Abstract Within the framework of quantum refereed steering games, quantum steerability can be certified without any assumption on the underlying state nor the measurements involved. Such a scheme is termed the measurement-device-independent (MDI) scenario. Here, we introduce a measure of steerability in an MDI scenario, i.e., the result merely depends on the observed statistics and the quantum inputs. We prove that such a measure satisfies the convex steering monotone. Moreover, it is robust against not only measurement biases but also losses. We also experimentally estimate the amount of the measure with an entangled photon source. As two by-products, our experimental results provide lower bounds on an entanglement measure of the underlying state and an incompatible measure of the involved measurement. Our research paves a way for exploring one-side device-independent quantum information processing within an MDI framework.
Abstract Within the framework of quantum refereed steering games, quantum steerability can be certified without any assumption on the underlying state nor the measurements involved. Such a scheme is termed the measurement-device-independent (MDI) scenario. Here, we introduce a measure of steerability in an MDI scenario, i.e., the result merely depends on the observed statistics and the quantum inputs. We prove that such a measure satisfies the convex steering monotone. Moreover, it is robust against not only measurement biases but also losses. We also experimentally estimate the amount of the measure with an entangled photon source. As two by-products, our experimental results provide lower bounds on an entanglement measure of the underlying state and an incompatible measure of the involved measurement. Our research paves a way for exploring one-side device-independent quantum information processing within an MDI framework.
The fact that nonlocality implies steering enables one to certify steerability by using a Bell inequality violation. Such a certification is device-independent (DI), i.e., one makes no assumption neither on the underlying state nor on the measurements. However, not all steerable states can violate a Bell inequality. Here, we systematically construct a collection of witnesses for steerable resources, defined by assemblages, in a measurement-device-independent (MDI) scenario. The inputs driving the measurement are replaced by a set of tomographically complete quantum states, and neither the detectors nor the underlying state is characterized. We show that all steerable assemblages can be detected by properly chosen witnesses. Furthermore, we introduce the first measure of steerability in an MDI scenario and show that such a measure is a standard one, i.e., a steering monotone, by proving that it is equivalent to the steering robustness.
Quantum steering captures the ability of one party, through local measurements on a shared entangled state, to affect the conditional states held by distant parties in a way that admits no local explanation. Its device-independent (DI) quantification -- requiring no characterization of any state or measurement -- has been developed in the bipartite setting, notably through the framework of assemblage moment matrices (AMMs) [Phys. Rev. Lett. 116, 240401 (2016)], but has remained largely unexplored beyond it. Here, we extend the AMM framework to tripartite steering, covering both the scenario in which two parties jointly steer a third one (2-steer-1) and that in which a single party steers the remaining two (1-steer-2). For each scheme, we construct a semidefinite program that, from the observed correlations -- or merely from the violation of a Bell inequality -- yields lower bounds on the steering robustness of the underlying assemblage. As a by-product, our bounds also certify, in a DI manner, the incompatibility of the measurements performed by the steering parties.
Abstract The semi-device-independent (DI) scenario requires measurement outcomes to be perfectly accurate, which is generally unattainable in experiments. To address this limitation, we consider an measurement-DI (MDI) scheme that relaxes the constraints on measurement outcomes. However, a fully MDI framework imposes strong quantum capability requirements on all communicating parties. To overcome this, we propose a semi-MDI (SMDI) framework and demonstrate its security within a communication channel. Building on this, we introduce a quantum steering distillation protocol based on the SMDI framework that can tolerate arbitrary imprecise measurements. Furthermore, we successfully distill mixed steerable states, demonstrating that even imperfect states can be distilled into maximally steerable states within the allowed range of measurement errors.
Abstract If the presence of entanglement could be certified in a device-independent (DI) way, it is likely to provide various quantum information processing tasks with unconditional security. Recently, it was shown that a DI protocol, combining measurement-device-independent techniques with self-testing, is able to verify all entangled states, however, it imposes demanding requirements on its experimental implementation. In this work, we propose a much less-demanding protocol based on Einstein-Podolsky-Rosen (EPR) steering to certify entanglement. We establish a complete framework for DI verification of EPR steering in which all steerable states could be verified. We then analyze its robustness towards noise and imperfections of self-testing by considering the measurement scenario with three settings at each side. Finally, a four-photon experiment is implemented to demonstrate that even Bell local states can be device-independently verified. Our work may pave the way for realistic applications of secure quantum information tasks.
Extending the concept of steerability for quantum states, channel steerability is an ability to remotely control the given channel from a coherently extended party. Verification of channel steering can be understood as certifying coherence of the channel in a one-sided device-independent manner with respect to a bystander. Here we propose a method to verify channel steering in a measurement-device-independent way. To do this, we first obtain Choi matrices from given channels and use the canonical method of measurement-device-independent verification of quantum steering. As a consequence, exploiting channel-state duality which interconverts steerability of channels and that of states, channel steering is verified. We further analyze the effect of imperfect preparation of entangled states used in the verification protocol, and find that the threshold of the undesired noise that we can tolerate is bounded from below by steering robustness.
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 party's 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 1.106±0.023 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.