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Register a new userOperational quantification of continuous-variable quantum resources
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The diverse range of resources which underlie the utility of quantum states in practical tasks motivates the development of universally applicable methods to measure and compare resources of different types. However, many of such approaches were hitherto limited to the finite-dimensional setting or were not connected with operational tasks. We overcome this by introducing a general method of quantifying resources for continuous-variable quantum systems based on the robustness measure, applicable to a plethora of physically relevant resources such as optical nonclassicality, entanglement, genuine non-Gaussianity, and coherence. We demonstrate in particular that the measure has a direct operational interpretation as the advantage enabled by a given state in a class of channel discrimination tasks. We show that the robustness constitutes a well-behaved, bona fide resource quantifier in any convex resource theory, contrary to a related negativity-based measure known as the standard robustness. Furthermore, we show the robustness to be directly observable -- it can be computed as the expectation value of a single witness operator -- and establish general methods for evaluating the measure. Explicitly applying our results to the relevant resources, we demonstrate the exact computability of the robustness for several classes of states.
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We investigate continuous variable quantum teleportation using non-Gaussian states of the radiation field as entangled resources. We compare the performance of different classes of degaussified resources, including two-mode photon-added and two-mode photon-subtracted squeezed states. We then introduce a class of two-mode squeezed Bell-like states with one-parameter dependence for optimization. These states interpolate between and include as subcases different classes of degaussified resources. We show that optimized squeezed Bell-like resources yield a remarkable improvement in the fidelity of teleportation both for coherent and nonclassical input states. The investigation reveals that the optimal non-Gaussian resources for continuous variable teleportation are those that most closely realize the simultaneous maximization of the content of entanglement, the degree of affinity with the two-mode squeezed vacuum and the, suitably measured, amount of non-Gaussianity.
We introduce and discuss a set of tunable two-mode states of continuous-variable systems, as well as an efficient scheme for their experimental generation. This novel class of tunable entangled resources is defined by a general ansatz depending on two experimentally adjustable parameters. It is very ample and flexible as it encompasses Gaussian as well as non-Gaussian states. The latter include, among others, known states such as squeezed number states and de-Gaussified photon-added and photon-subtracted squeezed states, the latter being the most efficient non-Gaussian resources currently available in the laboratory. Moreover, it contains the classes of squeezed Bell states and even more general non-Gaussian resources that can be optimized according to the specific quantum technological task that needs to be realized. The proposed experimental scheme exploits linear optical operations and photon detections performed on a pair of uncorrelated two--mode Gaussian squeezed states. The desired non-Gaussian state is then realized via ancillary squeezing and conditioning. Two independent, freely tunable experimental parameters can be exploited to generate different states and to optimize the performance in implementing a given quantum protocol. As a concrete instance, we analyze in detail the performance of different states considered as resources for the realization of quantum teleportation in realistic conditions. For the fidelity of teleportation of an unknown coherent state, we show that the resources associated to the optimized parameters outperform, in a significant range of experimental values, both Gaussian twin beams and photon-subtracted squeezed states.
We study asymptotic state transformations in continuous variable quantum resource theories. In particular, we prove that monotones displaying lower semicontinuity and strong superadditivity can be used to bound asymptotic transformation rates in these settings. This removes the need for asymptotic continuity, which cannot be defined in the traditional sense for infinite-dimensional systems. We consider three applications, to the resource theories of (I) optical nonclassicality, (II) entanglement, and (III) quantum thermodynamics. In cases (II) and (III), the employed monotones are the (infinite-dimensional) squashed entanglement and the free energy, respectively. For case (I), we consider the measured relative entropy of nonclassicality and prove it to be lower semicontinuous and strongly superadditive. Our technique then yields computable upper bounds on asymptotic transformation rates including those achievable under linear optical elements. We also prove a number of results which ensure the measured relative entropy of nonclassicality to be bounded on any physically meaningful state, and to be easily computable for some class of states of interest, e.g., Fock diagonal states. We conclude by applying our findings to the problem of cat state manipulation and noisy Fock state purification.
Recently, various non-classical properties of quantum states and channels have been characterized through an advantage they provide in specific quantum information tasks over their classical counterparts. Such advantage can be typically proven to be quantitative, in that larger amounts of quantum resources lead to better performance in the corresponding tasks. So far, these characterizations have been established only in the finite-dimensional setting. In this manuscript, we present a technique for extending the known results to the infinite-dimensional regime. The technique relies on approximating infinite-dimensional resource measures by their finite-dimensional counterparts. We give a sufficient condition for the approximation procedure to be tight, i.e. to match with established infinite-dimensional resource quantifiers, and another sufficient condition for the procedure to match with relevant extensions of these quantifiers. We show that various continuous variable quantum resources fall under these conditions, hence, giving them an operational interpretation through the advantage they can provide in so-called quantum games. Finally, we extend the interpretation to the max relative entropy in the infinite-dimensional setting.
We investigate continuous variable (CV) quantum teleportation using relevant classes of non-Gaussian states of the radiation field as entangled resources. First, we introduce the class two-mode squeezed symmetric superposition of Fock states, including finite truncations of twin-beam Gaussian states as special realizations. These states depend on a set of free independent parameters that can be adjusted for the optimization of teleportation protocols, with an enhancement of the success probability of teleportation both for coherent and Fock input states. We show that the optimization procedure reduces the entangled resources to truncated twin beam states, which thus represents an optimal class of non-Gaussian resources for quantum teleportation. We then introduce a further class of two-mode non-Gaussian entangled resources, in the form of squeezed cat-like states. We analyze the performance and the properties of such states when optimized for (CV) teleportation, and compare them to the optimized squeezed Bell-like states introduced in a previous work cite{CVTelepNoi}. We discuss how optimal resources for teleportation are characterized by a suitable balance of entanglement content and squeezed vacuum affinity. We finally investigate the effects of thermal noise on the efficiency of quantum teleportation. To this aim, a convenient framework is to describe noisy entangled resources as linear superpositions of non-Gaussian state and thermal states. Although the presence of the thermal component strongly reduces the teleportation fidelity, noisy non-Gaussian states remain preferred resources when compared to noisy twin-beam Gaussian states.
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