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IEEE/LEOS Summer Topical Meetings

Robust self-test of high-dimension mutually unbiased bases with commercial multi-core fiber

Máté Farkas, Nayda Guerrero, Jaime Cariñe, Gustavo Cañas, G. Lima

Published Jul 1, 2020• 1 citation
Publisher

Abstract

We perform a robust self-testing certification of two four-dimensional mutually unbiased bases in a high-quality optical configuration built with commercial multicore fiber. We also evaluate the randomness produced. Our results represent an important step towards practical self-testing in high-dimensional quantum information technologies.

DOI
10.1109/sum48678.2020.9161066

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We perform a robust self-testing certification of two four-dimensional mutually unbiased bases in a high-quality optical configuration built with commercial multicore fiber. We also evaluate the randomness produced. Our results represent an important step towards practical self-testing in high-dimensional quantum information technologies.
In the device-independent quantum-information approach, the implementation of a given task can be self-tested solely from the recorded statistics and without detailed models for the employed devices. Even though experimentally demanding, it provides appealing verification schemes for advanced quantum technologies that naturally fulfil the associated requirements. In this work, we experimentally study whether self-testing protocols can be adopted to certify the proper functioning of quantum devices built with modern space-division multiplexing optical fiber technology. Specifically, we consider the prepare-and-measure protocol of Farkas and Kaniewski [Phys. Rev. A 99, 032316 (2019)] for self-testing measurements corresponding to mutually unbiased bases (MUBs) in a dimension d>2d>2d>2. In our scheme, the state preparation and measurement stages are implemented using a multiarm interferometer built with multicore optical fibers and related components. Due to the high overlap of the interferometer's optical modes achieved with this technology, we are able to reach the required visibilities for self-testing the implementation of two four-dimensional MUBs. We also quantify two operational quantities of the measurements: (i) the incompatibility robustness, connected to Bell violations, and (ii) the randomness extractable from the outcomes. Since MUBs lie at the core of several quantum-information protocols, our results are of practical interest for future quantum works relying on space-division multiplexing optical fibers.
Certifying entanglement is an important step in the development of many quantum technologies, especially for higher-dimensional systems, where entanglement promises increased capabilities for quantum communication and computation. A key feature distinguishing entanglement from classical correlations is the occurrence of correlations for complementary measurement bases. In particular, mutually unbiased bases (MUBs) are a paradigmatic example that is well-understood and routinely employed for entanglement certification. However, implementing unbiased measurements exactly is challenging and not generically possible for all physical platforms. Here, we extend the entanglement-certification toolbox from correlations in MUBs to arbitrary bases. This practically significant simplification paves the way for efficient characterizations of high-dimensional entanglement in a wide range of physical systems. Furthermore, we introduce a simple three-MUBs construction for all dimensions without using the Wootters-Fields construction, potentially simplifying experimental requirements when measurements in more than two MUBs are needed, especially in high-dimensional settings.
Mutually unbiased bases (MUBs) constitute the canonical example of incompatible quantum measurements. One standard application of MUBs is the task known as quantum random access code (QRAC), in which classical information is encoded in a quantum system, and later part of it is recovered by performing a quantum measurement. We analyze a specific class of QRACs, known as the ${2}^{d}\ensuremath{\rightarrow}1$ QRAC, in which two classical dits are encoded in a ddd-dimensional quantum system. It is known that among rank-1 projective measurements MUBs give the best performance. We show (for every ddd) that this cannot be improved by employing nonprojective measurements. Moreover, we show that the optimal performance can only be achieved by measurements which are rank-1 projective and mutually unbiased. In other words, the ${2}^{d}\ensuremath{\rightarrow}1$ QRAC is a self-test for a pair of MUBs in the prepare-and-measure scenario. To make the self-testing statement robust we propose measures which characterize how well a pair of (not necessarily projective) measurements satisfies the MUB conditions and show how to estimate these measures from the observed performance. Similarly, we derive explicit bounds on operational quantities like the incompatibility robustness or the amount of uncertainty generated by the uncharacterized measurements. For low dimensions the robustness of our bounds is comparable to that of currently available technology, which makes them relevant for existing experiments. Last, our results provide essential support for a recently proposed method for solving the long-standing existence problem of MUBs.
Multi-port beam splitters are cornerstone devices for high-dimensional quantum information tasks, which can outperform the two-dimensional ones. Nonetheless, the fabrication of such devices has proven to be challenging with progress only recently achieved with the advent of integrated photonics. Here, we report on the production of high-quality N × N (with N = 4 , 7 ) multi-port beam splitters based on a new scheme for manipulating multi-core optical fibers. By exploring their compatibility with optical fiber components, we create four-dimensional quantum systems and implement the measurement-device-independent random number generation task with a programmable four-arm interferometer operating at a 2 MHz repetition rate. Due to the high visibilities observed, we surpass the one-bit limit of binary protocols and attain 1.23 bits of certified private randomness per experimental round. Our result demonstrates that fast switching, low loss, and high optical quality for high-dimensional quantum information can be simultaneously achieved with multi-core fiber technology.
In quantum information, complementarity of quantum mechanical observables plays a key role. The eigenstates of two complementary observables form a pair of mutually unbiased bases (MUBs). More generally, a set of MUBs consists of bases that are all pairwise unbiased. Except for specific dimensions of the Hilbert space, the maximal sets of MUBs are unknown in general. Even for a dimension as low as six, the identification of a maximal set of MUBs remains an open problem, although there is strong numerical evidence that no more than three simultaneous MUBs do exist. Here, by exploiting a newly developed holographic technique, we implement and test different sets of three MUBs for a single photon six-dimensional quantum state (a "qusix"), encoded exploiting polarization and orbital angular momentum of photons. A close agreement is observed between theory and experiments. Our results can find applications in state tomography, quantitative wave-particle duality, quantum key distribution.
High-dimensional entanglement is a valuable resource for secure and efficient quantum information processing. A major challenge for practical use of multidimensional quantum systems is the establishment of controls over arbitrary superposition states in realistic conditions. This work demonstrates spatially entangled photon pairs propagating through two separate four-core optical fibers with the amplitudes and phases of the superposition being independently controllable. Using quantum state analyzers that can detect arbitrary multicore superposition states, Bell-type CGLMP inequalities in two, three, and four dimensions are directly tested. Enhanced violation of the inequality by slight nonmaximality of entanglement is also demonstrated.