01762nas a2200133 4500008004100000245007100041210006900112260001400181520134900195100001601544700001801560700001301578856003701591 2023 eng d00aParallel self-testing of EPR pairs under computational assumptions0 aParallel selftesting of EPR pairs under computational assumption c3/29/20233 a
Self-testing is a fundamental feature of quantum mechanics that allows a classical verifier to force untrusted quantum devices to prepare certain states and perform certain measurements on them. The standard approach assumes at least two spatially separated devices. Recently, Metger and Vidick [Quantum, 2021] showed that a single EPR pair of a single quantum device can be self-tested under computational assumptions. In this work, we generalize their results to give the first parallel self-test of N EPR pairs and measurements on them in the single-device setting under the same computational assumptions. We show that our protocol can be passed with probability negligibly close to 1 by an honest quantum device using poly(N) resources. Moreover, we show that any quantum device that fails our protocol with probability at most ϵ must be poly(N,ϵ)-close to being honest in the appropriate sense. In particular, our protocol can test any distribution over tensor products of computational or Hadamard basis measurements, making it suitable for applications such as device-independent quantum key distribution under computational assumptions. Moreover, a simplified version of our protocol is the first that can efficiently certify an arbitrary number of qubits of a single cloud quantum computer using only classical communication.
1 aFu, Honghao1 aWang, Daochen1 aZhao, Qi uhttps://arxiv.org/abs/2201.1343001762nas a2200133 4500008004100000245007100041210006900112260001400181520134900195100001601544700001801560700001301578856003701591 2023 eng d00aParallel self-testing of EPR pairs under computational assumptions0 aParallel selftesting of EPR pairs under computational assumption c3/29/20233 aSelf-testing is a fundamental feature of quantum mechanics that allows a classical verifier to force untrusted quantum devices to prepare certain states and perform certain measurements on them. The standard approach assumes at least two spatially separated devices. Recently, Metger and Vidick [Quantum, 2021] showed that a single EPR pair of a single quantum device can be self-tested under computational assumptions. In this work, we generalize their results to give the first parallel self-test of N EPR pairs and measurements on them in the single-device setting under the same computational assumptions. We show that our protocol can be passed with probability negligibly close to 1 by an honest quantum device using poly(N) resources. Moreover, we show that any quantum device that fails our protocol with probability at most ϵ must be poly(N,ϵ)-close to being honest in the appropriate sense. In particular, our protocol can test any distribution over tensor products of computational or Hadamard basis measurements, making it suitable for applications such as device-independent quantum key distribution under computational assumptions. Moreover, a simplified version of our protocol is the first that can efficiently certify an arbitrary number of qubits of a single cloud quantum computer using only classical communication.
1 aFu, Honghao1 aWang, Daochen1 aZhao, Qi uhttps://arxiv.org/abs/2201.1343001289nas a2200169 4500008004100000245004100041210004100082260001400123520084200137100002300979700001601002700001801018700001201036700001701048700001701065856003701082 2023 eng d00aStreaming quantum state purification0 aStreaming quantum state purification c9/28/20233 aQuantum state purification is the task of recovering a nearly pure copy of an unknown pure quantum state using multiple noisy copies of the state. This basic task has applications to quantum communication over noisy channels and quantum computation with imperfect devices, but has only been studied previously for the case of qubits. We derive an efficient purification procedure based on the swap test for qudits of any dimension, starting with any initial error parameter. Treating the initial error parameter and the dimension as constants, we show that our procedure has sample complexity asymptotically optimal in the final error parameter. Our protocol has a simple recursive structure that can be applied when the states are provided one at a time in a streaming fashion, requiring only a small quantum memory to implement.
1 aChilds, Andrew, M.1 aFu, Honghao1 aLeung, Debbie1 aLi, Zhi1 aOzols, Maris1 aVyas, Vedang uhttps://arxiv.org/abs/2309.1638701123nas a2200133 4500008004100000245012100041210006900162260001500231300000800246490000600254520067600260100001600936856003700952 2022 eng d00aConstant-sized correlations are sufficient to robustly self-test maximally entangled states with unbounded dimension0 aConstantsized correlations are sufficient to robustly selftest m c01/03/2022 a6140 v63 aWe show that for any prime odd integer d, there exists a correlation of size Θ(r) that can robustly self-test a maximally entangled state of dimension 4d−4, where r is the smallest multiplicative generator of Z∗d. The construction of the correlation uses the embedding procedure proposed by Slofstra (Forum of Mathematics, Pi. Vol. 7, (2019)). Since there are infinitely many prime numbers whose smallest multiplicative generator is at most 5 (M. Murty The Mathematical Intelligencer 10.4 (1988)), our result implies that constant-sized correlations are sufficient for robust self-testing of maximally entangled states with unbounded local dimension.
