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1. All real projective measurements can be self-tested

   https://doi.org/10.1038/s41567-024-02584-z  

   Chen, Ranyiliu; Mančinska, Laura; Volčič, Jurij (October 2024, Nature Physics)

   Abstract Entangled quantum systems feature non-local correlations that are stronger than could be realized classically. This property makes it possible to perform self-testing, the strongest form of quantum functionality verification, which allows a classical user to deduce the quantum state and measurements used to produce a given set of measurement statistics. While self-testing of quantum states is well understood, self-testing of measurements, especially in high dimensions, remains relatively unexplored. Here we prove that every real projective measurement can be self-tested. Our approach employs the idea that existing self-tests can be extended to verify additional untrusted measurements, known as post-hoc self-testing. We formalize the method of post-hoc self-testing and establish the condition under which it can be applied. Using this condition, we construct self-tests for all real projective measurements. We build on this result to develop an iterative self-testing technique that provides a clear methodology for constructing new self-tests from pre-existing ones. 

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2. Entanglement generation in a quantum network at distance-independent rate

   https://doi.org/10.1038/s41534-022-00536-0  

   Patil, Ashlesha; Pant, Mihir; Englund, Dirk; Towsley, Don; Guha, Saikat (May 2022, npj Quantum Information)

   Abstract We develop a protocol for entanglement generation in the quantum internet that allows a repeater node to usen-qubit Greenberger-Horne-Zeilinger (GHZ) projective measurements that can fusensuccessfully entangledlinks, i.e., two-qubit entangled Bell pairs shared acrossnnetwork edges, incident at that node. Implementingn-fusion, forn ≥ 3, is in principle not much harder than 2-fusions (Bell-basis measurements) in solid-state qubit memories. If we allow even 3-fusions at the nodes, we find—by developing a connection to a modified version of the site-bond percolation problem—that despite lossy (hence probabilistic) link-level entanglement generation, and probabilistic success of the fusion measurements at nodes, one can generate entanglement between end parties Alice and Bob at a rate that stays constant as the distance between them increases. We prove that this powerful network property is not possible to attain with any quantum networking protocol built with Bell measurements and multiplexing alone. We also design a two-party quantum key distribution protocol that converts the entangled states shared between two nodes into a shared secret, at a key generation rate that is independent of the distance between the two parties. 

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3. Succinct Arguments for QMA from Standard Assumptions via Compiled Nonlocal Games

   https://doi.org/10.1109/FOCS61266.2024.00078  

   Metger, Tony; Natarajan, Anand; Zhang, Tina (October 2024, IEEE)

   We construct a succinct classical argument system for QMA, the quantum analogue of NP, from generic and standard cryptographic assumptions. Previously, building on the prior work of Mahadev (FOCS '18), Bartusek et al. (CRYPTo ‘22) also constructed a succinct classical argument system for Q M A. However, their construction relied on post-quantumly secure indistinguishability obfuscation, a very strong primitive which is not known from standard cryptographic assumptions. In contrast, the primitives we use (namely, collapsing hash functions and a mild version of quantum homomorphic encryption) are much weaker and are implied by standard assumptions such as LWE. Our protocol is constructed using a general transformation which was designed by Kalai et al. (STOC '23) as a candidate method to compile any quantum nonlocal game into an argument system. Our main technical contribution is to analyze the soundness of this transformation when it is applied to a succinct self-test for Pauli measurements on maximally entangled states, the latter of which is a key component in the proof of MIP * = R E in Quantum complexity. 

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4. Towards Multiparty Computation Withstanding Coercion of All Parties

   Canetti, Ran; Poburinnaya, Oxana (November 2021, Theory of Cryptography Conference)

   null (Ed.)

   Incoercible multi-party computation (Canetti-Gennaro ’96) allows parties to engage in secure computation with the additional guarantee that the public transcript of the computation cannot be used by a coercive outsider to verify representations made by the parties regarding their inputs, outputs, and local random choices. That is, it is guaranteed that the only deductions regarding the truthfulness of such representations, made by an outsider who has witnessed the communication among the parties, are the ones that can be drawn just from the represented inputs and outputs alone. To date, all incoercible secure computation protocols withstand coercion of only a fraction of the parties, or else assume that all parties use an execution environment that makes some crucial parts of their local states physically inaccessible even to themselves. We consider, for the first time, the setting where all parties are coerced, and the coercer expects to see the entire history of the computation. We allow both protocol participants and external attackers to access a common reference string which is generated once and for all by an uncorruptable trusted party. In this setting we construct: - A general multi-party function evaluation protocol, for any number of parties, that withstands coercion of all parties, as long as all parties use the prescribed ``faking algorithm'' upon coercion. This holds even if the inputs and outputs represented by coerced parties are globally inconsistent with the evaluated function. - A general two-party function evaluation protocol that withstands even the %``mixed'' case where some of the coerced parties do follow the prescribed faking algorithm. (For instance, these parties might collude with the coercer and disclose their true local states.) This protocol is limited to functions where the input of at least one of the parties is taken from a small (poly-size) domain. It uses fully deniable encryption with public deniability for one of the parties; when instantiated using the fully deniable encryption of Canetti, Park, and Poburinnaya (Crypto'20), it takes 3 rounds of communication. Both protocols operate in the common reference string model, and use fully bideniable encryption (Canetti Park and Poburinnaya, Crypto'20) and sub-exponential indistinguishability obfuscation. Finally, we show that protocols with certain communication pattern cannot be incoercible, even in a weaker setting where only some parties are coerced. 

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5. Demonstration of optimal non-projective measurement of binary coherent states with photon counting

   https://doi.org/10.1038/s41534-022-00595-3  

   DiMario, M. T.; Becerra, F. E. (July 2022, npj Quantum Information)

   Abstract Quantum state discrimination is a central problem in quantum measurement theory, with applications spanning from quantum communication to computation. Typical measurement paradigms for state discrimination involve a minimum probability of error or unambiguous discrimination with a minimum probability of inconclusive results. Alternatively, an optimal inconclusive measurement, a non-projective measurement, achieves minimal error for a given inconclusive probability. This more general measurement encompasses the standard measurement paradigms for state discrimination and provides a much more powerful tool for quantum information and communication. Here, we experimentally demonstrate the optimal inconclusive measurement for the discrimination of binary coherent states using linear optics and single-photon detection. Our demonstration uses coherent displacement operations based on interference, single-photon detection, and fast feedback to prepare the optimal feedback policy for the optimal non-projective quantum measurement with high fidelity. This generalized measurement allows us to transition among standard measurement paradigms in an optimal way from minimum error to unambiguous measurements for binary coherent states. As a particular case, we use this general measurement to implement the optimal minimum error measurement for phase-coherent states, which is the optimal modulation for communications under the average power constraint. Moreover, we propose a hybrid measurement that leverages the binary optimal inconclusive measurement in conjunction with sequential, unambiguous state elimination to realize higher dimensional inconclusive measurements of coherent states. 

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