Quantum steering is the ability to remotely prepare different quantum states by using entangled pairs as a resource. Very recently, the concept of steering has been quantified with the use of inequalities, leading to substantial applications in quantum information and communication science. Here, we highlight that there exists a natural temporal analog of the steering inequality when considering measurements on a single object at different times. We give nontrivial operational meaning to violations of this temporal inequality by showing that it is connected to the security bound in the Bennett-Brassard 1984 protocol and thus may have applications in quantum communication.
Quantum steering is the ability to remotely prepare different quantum states by using entangled pairs as a resource. Very recently, the concept of steering has been quantified with the use of inequalities, leading to substantial applications in quantum information and communication science. Here, we highlight that there exists a natural temporal analog of the steering inequality when considering measurements on a single object at different times. We give nontrivial operational meaning to violations of this temporal inequality by showing that it is connected to the security bound in the Bennett-Brassard 1984 protocol and thus may have applications in quantum communication.
Temporal steering is a form of temporal correlation between the initial and final state of a quantum system. It is a temporal analogue of the famous Einstein-Podolsky-Rosen (spatial) steering. We demonstrate, by measuring the photon polarization, that temporal steering allows two parties to verify if they have been interacting with the same particle, even if they have no information about what happened with the particle in between the measurements. This is the first experimental study of temporal steering. We also performed experimental tests, based on the violation of temporal steering inequalities, of the security of two quantum key distribution protocols against individual attacks. Thus, these results can lead to applications for secure quantum communications and quantum engineering.
Temporal steering, which is a temporal analog of Einstein-Podolsky-Rosen steering, refers to temporal quantum correlations between the initial and final state of a quantum system. Our analysis of temporal steering inequalities in relation to the average quantum bit error rates reveals the interplay between temporal steering and quantum cloning, which guarantees the security of quantum key distribution based on mutually unbiased bases against individual attacks. The key distributions analyzed here include the Bennett-Brassard 1984 protocol and the six-state 1998 protocol by Bruss. Moreover, we define a temporal steerable weight, which enables us to identify a kind of monogamy of temporal correlation that is essential to quantum cryptography and useful for analyzing various scenarios of quantum causality.
Quantum steering, also called Einstein-Podolsky-Rosen steering, is the intriguing phenomenon associated with the ability of spatially separated observers to steer---by means of local measurements---the set of conditional quantum states accessible by a distant party. In the light of quantum information, all steerable quantum states are known to be resources for quantum information processing tasks. Here, via a quantity dubbed steering fraction, we derive a simple, but general criterion that allows one to identify quantum states that can exhibit quantum steering (without having to optimize over the measurements performed by each party), thus making an important step towards the characterization of steerable quantum states. The criterion, in turn, also provides upper bounds on the largest steering-inequality violation achievable by arbitrary finite-dimensional maximally entangled states. For the quantification of steerability, we prove that a strengthened version of the steering fraction is a convex steering monotone and demonstrate how it is related to two other steering monotones, namely, steerable weight and steering robustness. Using these tools, we further demonstrate the superactivation of steerability for a well-known family of entangled quantum states, i.e., we show how the steerability of certain entangled, but unsteerable quantum states can be recovered by allowing joint measurements on multiple copies of the same state. In particular, our approach allows one to explicitly construct a steering inequality to manifest this phenomenon. Finally, we prove that there exist examples of quantum states (including some which are unsteerable under projective measurements) whose steering-inequality violation can be arbitrarily amplified by allowing joint measurements on as little as three copies of the same state. For completeness, we also demonstrate how the largest steering-inequality violation can be used to bound the largest Bell-inequality violation and derive, analogously, a simple sufficient condition for Bell nonlocality from the latter.
Steerability is a characteristic of quantum correlations lying between entanglement and Bell nonlocality. Understanding how these steering correlations can be shared between different parties has profound applications in ensuring the security of quantum communication protocols. Here we show that at most two bipartite reduced states of a three-qubit state can violate the three-setting CJWR linear steering inequality, contrary to the two-setting linear steering inequality. This result explains that quantum steering correlations have limited shareability properties apart from the conventional 'nonshareable' monogamy constraint. In contrast to the two-measurement-setting scenario, the three-setting scenario turns out to be more useful for developing a deeper understanding of the shareability of tripartite steering correlations. Apart from the distribution of steering correlations, several relations between reduced bipartite steering, different measures of bipartite entanglement of reduced states, and genuine tripartite entanglement are presented here. The results enable the detection of different kinds of tripartite entanglement.
We show how single system steering can be exhibited by classical light, a feature originating from superposition in classical optics that also enables entanglement and Bell-violation by classical light beams. Single system steering is the temporal analogue of Einstein-Podolsky-Rosen (EPR) steering in the quantum domain, enabling control of the state of a remote system, and can hence be connected to the security of secret key generation between two remote parties. We derive the steering criterion for a single mode coherent state when displaced parity measurements are performed at two different times. The security bound of the Bennett-Brassard 1984 (BB84) protocol under the gaussian cloning attack is calculated to yield an, in principle, ideal and quantum-like key rate using a fine-grained uncertainty relation corresponding to the classical phase space.
The wave-particle duality of light has led to two different encodings of optical quantum information. One approach, refered as the discrete-variable (DV) one, relies on finite dimensional quantum systems, while the other one, refered as the continuous-variable (CV) one, is based on wave-like states belonging to an infinite dimensional Hilbert space. These two encodings have historically been separated, but recently, new hybrid protocols which aim at combining the two complementary encodings have emerged [1]. In that prospect our recent demonstration of the measurement-induced generation of hybrid entanglement between discrete and continuous-variable quantum states generated using optical parametric oscillators [2], located at distant places and connected by a lossy channel, has opened the way to the implementation of hybrid protocols and heterogeneous quantum networks. Here we will report the first protocols based on this resource: the remote preparation of continuous-variable qubits [3], and a violation of an Einstein-Podolosky-Rosen steering inequality [4].