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arXiv:2010.09223 · Physical Review A

Distillation of genuine tripartite Einstein-Podolsky-Rosen steering

Shashank Gupta, Debarshi Das, A. S. Majumdar

Published Aug 9, 2021• 12 citations
arXivHTMLPDF

Abstract

We show that a perfectly genuine tripartite steerable assemblage can be distilled from partially genuine tripartite EPR steerable assemblages. In particular, we consider two types of hybrid scenarios: one-sided device-independent scenario (where one observer is untrusted, and other two observers are trusted) and two-sided device-independent scenario (where two observers are untrusted, and one observer is trusted). In both scenarios, we show distillation of perfectly genuine steerable assemblage of three-qubit Greenberger-Horne-Zeilinger states or three-qubit W states from many copies of initial partially genuine steerable assemblages of the corresponding states. In each of these cases, we demonstrate that at least one copy of a perfectly genuine steerable assemblage can be distilled with certainty from infinitely many copies of initial assemblages. In case of practical scenarios employing finite copies, we show that the efficiency of our distillation protocols reaches near perfect levels using only a few number of initial assemblages.

DOI
10.1103/physreva.104.022409

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Chinese Journal of Electronics•Mar 1, 2026•1 citation
We show that a perfectly genuine tripartite steerable assemblage can be distilled from partially genuine tripartite EPR steerable assemblages. In particular, we consider two types of hybrid scenarios: one-sided device-independent scenario (where one observer is untrusted, and other two observers are trusted) and two-sided device-independent scenario (where two observers are untrusted, and one observer is trusted). In both scenarios, we show distillation of perfectly genuine steerable assemblage of three-qubit Greenberger-Horne-Zeilinger states or three-qubit W states from many copies of initial partially genuine steerable assemblages of the corresponding states. In each of these cases, we demonstrate that at least one copy of a perfectly genuine steerable assemblage can be distilled with certainty from infinitely many copies of initial assemblages. In case of practical scenarios employing finite copies, we show that the efficiency of our distillation protocols reaches near perfect levels using only a few number of initial assemblages.
Multipartite Einstein-Podolsky-Rosen (EPR) steering admits multipartite entanglement in the presence of uncharacterized verifiers, enabling practical applications in semi-device-independent protocols. Such applications generally require stronger steerability, while the unavoidable noise weakens steerability and consequently degrades the performance of quantum information processing. Here, we propose the local filtering operation that can maximally distill genuine tripartite EPR steering from N copies of three-qubit generalized Greenberger-Horne-Zeilinger states, in the context of two semi-device-independent scenarios. The optimal filtering operation is determined by the maximization of assemblage fidelity. Analytical and numerical results indicate the advantage of the proposed filtering operation when N is finite and the steerability of initial assemblages is weak. Experimentally, a proof-of-principle demonstration of two-copy distillation is realized with the optical system. The advantage of the optimal local filtering operation is confirmed by the distilled assemblage in terms of higher assemblage fidelity with perfectly genuine tripartite steerable assemblages, as well as the greater violation of the inequality to witness genuine tripartite steerable assemblages. Our results benefit the distillation of multipartite EPR steering in practice, where the number of copies of initial assemblages is generally finite.
We show-both theoretically and experimentally-that Einstein-Podolsky-Rosen steering can be distilled. We present a distillation protocol that outputs a perfectly correlated system-the singlet assemblage-in the asymptotic infinite-copy limit, even for inputs that are arbitrarily close to being unsteerable. As figures of merit for the protocol's performance, we introduce the assemblage fidelity and the singlet-assemblage fraction. These are potentially interesting quantities on their own beyond the current scope. Remarkably, the protocol works well also in the nonasymptotic regime of few copies, in the sense of increasing the singlet-assemblage fraction. We demonstrate the efficacy of the protocol using a hyperentangled photon pair encoding two copies of a two-qubit state. This represents to our knowledge the first observation of deterministic steering concentration. Our findings are not only fundamentally important but may also be useful for semi-device-independent protocols in noisy quantum networks.
We consider the task of certification of genuine entanglement of tripartite states. We first present an all-versus-nothing proof of tripartite Einstein-Podolsky-Rosen (EPR) steering by demonstrating the non-existence of a local hidden state (LHS) model in the tripartite network as a motivation to our main result. A full logical contradiction of the predictions of the LHS model with quantum mechanical outcome statistics for any three-qubit generalized Greenberger-Horne-Zeilinger (GGHZ) states and pure W-class states is shown, using which, one can distinguish between the GGHZ and W-class states in the two-sided device-independent (2SDI) steering scenario. We next formulate a 2SDI fine-grained steering inequality for the tripartite scenario. We show that the maximum quantum violation of this FGI can be used to certify genuine entanglement of three-qubit pure states.
Einstein-Podolsky-Rosen (EPR) steering is a form of quantum nonlocality which is intermediate between entanglement and Bell nonlocality. EPR steering is a resource for quantum key distribution that is device independent on only one side in that it certifies bipartite entanglement when one party's device is not characterized while the other party's device is fully characterized. In this work, we introduce two types of genuine tripartite EPR steering, and derive two steering inequalities to detect them. In a semi-device-independent scenario where only the dimensions of two parties are assumed, the correlations which violate one of these inequalities also certify genuine tripartite entanglement. It is known that Alice can demonstrate bipartite EPR steering to Bob if and only if her measurement settings are incompatible. We demonstrate that quantum correlations can also detect tripartite EPR steering from Alice to Bob and Charlie, even if Charlie's measurement settings are compatible.
We investigate the possibility of multiple uses of a single copy of a three-qubit state for detecting genuine tripartite Einstein-Podolsky-Rosen (EPR) steering. A pure three-qubit state of either the Greenberger-Horne-Zeilinger (GHZ) type or WWW type is shared between two fixed observers in two wings and a sequence of multiple observers in the third wing who perform unsharp or nonprojective measurements. The measurement settings of each of the multiple observers in the third wing are independent and uncorrelated with the measurement settings and outcomes of the previous observers. In such setup, we investigate all possible types of ($2\ensuremath{\rightarrow}1$) and ($1\ensuremath{\rightarrow}2$) genuine tripartite EPR steering. For each case, we obtain an upper limit on the number of observers on the third wing who can demonstrate genuine EPR steering through the quantum violation of an appropriate tripartite steering inequality. We show that the GHZ state allows for a higher number of observers compared to the WWW state. Additionally, ($1\ensuremath{\rightarrow}2$) genuine steering is possible for a larger range of sharpness parameters compared to ($2\ensuremath{\rightarrow}1$) genuine steering cases.
Quantum steering is a critical resource for multiple parties in real networks. Due to its inherent properties, new steerable resources cannot be generated using only free operations, and reallocating Einstein-Podolsky-Rosen steering within networks of certain structures has significant challenges. Therefore, this paper proposes a distillation scheme that selects remaining three-qubit states with bipartite steering components and distills them to yield a state with purer steerability. Based on different construction of communication networks, our protocol combines scenario-specific distillation strategies to obtain high-fidelity steerable states using a low number of copies via distinct measurement operations. The results indicate that our scheme eliminates the need to reallocate new steering states, reduces the steerable resources required for distillation, and remains robust to measurement defects. Furthermore, we introduce a framework for determining the presence of bipartite steerable in three-qubit states.