Using Venn diagrams, we classify the different types of two-mode Gaussian continuous variable quantum correlation including directional entanglement and Einstein-Podolsky-Rosen (EPR) steering. We establish unified signatures for one- and two-way quantum steering, entanglement, and discord beyond entanglement in terms of an EPR-type variance. By focusing on Gaussian states, we link an optimized condition for entanglement based on an EPR variance to the Simon-Peres condition. This allows us to quantify the asymmetry of the Gaussian entanglement, and to relate the asymmetry to a directional quantum teleportation protocol where Alice and Bob possess asymmetrically noisy channels. Our analysis enables a determination of the type and direction of quantum correlation in a way that is easily measured in experiment. We also find that for symmetric states, when discord exceeds a certain threshold, the states are necessarily steerable.
Using Venn diagrams, we classify the different types of two-mode Gaussian continuous variable quantum correlation including directional entanglement and Einstein-Podolsky-Rosen (EPR) steering. We establish unified signatures for one- and two-way quantum steering, entanglement, and discord beyond entanglement in terms of an EPR-type variance. By focusing on Gaussian states, we link an optimized condition for entanglement based on an EPR variance to the Simon-Peres condition. This allows us to quantify the asymmetry of the Gaussian entanglement, and to relate the asymmetry to a directional quantum teleportation protocol where Alice and Bob possess asymmetrically noisy channels. Our analysis enables a determination of the type and direction of quantum correlation in a way that is easily measured in experiment. We also find that for symmetric states, when discord exceeds a certain threshold, the states are necessarily steerable.
Steering is a manifestation of quantum correlations that embodies the Einstein-Podolsky-Rosen (EPR) paradox. While there have been recent attempts to quantify steering, continuous variable systems remained elusive. We in-troduce a steering measure for two-mode continuous variable systems that is valid for arbitrary states. The measure is based on the violation of an optimized variance test for the EPR paradox, and admits a computable and exper-imentally friendly lower bound only depending on the second moments of the state, which reduces to a recently proposed quantifier of steerability by Gaussian measurements. We further show that Gaussian states are extremal with respect to our measure, minimizing it among all continuous variable states with fixed second moments. As a byproduct of our analysis, we generalize and relate well-known EPR-steering criteria. Finally an operational inter-pretation is provided, as the proposed measure is shown to quantify the optimal guaranteed key rate in semi-device independent quantum key distribution. 1.
Steering is a manifestation of quantum correlations that embodies the Einstein–Podolsky–Rosen (EPR) paradox. While there have been recent attempts to quantify steering, continuous variable systems remained elusive. We introduce a steering measure for two-mode continuous variable systems that is valid for arbitrary states. The measure is based on the violation of an optimized variance test for the EPR paradox by quadrature measurements and admits a computable and experimentally friendly lower bound only depending on the second moments of the state, which reduces to a recently proposed quantifier of steerability by Gaussian measurements. We further show that Gaussian states are extremal with respect to our measure, minimizing it among all continuous variable states with fixed second moments. As a byproduct of our analysis, we generalize and relate well-known EPR-steering criteria. Finally an operational interpretation is provided, as the proposed measure is shown to quantify a guaranteed key rate in semi-device-independent quantum key distribution.
We propose and demonstrate a standard form of Einstein-Podolsky-Rosen (EPR) steering for an arbitrary bipartite Gaussian state under which a simple EPR steering criterion for two-photon correlation can be achieved. In terms of a beam splitter preparing three different steerable states, we further test that the simplified criterion is reliable and efficient when it is used to determine whether an arbitrary bipartite Gaussian state is steerable or not. Based on the same theoretical framework, the standard form and criterion of entanglement are reconstructed and discussed. Furthermore, it is found that EPR steering requires stronger two-photon correlation than entanglement, while its direction is strictly dependent on the mean photon number of two light modes. Moreover, the inherent asymmetric feature can be intuitively embodied in the corresponding criteria, and the essential difference and inherent relation between two standard forms is revealed. We hope the present results could be helpful for potential applications in quantum information processing.
