© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:2311.09873 · Photonics Research

Experimental distillation of tripartite quantum steering with an optimal local filtering operation

Qian-Xi Zhang, Xiao‐Xu Fang, He Lu

Published Dec 19, 2023• 5 citations

Abstract

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.

DOI: 10.1364/prj.506855

Related papers

Distillation of genuine tripartite Einstein-Podolsky-Rosen steering

Shashank Gupta, Debarshi Das, A. S. Majumdar

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.

arXiv:2010.09223•Physical Review A•Aug 9, 2021•12 citations

Distillation of Quantum Steering

Ranieri Nery, Márcio M. Taddei, P. Sahium +3 more

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.

arXiv:1906.00991•Physical Review Letters•Mar 26, 2020•33 citations

Genuine Einstein–Podolsky–Rosen steering of generalized three-qubit states via unsharp measurements

Yuyu Chen, Fen-Zhuo Guo, Shi-Hui Wei +1 more

We aim to explore all possible scenarios of (1 → 2) (where one wing is untrusted and the others two wings are trusted) and (2 → 1) (where two wings are untrusted, and one wing is trusted) genuine tripartite Einstein–Podolsky–Rosen (EPR) steering. The generalized Greenberger–Horne–Zeilinger (GHZ) state is shared between three spatially separated parties, Alice, Bob and Charlie. In both (1 → 2) and (2 → 1), we discuss the untrusted party and trusted party performing a sequence of unsharp measurements, respectively. For each scenario, we deduce an upper bound on the number of sequential observers who can demonstrate genuine EPR steering through the quantum violation of tripartite steering inequality. The results show that the maximum number of observers for the generalized GHZ states can be the same with that of the maximally GHZ state in a certain range of state parameters. Moreover, both the sharpness parameters range and the state parameters range in the scenario of (1 → 2) steering are larger than those in the scenario of (2 → 1) steering.

Chinese Physics B•Dec 16, 2022•6 citations

"All-versus-nothing" proof of tripartite quantum steering and genuine entanglement certification in the two-sided device-independent scenario

Shashank Gupta, Debarshi Das, Chellasamy Jebarathinam +3 more

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.

•Oct 28, 2019•0 citations

Detecting genuine multipartite entanglement in steering scenarios

Chellasamy Jebarathinam

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.

arXiv:1510.08800•Physical Review A•May 5, 2016•16 citations

Observation of collective Einstein-Podolsky-Rosen steering in three-qubit systems

Wen-Qi Fan, Yongjian Gu, Ya Xiao

Collective Einstein-Podolsky-Rosen (EPR) steering is a unique multipartite resource that enables the realization of more secure communication protocols. However, due to the lack of suitable experimental criteria, research on collective EPR steering has so far been limited to continuous variable systems. Here, we employ the coherence-based collective EPR steering criteria proposed by Mondal et al. [Phys. Rev. A 99, 012312 (2019)] and develop a semidefinite programming method to find the optimal measurement settings. Experimentally, we take the three-qubit generalized Greenberger-Horne-Zeilinger states and generalized $W$ states as examples, demonstrating that collective EPR steering can be observed by detecting the average ${l}_{1}$ norm of coherence of the steered subsystem. We also explored the effect of measurement settings on complementarity relations between different collective steering criteria, and established a connection between collective steering and coherence complementarity. Our paper fills a gap in the verification of collective steerability in discrete variable systems and reveals a profound connection between EPR steering and quantum coherence.

Physical Review A•Mar 12, 2025•2 citations

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 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.

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 aim to explore all possible scenarios of (1 → 2) (where one wing is untrusted and the others two wings are trusted) and (2 → 1) (where two wings are untrusted, and one wing is trusted) genuine tripartite Einstein–Podolsky–Rosen (EPR) steering. The generalized Greenberger–Horne–Zeilinger (GHZ) state is shared between three spatially separated parties, Alice, Bob and Charlie. In both (1 → 2) and (2 → 1), we discuss the untrusted party and trusted party performing a sequence of unsharp measurements, respectively. For each scenario, we deduce an upper bound on the number of sequential observers who can demonstrate genuine EPR steering through the quantum violation of tripartite steering inequality. The results show that the maximum number of observers for the generalized GHZ states can be the same with that of the maximally GHZ state in a certain range of state parameters. Moreover, both the sharpness parameters range and the state parameters range in the scenario of (1 → 2) steering are larger than those in the scenario of (2 → 1) steering.

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.

Collective Einstein-Podolsky-Rosen (EPR) steering is a unique multipartite resource that enables the realization of more secure communication protocols. However, due to the lack of suitable experimental criteria, research on collective EPR steering has so far been limited to continuous variable systems. Here, we employ the coherence-based collective EPR steering criteria proposed by Mondal et al. [Phys. Rev. A 99, 012312 (2019)] and develop a semidefinite programming method to find the optimal measurement settings. Experimentally, we take the three-qubit generalized Greenberger-Horne-Zeilinger states and generalized

W

states as examples, demonstrating that collective EPR steering can be observed by detecting the average

{l}_{1}

norm of coherence of the steered subsystem. We also explored the effect of measurement settings on complementarity relations between different collective steering criteria, and established a connection between collective steering and coherence complementarity. Our paper fills a gap in the verification of collective steerability in discrete variable systems and reveals a profound connection between EPR steering and quantum coherence.