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arXiv:1503.00612 · Physical Review A

Temporal steering and security of quantum key distribution with mutually unbiased bases against individual attacks

Karol Bartkiewicz, Antonín Černoch, Karel Lemr, Adam Miranowicz, Franco Nori

Published Jun 28, 2016• 58 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.93.062345

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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.
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.
Einstein--Podolsky--Rosen (EPR) steering allows Alice to remotely prepare a state in some specific bases for Bob through her choice of measurements. The temporal analog of EPR steering, temporal steering, also reveals the steerability of a single system between different times. Focusing on a four-dimensional system, here we investigate the dynamics of the temporal steering measures, the temporal steering robustness, using five mutually unbiased bases. As an example of an application, we use these measures to examine the temporal correlations in a radical pair model of magnetoreception. We find that, due to interactions with a static nuclear spin, the radical pair model exhibits strong non-Markovianity.
Einstein-Podolsky-Rosen (EPR) steering is a type of quantum correlation which allows one to remotely prepare, or steer, the state of a distant quantum system. While EPR steering can be thought of as a purely spatial correlation, there does exist a temporal analogue, in the form of single-system temporal steering. However, a precise quantification of such temporal steering has been lacking. Here, we show that it can be measured, via semidefinite programing, with a temporal steerable weight, in direct analogy to the recently proposed EPR steerable weight. We find a useful property of the temporal steerable weight in that it is a nonincreasing function under completely positive trace-preserving maps and can be used to define a sufficient and practical measure of strong non-Markovianity.
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.
Einstein-Podolsky-Rosen (EPR) steering is a type of quantum correlation which allows one to remotely prepare, or steer, the state of a distant quantum system. While EPR steering can be thought of as a purely spatial correlation there does exist a temporal analogue, in the form of single-system temporal steering. However, a precise quantification of such temporal steering has been lacking. Here we show that it can be measured, via semidefinite programming, with a temporal steerable weight, in direct analogy to the recently proposed EPR steerable weight. We find a unique application for both, this and a spatio-temporal extension, by showing that they are monotonically-decreasing functions under completely-positive trace-preserving maps and thus can be used to define a practical measure of strong non-Markovianity. Finally, we discuss how a spatio-temporal steerable weight can be used to check whether two nodes of a quantum network are quantum connected.
Einstein-Podolsky-Rosen (EPR) steering describes how different ensembles of quantum states can be remotely prepared by measuring one particle of an entangled pair. Here, we investigate quantum steering for single quantum ddd-dimensional systems (qudits) and devise efficient conditions to certify the steerability therein, which we find are applicable both to single-system steering and EPR steering. In the single-system case our steering conditions enable the unambiguous ruling out of generic classical means of mimicking steering. Ruling out ``false-steering'' scenarios has implications for securing channels against both cloning-based individual attack and coherent attacks when implementing quantum key distribution using qudits. We also show that these steering conditions also have applications in quantum computation, in that they can serve as an efficient criterion for the evaluation of quantum logic gates of arbitrary size. Finally, we describe how the nonlocal EPR variant of these conditions also function as tools for identifying faithful one-way quantum computation, secure entanglement-based quantum communication, and genuine multipartite EPR steering.