Quantum states can be correlated in ways beyond what is possible for classical states. These correlations are considered as the main resource for quantum computation and communication tasks. In this thesis, I present my studies on the different forms of Quantum Correlations known as "Quantum Discord", "Einstein-Podolsky-Rosen(EPR) Steering" and "Bel-type correlations" in the continuous-variable quantum states and investigate their practical applications for the secure quantum communication. While previously quantum entanglement was considered as the only form of quantum correlation, in the recent years a notion known as quantum discord which captures extra quantum correlations beyond entanglement was introduced by Ollivier and Zurek. This sort of non-classicality that can exist even in separable states, has raised so much aspiration for the potential applications, as they are less fragile than the entangled states. Therefore, of especial interest is to know if a bipartite quantum state is discordant or not. In this thesis I will describe the simple and efficient experimental technique that we have introduced and experimentally implemented to verify quantum discord in unknown Gaussian states and a certain class of non-Gaussian states. According to our method, the peak separation between the marginal distributions of one subsystem conditioned on two different outcomes of homodyne measurement conducted on the other subsystem is an indication of nonzero quantum discord. We implemented this method experimentally by preparing bipartite Gaussian and non-Gaussian states and proved nonzero quantum discord in all the prepared states. Though quantum key distribution has become a mature technology, the possibility of hacking the devices used in the quantum communications has motivated the scientists to develop the schemes where one or non of the devices used by the communicating parties need to be trusted. Quantum correlations are the key to develop these schemes. Particularly, EPR steering is connected to the one-sided-deviceindependent quantum key distribution in which devices of one party are solely trusted and Bell-type correlations to the fully device-independent quantum key distribution where non of the apparatuses of the communicating parties is trusted. Here, I will present the result of our theoretical and experimental research to develop one-sided-device-independent quantum key distribution in continuous variables. We identify all Gaussian protocols that can in principle be one-sided-device independent. This consists of 6 protocols out of 16 possible Gaussian protocols, which surprisingly includes the protocol that applies only coherent states. We experimentally implemented both the entanglement-based and coherent state protocols and manifested their loss tolerance. Our results open the door for the practical secure quantum communications, asserting the link between the EPR-steering andone-sided-device-independence. Due to the maturity of quantum information using continuous variables, it is important to develop a Bell-type inequality in this regime. Despite its fundamental importance, Bell-type correlation is linked to the device-independent quantum key distribution. I developed a computer modelling based on the proposal of ref [1, 2] to demonstrate continuous-variable Bell-type correlation. The results of my computer simulations that are presented in this thesis show the feasibility of these proposals, which makes the real-life implementation of continuous-variable device-independent quantum key distribution possible.
This PhD Dissertation collects results of my own work on the topic of continuous variable (CV) quantum teleportation, which is one of the most important applications of quantum entanglement, as well as on the understanding, quantification, detection, and applications of a type of quantum correlations known as Einstein-Podolsky-Rosen (EPR) steering, for both bipartite and multipartite systems and with a main focus on CV systems. For the first results, we examine and compare two fundamentally different teleportation schemes; the well-known continuous variable scheme of Vaidman, Braunstein and Kimble, and a recently proposed hybrid scheme by Andersen and Ralph. We analyse the teleportation of ensembles of arbitrary pure single-mode Gaussian states using these schemes and compare their performance against classical strategies that utilize no entanglement (benchmarks). Our analysis brings into question any advantage due to non-Gaussianity for quantum teleportation of Gaussian states. For the second part of the results, we study bipartite EPR-steering. We propose a novel powerful method to detect steering in quantum systems of any dimension in a systematic and hierarchical way. Our method includes previous results of the literature as special cases on one hand, and goes beyond them on the other. We proceed to the quantification of steering-type correlations, and introduce a measure of steering for arbitrary bipartite Gaussian states, prove many useful properties, and provide with an operational interpretation of the proposed measure in terms of the key rate in one-sided device independent quantum key distribution. Finally, we show how the Gaussian steering measure gives a lower bound to a more general quantifier of which Gaussian states are proven to be extremal. We proceed to the study of multipartite steering, and derive laws for the distribution of Gaussian steering among different parties in multipartite Gaussian states. We define an indicator of collective steering-type correlations, which is interpreted operationally in terms of the guaranteed secret key rate in the multi-party cryptographic task of quantum secret sharing. The final results look at the cryptographical task of quantum secret sharing, whose security has remained unproven almost two decades after its original conception. By utilizing intuition and ideas from steering, we manage to establish for the first time an unconditional security proof for CV entanglement-based quantum secret sharing schemes, and demonstrate their practical feasibility. Our results establish quantum secret sharing as a viable and practically relevant primitive for quantum communication technologies.
Quantum steering is a stronger form of quantum entanglement and is considered to rigorously address the nonlocal correlation in the original Einstein–Podolsky–Rosen paradox. We study the quantum steerability of two classes of continuous-variable (CV) entangled states that are most often employed for CV quantum informatics-entangled coherent states (ECSs) and two-mode-squeezed vacuum (TMSV). We test the two steering criteria by utilizing Heisenberg and entropic uncertainty relations, respectively, and find that the latter can reveal the steerability of ECSs of any size and parity, whereas the former scarcely can. The steering behaviors of the two states are investigated and compared when they experience a noisy environment, i.e., an amplitude damping channel. When the noise is added asymmetrically, e.g., when only one party of the bipartite system is subject to noise, quantum steering can be possible only in one direction, e.g., Alice on Bob’s state but not Bob on Alice’s state. We show the emergence of this one-directional steering for both ECSs and the TMSV in a certain parameter range under decoherence.