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arXiv:1811.12259 · New Journal of Physics

Genuine temporal correlations can certify the quantum dimension

Cornelia Spee, Hendrik Siebeneich, Timm F. Gloger, Peter Kaufmann, M. Johanning, Matthias Kleinmann, Christof Wunderlich, Otfried Gühne

Published Jan 17, 2020• 21 citations
arXivHTMLPDF

Abstract

Abstract Temporal correlations in quantum mechanics are the origin of several non-classical phenomena, but they depend on the dimension of the underlying quantum system. This allows one to use such correlations for the certification of a minimal Hilbert space dimension. Here we provide a theoretical proposal and an experimental implementation of a device-independent dimension test, using temporal correlations observed on a single trapped 171Yb+ ion. Our test goes beyond the prepare-and-measure scheme of previous approaches, demonstrating the advantage of genuine temporal correlations.

DOI
10.1088/1367-2630/ab6d42

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Abstract Temporal correlations in quantum mechanics are the origin of several non-classical phenomena, but they depend on the dimension of the underlying quantum system. This allows one to use such correlations for the certification of a minimal Hilbert space dimension. Here we provide a theoretical proposal and an experimental implementation of a device-independent dimension test, using temporal correlations observed on a single trapped 171Yb+ ion. Our test goes beyond the prepare-and-measure scheme of previous approaches, demonstrating the advantage of genuine temporal correlations.
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Quantum memories are key components of emerging quantum technologies. They are designed to store quantum states and retrieve them on demand without losing features such as superposition and entanglement. Verifying that a memory preserves these features is indispensable for applications such as quantum computation, cryptography and networks, yet no general and assumption-free method has been available. Here, we present a device-independent approach for certifying black-box quantum memories, requiring no trust in any part of the experimental setup. We do so by probing quantum systems at two points in time and then confronting the observed temporal correlations against classical causal models through violations of causal inequalities. We perform a proof-of-principle experiment in a trapped-ion quantum processor, where we certify 35 ms of a qubit memory. Our method establishes temporal correlations and causal modelling as practical and powerful tool for benchmarking key ingredients of quantum technologies, such as quantum gates or implementations of algorithms.
The emergence of quantum theory at the beginning of 20−th-th−th century has changed our view of the microscopic world and has led to applications such as quantum teleportation, quantum random number generation and quantum computation to name a few, that could never have been realised using classical systems. One such application that has attracted considerable attention lately is device-independent (DI) certification of composite quantum systems. The basic idea behind it is to treat a given device as a black box that given some input generates an output, and then to verify whether it works as expected by only studying the statistics generated by this device. The novelty of these certification schemes lies in the fact that one can almost completely characterise the device (up to certain equivalences) under minimal physically well-motivated assumptions such as that the device is described using quantum theory. The resource required in most of these certification schemes is quantum non-locality. In this thesis, we construct schemes to device-independently certify quantum states and quantum measurements in Hilbert spaces of arbitrary dimension along with the optimal amount randomness that one can extract from any quantum system of arbitrary dimension.
Certifying quantum behavior from classically accessible data is essential for secure communication and scalable quantum technologies. While powerful certification methods such as Bell nonlocality and quantum steering exist, their implementation typically requires entanglement or additional assumptions, and experimental demonstrations mainly focus on low-dimensional systems. In minimal prepare-and-measure scenarios, where a sender encodes information into quantum states and a receiver performs a single measurement, robust certification becomes particularly challenging, especially in the presence of noise and in higher-dimensional Hilbert spaces. Here, we propose, design, and experimentally implement a protocol that certifies quantumness between two distant parties without the need for preshared resources or measurement incompatibility. The experiments are carried out using the orbital angular momentum degrees of freedom of single photons, chosen for providing increased dimensionality that is scalable. We demonstrate the robustness of the protocol through rank-stability analysis of the observed correlations, which enables the certification of non-classicality even in the presence of noise. Our results provide a practical route to validate high-dimensional quantum communication systems and open new possibilities for secure and dimension-efficient quantum information processing.
Correlations obtained from sequences of measurements have been employed to distinguish among different physical theories or to witness the dimension of a system. In this work, we show that they can also be used to establish semi-device-independent lower bounds on the purity of the initial quantum state or even on one of the postmeasurement states. For single systems, this provides information on the quality of the preparation procedures of pure states or the implementation of measurements with anticipated pure postmeasurement states. For joint systems, one can combine our bound with results from entanglement theory to infer an upper bound on the concurrence based on the temporal correlations observed on a subsystem.