1 aFu, Honghao uhttps://arxiv.org/abs/1911.0149402078nas a2200277 4500008004100000245006700041210006600108260001500174520125200189100002201441700001801463700002501481700002101506700002401527700002501551700002101576700002001597700002501617700002601642700001601668700001901684700002301703700001801726700001901744856003701763 2021 eng d00aDevice-independent Randomness Expansion with Entangled Photons0 aDeviceindependent Randomness Expansion with Entangled Photons c01/28/20213 aWith the growing availability of experimental loophole-free Bell tests, it has become possible to implement a new class of device-independent random number generators whose output can be certified to be uniformly random without requiring a detailed model of the quantum devices used. However, all of these experiments require many input bits in order to certify a small number of output bits, and it is an outstanding challenge to develop a system that generates more randomness than is used. Here, we devise a device-independent spot-checking protocol which uses only uniform bits as input. Implemented with a photonic loophole-free Bell test, we can produce 24% more certified output bits (1,181,264,237) than consumed input bits (953,301,640), which is 5 orders of magnitude more efficient than our previous work [arXiv:1812.07786]. The experiment ran for 91.0 hours, creating randomness at an average rate of 3606 bits/s with a soundness error bounded by 5.7×10−7 in the presence of classical side information. Our system will allow for greater trust in public sources of randomness, such as randomness beacons, and the protocols may one day enable high-quality sources of private randomness as the device footprint shrinks.
1 aShalm, Lynden, K.1 aZhang, Yanbao1 aBienfang, Joshua, C.1 aSchlager, Collin1 aStevens, Martin, J.1 aMazurek, Michael, D.1 aAbellán, Carlos1 aAmaya, Waldimar1 aMitchell, Morgan, W.1 aAlhejji, Mohammad, A.1 aFu, Honghao1 aOrnstein, Joel1 aMirin, Richard, P.1 aNam, Sae, Woo1 aKnill, Emanuel uhttps://arxiv.org/abs/1912.1115801577nas a2200133 4500008004100000245008200041210006900123260001400192520114500206100001601351700001701367700002201384856003701406 2021 eng d00aThe membership problem for constant-sized quantum correlations is undecidable0 amembership problem for constantsized quantum correlations is und c1/26/20213 aWhen two spatially separated parties make measurements on an unknown entangled quantum state, what correlations can they achieve? How difficult is it to determine whether a given correlation is a quantum correlation? These questions are central to problems in quantum communication and computation. Previous work has shown that the general membership problem for quantum correlations is computationally undecidable. In the current work we show something stronger: there is a family of constant-sized correlations -- that is, correlations for which the number of measurements and number of measurement outcomes are fixed -- such that solving the quantum membership problem for this family is computationally impossible. Thus, the undecidability that arises in understanding Bell experiments is not dependent on varying the number of measurements in the experiment. This places strong constraints on the types of descriptions that can be given for quantum correlation sets. Our proof is based on a combination of techniques from quantum self-testing and from undecidability results of the third author for linear system nonlocal games.
1 aFu, Honghao1 aMiller, Carl1 aSlofstra, William uhttps://arxiv.org/abs/2101.1108701938nas a2200145 4500008004100000245007300041210006900114260001300183490000600196520143200202100001801634700001601652700001901668856010501687 2020 eng d00aEfficient randomness certification by quantum probability estimation0 aEfficient randomness certification by quantum probability estima c1/7/20200 v23 aFor practical applications of quantum randomness generation, it is important to certify and further produce a fixed block of fresh random bits with as few trials as possible. Consequently, protocols with high finite-data efficiency are preferred. To yield such protocols with respect to quantum side information, we develop quantum probability estimation. Our approach is applicable to device-independent as well as device-dependent scenarios, and it generalizes techniques from previous works [Miller and Shi, SIAM J. Comput. 46, 1304 (2017); Arnon-Friedman et al., Nat. Commun. 9, 459 (2018)]. Quantum probability estimation can adapt to changing experimental conditions, allows stopping the experiment as soon as the prespecified randomness goal is achieved, and can tolerate imperfect knowledge of the input distribution. Moreover, the randomness rate achieved at constant error is asymptotically optimal. For the device-independent scenario, our approach certifies the amount of randomness available in experimental results without first searching for relations between randomness and violations of fixed Bell inequalities. We implement quantum probability estimation for device-independent randomness generation in the CHSH Bell-test configuration, and we show significant improvements in finite-data efficiency, particularly at small Bell violations which are typical in current photonic loophole-free Bell tests.
