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Steering between outputs of a beamsplitter using Gaussian states of light with excess noise

Eugenia Benech, A. Auyuanet, A. Lezama

Published Mar 18, 2021• 0 citations
OpenAlex

Abstract

We have studied the conditions for quantum steering between output modes when squeezed Gaussian light and vacuum mix in a beamsplitter as a function of the amount of squeezing and purity of the incident state. For Gaussian measurements, we find that for sufficiently strong squeezing, steering is possible regardless of the purity of the incident state. Two different types of non-Gaussian measurements were also considered. For one of them, an increase with respect to Gaussian measurements of the set of two-way-steerable states is obtained only for unbalanced beamsplitters.

Related papers

Einstein-Podolsky-Rosen steering in symmetrical Gaussian states

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We have explored quantum Einstein-Podolsky-Rosen steering in symmetric two-mode Gaussian states using Gaussian and non-Gaussian measurements. For Gaussian measurements, we show that steering between the output modes of a symmetric beam splitter is possible regardless of purity when a threshold input-state quadrature variance compression is achieved. Using the non-Gaussian operators introduced in Ji et al. [Sci. Rep. 6, 29729 (2016)] we show that non-Gaussian measurements can outperform Gaussian measurements for symmetrical states. We also analyze the possibility of asymmetric measurements setups made possible by non-Gaussian measurements and provide examples where such asymmetry is optimal for revealing steering.

arXiv:2103.10418•Physical Review A•Oct 3, 2022•1 citation

Quantum steering of multimode Gaussian states by Gaussian measurements: monogamy relations and the Peres conjecture

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It is a topic of fundamental and practical importance how a quantum correlated state can be reliably distributed through a noisy channel for quantum information processing. The concept of quantum steering recently defined in a rigorous manner is relevant to study it under certain circumstances and here we address quantum steerability of Gaussian states to this aim. In particular, we attempt to reformulate the criterion for Gaussian steering in terms of local and global purities and show that it is sufficient and necessary for the case of steering a 1-mode system by an N -mode system. It subsequently enables us to reinforce a strong monogamy relation under which only one party can steer a local system of 1-mode. Moreover, we show that only a negative partial-transpose state can manifest quantum steerability by Gaussian measurements in relation to the Peres conjecture. We also discuss our formulation for the case of distributing a two-mode squeezed state via one-way quantum channels making dissipation and amplification effects, respectively. Finally, we extend our approach to include non-Gaussian measurements, more precisely, all orders of higher-order squeezing measurements, and find that this broad set of non-Gaussian measurements is not useful to demonstrate steering for Gaussian states beyond Gaussian measurements.

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Quantum steering-a strong correlation to be verified even when one party or its measuring device is fully untrusted-not only provides a profound insight into quantum physics but also offers a crucial basis for practical applications. For continuous-variable (CV) systems, Gaussian states among others have been extensively studied, however, mostly confined to Gaussian measurements. While the fulfilment of Gaussian criterion is sufficient to detect CV steering, whether it is also necessary for Gaussian states is a question of fundamental importance in many contexts. This critically questions the validity of characterizations established only under Gaussian measurements like the quantification of steering and the monogamy relations. Here, we introduce a formalism based on local uncertainty relations of non-Gaussian measurements, which is shown to manifest quantum steering of some Gaussian states that Gaussian criterion fails to detect. To this aim, we look into Gaussian states of practical relevance, i.e. two-mode squeezed states under a lossy and an amplifying Gaussian channel. Our finding significantly modifies the characteristics of Gaussian-state steering so far established such as monogamy relations and one-way steering under Gaussian measurements, thus opening a new direction for critical studies beyond Gaussian regime.

