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Register a new userExperimental investigation of partially entangled states for device-independent randomness generation and self-testing protocols
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Previous theoretical works showed that all pure two-qubit entangled states can generate one bit of local randomness and can be self-tested through the violation of proper Bell inequalities. We report an experiment in which nearly pure partially entangled states of photonic qubits are produced to investigate these tasks in a practical scenario. We show that small deviations from the ideal situation make low entangled states impractical to self-testing and randomness generation using the available techniques. Our results show that in practice lower entanglement implies lower randomness generation, recovering the intuition that maximally entangled states are better candidates for deviceindependent quantum information processing.
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In a measurement-device-independent or quantum-refereed protocol, a referee can verify whether two parties share entanglement or Einstein-Podolsky-Rosen (EPR) steering without the need to trust either of the parties or their devices. The need for trusting a party is substituted by a quantum channel between the referee and that party, through which the referee encodes the measurements to be performed on that partys subsystem in a set of nonorthogonal quantum states. In this Letter, an EPR-steering inequality is adapted as a quantum-refereed EPR-steering witness, and the trust-free experimental verification of higher dimensional quantum steering is reported via preparing a class of entangled photonic qutrits. Further, with two measurement settings, we extract $1.106pm0.023$ bits of private randomness per every photon pair from our observed data, which surpasses the one-bit limit for projective measurements performed on qubit systems. Our results advance research on quantum information processing tasks beyond qubits.
With 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 $5.7times 10^{-7}$ 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.
Self-testing protocols are methods to determine the presence of shared entangled states in a device independent scenario, where no assumptions on the measurements involved in the protocol are made. A particular type of self-testing protocol, called parallel self-testing, can certify the presence of copies of a state, however such protocols typically suffer from the problem of requiring a number of measurements that increases with respect to the number of copies one aims to certify. Here we propose a procedure to transform single-copy self-testing protocols into a procedure that certifies the tensor product of an arbitrary number of (not necessarily equal) quantum states, without increasing the number of parties or measurement choices. Moreover, we prove that self-testing protocols that certify a state and rank-one measurements can always be parallelized to certify many copies of the state. Our results suggest a method to achieve device-independent unbounded randomness expansion with high-dimensional quantum states.
The intrinsic random nature of quantum physics offers novel tools for the generation of random numbers, a central challenge for a plethora of fields. Bell non-local correlations obtained by measurements on entangled states allow for the generation of bit strings whose randomness is guaranteed in a device-independent manner, i.e. without assumptions on the measurement and state-generation devices. Here, we generate this strong form of certified randomness on a new platform: the so-called instrumental scenario, which is central to the field of causal inference. First, we theoretically show that certified random bits, private against general quantum adversaries, can be extracted exploiting device-independent quantum instrumental-inequality violations. To that end, we adapt techniques previously developed for the Bell scenario. Then, we experimentally implement the corresponding randomness-generation protocol using entangled photons and active feed-forward of information. Moreover, we show that, for low levels of noise, our protocol offers an advantage over the simplest Bell-nonlocality protocol based on the Clauser-Horn-Shimony-Holt inequality.
Applications 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 a certified error bounded by $2^{-64}approx 5.42times 10^{-20}$.
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