1 aZhang, Yanbao1 aFu, Honghao1 aKnill, Emanuel uhttps://quics.umd.edu/publications/efficient-randomness-certification-quantum-probability-estimation01465nas a2200265 4500008004100000245006700041210006500108260001500173490000800188520070100196100001800897700002200915700002500937700002400962700002500986700001801011700002101029700002001050700002501070700001601095700001701111700001501128700001901143856003701162 2020 eng d00aExperimental Low-Latency Device-Independent Quantum Randomness0 aExperimental LowLatency DeviceIndependent Quantum Randomness c12/24/20190 v1243 aApplications of randomness such as private key generation and public randomness beacons require small blocks of certified random bits on demand. Device-independent quantum random number generators can produce such random bits, but existing quantum-proof protocols and loophole-free implementations suffer from high latency, requiring many hours to produce any random bits. We demonstrate device-independent quantum randomness generation from a loophole-free Bell test with a more efficient quantum-proof protocol, obtaining multiple blocks of 512 bits with an average experiment time of less than 5 min per block and with certified error bounded by 2−64≈5.42×10−20.
1 aZhang, Yanbao1 aShalm, Lynden, K.1 aBienfang, Joshua, C.1 aStevens, Martin, J.1 aMazurek, Michael, D.1 aNam, Sae, Woo1 aAbellán, Carlos1 aAmaya, Waldimar1 aMitchell, Morgan, W.1 aFu, Honghao1 aMiller, Carl1 aMink, Alan1 aKnill, Emanuel uhttps://arxiv.org/abs/1812.0778601139nas a2200133 4500008004100000245004700041210004600088260001200134300001100146520077800157100001600935700001700951856003700968 2018 eng d00aLocal randomness: Examples and application0 aLocal randomness Examples and application c03/2018 a0323243 aWhen two players achieve a superclassical score at a nonlocal game, their outputs must contain intrinsic randomness. This fact has many useful implications for quantum cryptography. Recently it has been observed [C. Miller and Y. Shi, Quantum Inf. Computat. 17, 0595 (2017)] that such scores also imply the existence of local randomness—that is, randomness known to one player but not to the other. This has potential implications for cryptographic tasks between two cooperating but mistrustful players. In the current paper we bring this notion toward practical realization, by offering near-optimal bounds on local randomness for the CHSH game, and also proving the security of a cryptographic application of local randomness (single-bit certified deletion).
1 aFu, Honghao1 aMiller, Carl uhttps://arxiv.org/abs/1708.0433801302nas a2200145 4500008004100000245011100041210006900152260001300221490000700234520073400241100001600975700001800991700002101009856012601030 2014 eng d00aWhen the asymptotic limit offers no advantage in the local-operations-and-classical-communication paradigm0 aWhen the asymptotic limit offers no advantage in the localoperat c5/9/20140 v893 aWe consider bipartite LOCC, the class of operations implementable by local quantum operations and classical communication between two parties. Surprisingly, there are operations that can be approximated to arbitrary precision but are impossible to implement exactly if only a finite number of messages are exchanged. This significantly complicates the analysis of what can or cannot be approximated with LOCC. Toward alleviating this problem, we exhibit two scenarios in which allowing vanishing error does not help. The first scenario is implementation of projective measurements with product measurement operators. The second scenario is the discrimination of unextendable product bases on two three-dimensional systems.
1 aFu, Honghao1 aLeung, Debbie1 aMancinska, Laura uhttps://quics.umd.edu/publications/when-asymptotic-limit-offers-no-advantage-local-operations-and-classical-communication