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Abstract Steering is a type of quantum nonlocality that exhibits an inherent asymmetry between two observers. In a nondegenerate three‐level laser coupled to a two‐mode squeezed vacuum reservoir, under realistic experimental conditions, the Gaussian steering of two laser modes, and , generated within the cascade transitions, respectively are examined. It is found that the steerability is always higher than that from ; in addition, the steering asymmetry cannot exceed ln 2, which implies that the state never diverges to an extremal asymmetry state. It is shown how squeezed noise can play a constructive role in realizing one‐way steering. As the main result, it is demonstrated that the state can exhibit one‐way steering solely from , which is shown to emerge as a consequence of the fact that the intensity difference of the modes and is verified to remain always positive, irrespective of the physical and environmental parameters of . The generated unidirectional one‐way steering may provide a useful resource for the distribution of the trust in future asymmetric quantum information tasks.

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Quantum steering of a two-mode Gaussian state using a quantum beat laser

Shakir Ullah, Haleema Sadia Qureshi, Fazal Ghafoor

We study the quantum steering of a two-mode Gaussian state evolved by a simple quantum beat laser with the cavity field being initially in arbitrary two single-mode Gaussian states and the lasing medium being driven by a strong classical field. In presence of the cavity damping, the quantum steering time of the two-mode Gaussian state increases with the relative intensity of the coupling fields, whereas the relative phase switches the steerable states into the non-steerable and vice versa. We further show that the higher the non-classicality of the initial cavity modes, the longer the time of steerability in the two-mode Gaussian state. Nonetheless, the quantum steering is irrespective of the influence from the purity of the initial cavity modes of the laser system.

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Nonclassicality according to the singularity or negativity of the Glauber $P$-function is a powerful resource in quantum information, with relevant implications in quantum optics. In a Gaussian setting, and for a system of two modes, we explore how $P$-nonclassicality may be conditionally generated or influenced on one mode by Gaussian measurements on the other mode. Starting from the class of two-mode squeezed thermal states (TMST), we introduce the notion of nonclassical steering (NS) and the graphical tool of Gaussian triangoloids. In particular, we derive a necessary and sufficient condition for a TMST to be nonclassically steerable and show that entanglement is necessary. We also apply our criterion to noisy propagation of a twin-beam state and evaluate the time after which NS is no longer achievable. We then generalize the notion of NS to the full set of Gaussian states of two modes and recognize that it may occur in a weak form, which does not imply entanglement, and in a strong form, which implies EPR steerability and, a fortiori, also entanglement. These two types of NS coincide exactly for TMSTs, and they merge with the previously known notion of EPR steering. By the same token, we recognize another operational interpretation of $P$-nonclassicality: It is the distinctive property that allows one-party entanglement verification on TMSTs.

