectation value of a witness with high statistical confidence provides a necessary and sufficient condition to confirm the generation of a genuine multipartite [3] and/or d-level entangled state [4]. In recent years, the experimental generation of complex quantum states has intensified the need for witnesses that are capable of detecting such systems and are experimentally optimal at the same time. This means that the witness should require the least measurement effort (in terms of number and complexity of the measurement settings), include only projections on single qudits, while at the same time possessing a high noise tolerance (Fig. 1a). However, "experimentally-friendly" witnesses capable of accomplishing these tasks have not been derived yet.
Abstract A central problem in fundamental physics is to witness the non-classicality of systems whose dynamics is not completely specified. For example, this arises in testing predictions that a macroscopic system, such as a living system, obeys quantum theory. Notoriously, also, it has been claimed that witnessing non-classicality in the gravitational field is practically impossible. Here, we propose a thought experiment that witnesses the non-classicality of a physical system by probing it with a qubit, without having to assume any specific dynamics on the physical system. Remarkably, this experiment does not require any quantum control of the system, involving only measuring a single classical observable on it. That non-classicality of a system can be established indirectly, by coupling it to a qubit, opens up exciting possibilities, for example, that quantum gravitational effects might be witnessed in the lab.