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.
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.
We propose a method to verify quantum steering for two-qubit states with an arbitrary amount of null results when both the steering and steered parties cannot be trusted. We converted the steering inequality proposed in a recent article [Phys. Rev. X 2, 031003 (2012)] to a corresponding measurement-device-independent steering criterion that depends on the heralding efficiency of the steering party, number of measurement settings, and imperfection of the state preparation. As a result, for a relative frequency of valid measurement outcomes ${\ensuremath{\eta}}_{h}$, the steering can be verified using a number of different measurement settings larger than $1/{\ensuremath{\eta}}_{h}$ and maximally entangled states. Furthermore, steerability is guaranteed as long as the measurement efficiency of the steered party is nonzero. Our result is useful for loss-tolerant and measurement-device-independent steering tasks.
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 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.
Entanglement lies at the heart of quantum mechanics, and has been identified as an essential resource for diverse applications in quantum information. If entanglement could be verified without any trust in the devices of observers, i.e., in a device-independent (DI) way, then high security could be guaranteed for various quantum information processing tasks. In this work, we propose and experimentally demonstrate a DI protocol to certify the presence of entanglement based on Einstein–Podolsky–Rosen (EPR) steering. We first establish the DI verification framework by taking advantage of a measurement-device-independent technique and self-testing, which is able to verify all bipartite EPR-steerable states. In the scenario of three-measurement settings per party, the protocol is robust in tolerance of inefficient measurements and imperfect self-testing. Moreover, a four-photon experiment is implemented for verification beyond Bell nonlocal states. Our work enables further insight into quantum physics and could facilitate realistic implementation of secure quantum information processing tasks.
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.
We consider a quantum steering scenario where Alice prepares a bipartite state, sends one subsystem to Bob through a quantum channel, and aims to convince him that their shared state is entangled. Bob, however, will never be convinced if the channel is steering-breaking, that is, if the channel destroys steerability for any input state. To verify that a channel renders a state useless for demonstrating steering, one must consider all possible measurements performed by Alice and check if the conditional states Bob receives admit a local-hidden-state (LHS) model. This is generally a hard problem since it requires considering an infinite number of measurement combinations. Here, we show that the method proposed in [Phys. Rev. Lett. 117, 190401 (2016); Phys. Rev. Lett. 117, 190402 (2016)] can be utilized to tackle this problem. Furthermore, owing to the intimate relation between steering and measurement incompatibility, our approach can faithfully certify whether a channel destroys incompatibility for any set of measurements. Finally, we propose an experimental criterion for certifying steering- and incompatibility-breaking channels, which may be of independent interest.