arXiv:2006.11912•Physical Review A•Feb 12, 2021•11 citations
We have studied the conditions for quantum steering between output modes when squeezed Gaussian light and vacuum mix in a beamsplitter as a function of the amount of squeezing and purity of the incident state. For Gaussian measurements, we find that for sufficiently strong squeezing, steering is possible regardless of the purity of the incident state. Two different types of non-Gaussian measurements were also considered. For one of them, an increase with respect to Gaussian measurements of the set of two-way-steerable states is obtained only for unbalanced beamsplitters.
We have explored quantum Einstein-Podolsky-Rosen steering in symmetric two-mode Gaussian states using Gaussian and non-Gaussian measurements. For Gaussian measurements, we show that steering between the output modes of a symmetric beam splitter is possible regardless of purity when a threshold input-state quadrature variance compression is achieved. Using the non-Gaussian operators introduced in Ji et al. [Sci. Rep. 6, 29729 (2016)] we show that non-Gaussian measurements can outperform Gaussian measurements for symmetrical states. We also analyze the possibility of asymmetric measurements setups made possible by non-Gaussian measurements and provide examples where such asymmetry is optimal for revealing steering.
It is a topic of fundamental and practical importance how a quantum correlated state can be reliably distributed through a noisy channel for quantum information processing. The concept of quantum steering recently defined in a rigorous manner is relevant to study it under certain circumstances and here we address quantum steerability of Gaussian states to this aim. In particular, we attempt to reformulate the criterion for Gaussian steering in terms of local and global purities and show that it is sufficient and necessary for the case of steering a 1-mode system by an N -mode system. It subsequently enables us to reinforce a strong monogamy relation under which only one party can steer a local system of 1-mode. Moreover, we show that only a negative partial-transpose state can manifest quantum steerability by Gaussian measurements in relation to the Peres conjecture. We also discuss our formulation for the case of distributing a two-mode squeezed state via one-way quantum channels making dissipation and amplification effects, respectively. Finally, we extend our approach to include non-Gaussian measurements, more precisely, all orders of higher-order squeezing measurements, and find that this broad set of non-Gaussian measurements is not useful to demonstrate steering for Gaussian states beyond Gaussian measurements.
Quantum steering-a strong correlation to be verified even when one party or its measuring device is fully untrusted-not only provides a profound insight into quantum physics but also offers a crucial basis for practical applications. For continuous-variable (CV) systems, Gaussian states among others have been extensively studied, however, mostly confined to Gaussian measurements. While the fulfilment of Gaussian criterion is sufficient to detect CV steering, whether it is also necessary for Gaussian states is a question of fundamental importance in many contexts. This critically questions the validity of characterizations established only under Gaussian measurements like the quantification of steering and the monogamy relations. Here, we introduce a formalism based on local uncertainty relations of non-Gaussian measurements, which is shown to manifest quantum steering of some Gaussian states that Gaussian criterion fails to detect. To this aim, we look into Gaussian states of practical relevance, i.e. two-mode squeezed states under a lossy and an amplifying Gaussian channel. Our finding significantly modifies the characteristics of Gaussian-state steering so far established such as monogamy relations and one-way steering under Gaussian measurements, thus opening a new direction for critical studies beyond Gaussian regime.
Abstract Steering is a type of quantum nonlocality that exhibits an inherent asymmetry between two observers. In a nondegenerate three‐level laser coupled to a two‐mode squeezed vacuum reservoir, under realistic experimental conditions, the Gaussian steering of two laser modes, and , generated within the cascade transitions, respectively are examined. It is found that the steerability is always higher than that from ; in addition, the steering asymmetry cannot exceed ln 2, which implies that the state never diverges to an extremal asymmetry state. It is shown how squeezed noise can play a constructive role in realizing one‐way steering. As the main result, it is demonstrated that the state can exhibit one‐way steering solely from , which is shown to emerge as a consequence of the fact that the intensity difference of the modes and is verified to remain always positive, irrespective of the physical and environmental parameters of . The generated unidirectional one‐way steering may provide a useful resource for the distribution of the trust in future asymmetric quantum information tasks.
We study the quantum steering of a two-mode Gaussian state evolved by a simple quantum beat laser with the cavity field being initially in arbitrary two single-mode Gaussian states and the lasing medium being driven by a strong classical field. In presence of the cavity damping, the quantum steering time of the two-mode Gaussian state increases with the relative intensity of the coupling fields, whereas the relative phase switches the steerable states into the non-steerable and vice versa. We further show that the higher the non-classicality of the initial cavity modes, the longer the time of steerability in the two-mode Gaussian state. Nonetheless, the quantum steering is irrespective of the influence from the purity of the initial cavity modes of the laser system.
Nonclassicality according to the singularity or negativity of the Glauber PPP-function is a powerful resource in quantum information, with relevant implications in quantum optics. In a Gaussian setting, and for a system of two modes, we explore how PPP-nonclassicality may be conditionally generated or influenced on one mode by Gaussian measurements on the other mode. Starting from the class of two-mode squeezed thermal states (TMST), we introduce the notion of nonclassical steering (NS) and the graphical tool of Gaussian triangoloids. In particular, we derive a necessary and sufficient condition for a TMST to be nonclassically steerable and show that entanglement is necessary. We also apply our criterion to noisy propagation of a twin-beam state and evaluate the time after which NS is no longer achievable. We then generalize the notion of NS to the full set of Gaussian states of two modes and recognize that it may occur in a weak form, which does not imply entanglement, and in a strong form, which implies EPR steerability and, a fortiori, also entanglement. These two types of NS coincide exactly for TMSTs, and they merge with the previously known notion of EPR steering. By the same token, we recognize another operational interpretation of PPP-nonclassicality: It is the distinctive property that allows one-party entanglement verification on TMSTs.