Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of the Optical Society of America B

Quantum steering for continuous-variable states

Chang‐Woo Lee, Se-Wan Ji, Hyunchul Nha

Published Aug 22, 2013• 14 citations
Publisher

Abstract

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.

DOI
10.1364/josab.30.002483

Related papers

One-way Einstein-Podolsky-Rosen Steering

Joseph Bowles, Tamás Vértesi, Marco Túlio Quintino +1 more

Einstein-Podolsky-Rosen steering is a form of quantum nonlocality exhibiting an inherent asymmetry between the observers, Alice and Bob. A natural question is then whether there exist entangled states which are one-way steerable, that is, Alice can steer Bob's state, but it is impossible for Bob to steer the state of Alice. So far, such a phenomenon has been demonstrated for continuous variable systems, but with a strong restriction on allowed measurements, namely, considering only Gaussian measurements. Here we present a simple class of entangled two-qubit states which are one-way steerable, considering arbitrary projective measurements. This shows that the nonlocal properties of entangled states can be fundamentally asymmetrical.

arXiv:1402.3607•Physical Review Letters•May 22, 2014•281 citations

Quantum steering for two-mode states with continuous-variable in laser channel

Kaimin Zheng, Jifeng Sun, Liyun Hu +1 more

Abstract Einstein–Podolsky–Rosen (EPR) steering is an important resource for one-sided device-independent quantum information processing. This steering property can be destroyed by the interaction between a quantum system and its environment in practical applications. In this paper, we employ the characteristic function representation of probability distributions to investigate the quantum steering of two-mode continuous-variable states in a laser channel, where both the gain factor and the loss effect are taken into account. Firstly, we analyse the steering time of the two-mode squeezed vacuum state under one-mode and two-mode laser channels, respectively. We find that the gain process introduces additional noise into the two-mode squeezed vacuum state, thereby reducing the steerable time. Secondly, by quantifying EPR steering, we show that two-side loss exhibits smaller steerability than one-side loss, although they share the same two-way steerable time. In addition, we find that the more-gained party can steer the other party’s state, whereas the other party cannot steer the gained party beyond a certain threshold value. In this sense, the gain effect in one party appears to be equivalent to the loss effect in the other party. Our results pave the way for the distillation of EPR steering and quantum information processing in practical quantum channels.

Chinese Physics B•Oct 28, 2025•0 citations

Quantum steering for two-mode states with Continuous-variable in laser channel

Kaimin Zheng, Jifeng Sun, Liyun Hu +1 more

The Einstein-Podolsky-Rosen steering is an important resource for one-sided device independent quantum information processing. This steering property will be destroyed during the interaction between quantum system and environment for some practical applications. In this paper, we use the representation of characteristic function for probability to examine the quantum steering of two-mode states with continuous-variable in laser channel, where both the gain factor and the loss effect are considered. Firstly, we analyse the steering time of two-mode squeezed vacuum state under one-mode and two-mode laser channel respectively. We find the gain process will introduce additional noise to the two-mode squeezed vacuum state such that the steerable time is reduced. Secondly, by quantising quantum Einstein-Podolsky-Rosen steering, it shows that two-side loss presents a smaller steerability than one-side loss although they share the same two-way steerable time. In addition, we find the more gained party can steer the others state, while the other party cannot steer the gained party in a certain threshold value. In this sense, it seems that the gain effect in one party is equivalent to the loss effect in the others party. Our results pave way for the distillation of Einstein-Podolsky-Rosen steering and the quantum information processing in practical quantum channels.

arXiv:2311.16658•Nov 28, 2023•0 citations

Quantification of Gaussian Quantum Steering

Ioannis Kogias, Antony R. Lee, Sammy Ragy +1 more

Einstein-Podolsky-Rosen steering incarnates a useful nonclassical correlation which sits between entanglement and Bell nonlocality. While a number of qualitative steering criteria exist, very little has been achieved for what concerns quantifying steerability. We introduce a computable measure of steering for arbitrary bipartite Gaussian states of continuous variable systems. For two-mode Gaussian states, the measure reduces to a form of coherent information, which is proven never to exceed entanglement, and to reduce to it on pure states. We provide an operational connection between our measure and the key rate in one-sided device-independent quantum key distribution. We further prove that Peres' conjecture holds in its stronger form within the fully Gaussian regime: namely, steering bound entangled Gaussian states by Gaussian measurements is impossible.

arXiv:1410.1637•Physical Review Letters•Feb 12, 2015•391 citations

Steering, Entanglement, Nonlocality, and the Einstein-Podolsky-Rosen Paradox

Howard M. Wiseman, S. J. Jones, Andrew C. Doherty

The concept of steering was introduced by Schrödinger in 1935 as a generalization of the Einstein-Podolsky-Rosen paradox for arbitrary pure bipartite entangled states and arbitrary measurements by one party. Until now, it has never been rigorously defined, so it has not been known (for example) what mixed states are steerable (that is, can be used to exhibit steering). We provide an operational definition, from which we prove (by considering Werner states and isotropic states) that steerable states are a strict subset of the entangled states, and a strict superset of the states that can exhibit Bell nonlocality. For arbitrary bipartite Gaussian states we derive a linear matrix inequality that decides the question of steerability via Gaussian measurements, and we relate this to the original Einstein-Podolsky-Rosen paradox.

arXiv:quant-ph/0612147•Physical Review Letters•Apr 6, 2007•1,572 citations

Einstein-Podolsky-Rosen Steering for Mixed Entangled Coherent States

S. Abdel‐Khalek, K. Berrada, Mariam Algarni +1 more

By using the Born Markovian master equation, we study the relationship among the Einstein-Podolsky-Rosen (EPR) steering, Bell nonlocality, and quantum entanglement of entangled coherent states (ECSs) under decoherence. We illustrate the dynamical behavior of the three types of correlations for various optical field strength regimes. In general, we find that correlation measurements begin at their maximum and decline over time. We find that quantum steering and nonlocality behave similarly in terms of photon number during dynamics. Furthermore, we discover that ECSs with steerability can violate the Bell inequality, and that not every ECS with Bell nonlocality is steerable. In the current work, without the memory stored in the environment, some of the initial states with maximal values of quantum steering, Bell nonlocality, and entanglement can provide a delayed loss of that value during temporal evolution, which is of interest to the current study.

Entropy•Oct 31, 2021•1 citation
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.
Einstein-Podolsky-Rosen steering is a form of quantum nonlocality exhibiting an inherent asymmetry between the observers, Alice and Bob. A natural question is then whether there exist entangled states which are one-way steerable, that is, Alice can steer Bob's state, but it is impossible for Bob to steer the state of Alice. So far, such a phenomenon has been demonstrated for continuous variable systems, but with a strong restriction on allowed measurements, namely, considering only Gaussian measurements. Here we present a simple class of entangled two-qubit states which are one-way steerable, considering arbitrary projective measurements. This shows that the nonlocal properties of entangled states can be fundamentally asymmetrical.
Abstract Einstein–Podolsky–Rosen (EPR) steering is an important resource for one-sided device-independent quantum information processing. This steering property can be destroyed by the interaction between a quantum system and its environment in practical applications. In this paper, we employ the characteristic function representation of probability distributions to investigate the quantum steering of two-mode continuous-variable states in a laser channel, where both the gain factor and the loss effect are taken into account. Firstly, we analyse the steering time of the two-mode squeezed vacuum state under one-mode and two-mode laser channels, respectively. We find that the gain process introduces additional noise into the two-mode squeezed vacuum state, thereby reducing the steerable time. Secondly, by quantifying EPR steering, we show that two-side loss exhibits smaller steerability than one-side loss, although they share the same two-way steerable time. In addition, we find that the more-gained party can steer the other party’s state, whereas the other party cannot steer the gained party beyond a certain threshold value. In this sense, the gain effect in one party appears to be equivalent to the loss effect in the other party. Our results pave the way for the distillation of EPR steering and quantum information processing in practical quantum channels.
The Einstein-Podolsky-Rosen steering is an important resource for one-sided device independent quantum information processing. This steering property will be destroyed during the interaction between quantum system and environment for some practical applications. In this paper, we use the representation of characteristic function for probability to examine the quantum steering of two-mode states with continuous-variable in laser channel, where both the gain factor and the loss effect are considered. Firstly, we analyse the steering time of two-mode squeezed vacuum state under one-mode and two-mode laser channel respectively. We find the gain process will introduce additional noise to the two-mode squeezed vacuum state such that the steerable time is reduced. Secondly, by quantising quantum Einstein-Podolsky-Rosen steering, it shows that two-side loss presents a smaller steerability than one-side loss although they share the same two-way steerable time. In addition, we find the more gained party can steer the others state, while the other party cannot steer the gained party in a certain threshold value. In this sense, it seems that the gain effect in one party is equivalent to the loss effect in the others party. Our results pave way for the distillation of Einstein-Podolsky-Rosen steering and the quantum information processing in practical quantum channels.
Einstein-Podolsky-Rosen steering incarnates a useful nonclassical correlation which sits between entanglement and Bell nonlocality. While a number of qualitative steering criteria exist, very little has been achieved for what concerns quantifying steerability. We introduce a computable measure of steering for arbitrary bipartite Gaussian states of continuous variable systems. For two-mode Gaussian states, the measure reduces to a form of coherent information, which is proven never to exceed entanglement, and to reduce to it on pure states. We provide an operational connection between our measure and the key rate in one-sided device-independent quantum key distribution. We further prove that Peres' conjecture holds in its stronger form within the fully Gaussian regime: namely, steering bound entangled Gaussian states by Gaussian measurements is impossible.
The concept of steering was introduced by Schrödinger in 1935 as a generalization of the Einstein-Podolsky-Rosen paradox for arbitrary pure bipartite entangled states and arbitrary measurements by one party. Until now, it has never been rigorously defined, so it has not been known (for example) what mixed states are steerable (that is, can be used to exhibit steering). We provide an operational definition, from which we prove (by considering Werner states and isotropic states) that steerable states are a strict subset of the entangled states, and a strict superset of the states that can exhibit Bell nonlocality. For arbitrary bipartite Gaussian states we derive a linear matrix inequality that decides the question of steerability via Gaussian measurements, and we relate this to the original Einstein-Podolsky-Rosen paradox.
By using the Born Markovian master equation, we study the relationship among the Einstein-Podolsky-Rosen (EPR) steering, Bell nonlocality, and quantum entanglement of entangled coherent states (ECSs) under decoherence. We illustrate the dynamical behavior of the three types of correlations for various optical field strength regimes. In general, we find that correlation measurements begin at their maximum and decline over time. We find that quantum steering and nonlocality behave similarly in terms of photon number during dynamics. Furthermore, we discover that ECSs with steerability can violate the Bell inequality, and that not every ECS with Bell nonlocality is steerable. In the current work, without the memory stored in the environment, some of the initial states with maximal values of quantum steering, Bell nonlocality, and entanglement can provide a delayed loss of that value during temporal evolution, which is of interest to the current study.