Recently, the quantumness of local correlations arising from separable states in the context of a Bell scenario has been studied and linked with superlocality [Phys. Rev. A 95, 032120 (2017)]. Here we investigate the quantumness of unsteerable correlations in the context of a given steering scenario. Generalizing the concept of superlocality, we define as supercorrelation the requirement for a larger dimension of the preshared randomness to simulate the correlations than that of the quantum states that generate them. Since unsteerable states form a subset of Bell local states, it is an interesting question whether certain unsteerable states can be supercorrelated. Here, we answer this question in the affirmative. In particular, the quantumness of certain unsteerable correlations can be pointed out by the notion of superunsteerability, the requirement for a larger dimension of the classical variable that the steering party has to preshare with the trusted party for simulating the correlations than that of the quantum states which reproduce them. This provides a generalized approach to quantify the quantumness of unsteerable correlations in convex operational theories.Recently, the quantumness of local correlations arising from separable states in the context of a Bell scenario has been studied and linked with superlocality [Phys. Rev. A 95, 032120 (2017)]. Here we investigate the quantumness of unsteerable correlations in the context of a given steering scenario. Generalizing the concept of superlocality, we define as supercorrelation the requirement for a larger dimension of the preshared randomness to simulate the correlations than that of the quantum states that generate them. Since unsteerable states form a subset of Bell local states, it is an interesting question whether certain unsteerable states can be supercorrelated. Here, we answer this question in the affirmative. In particular, the quantumness of certain unsteerable correlations can be pointed out by the notion of superunsteerability, the requirement for a larger dimension of the classical variable that the steering party has to preshare with the trusted party for simulating the correlations than that of the quantum states which reproduce them. This provides a generalized approach to quantify the quantumness of unsteerable correlations in convex operational theories.

arXiv:1705.05663Physical Review AJun 25, 201812 citations

Quantum correlations and separability

F. Selleri

Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimentoJan 1, 19804 citations

Detecting ${\boldsymbol~A}{\boldsymbol~B}{\boldsymbol~\rightarrow}{\boldsymbol~C}$ steering in tripartite quantum systemsDetecting ${\boldsymbol~A}{\boldsymbol~B}{\boldsymbol~\rightarrow}{\boldsymbol~C}$ steering in tripartite quantum systems

Cao Huai-xin, Yang Ying, XIAO Shu +1 more

In this paper, the detection problem of $AB\\rightarrow~C$ steering is discussed. Firstly, we give some relationships between the $AB\\rightarrow~C$ steering of $\\rho^{ABC}$ and $A\\rightarrow~C$ steering of the reduced state $\\rho^{AC}$ as well as $B\\rightarrow~C$ steering of the reduced state $\\rho^{BC}$ based ontheir definitions. Secondly, by deducing an inequality (called an steering inequality) for $AB\\rightarrow~C$ unsteerable states, a necessary condition for a quantum state to be $AB\\rightarrow~C$ unsteerable is obtained. Furthermore, the steering radius $S(\\rho)$ of a state $\\rho$ is defined and it is proved that when $\\rho$ is $AB\\rightarrow~C$ unsteerable, $S(\\rho)\\le1$ and that when $S(\\rho)>1$ , $t\\rho+(1-t)\\eta$ is $AB\\rightarrow~C$ steerable for each $t_0<t\\le1$ and for each $AB\\rightarrow~C$ unsteerable state $\\eta$ where $t_0=\\frac{2}{S(\\rho)+1}$ .Finally, $AB\\rightarrow~C$ steerability of the “partial convex combinations of the GHZ state, generalized GHZ state and the W-state with a $AB\\rightarrow~C$ unsteerable state are detected, respectively by using the obtained steering inequality.In this paper, the detection problem of $AB\\rightarrow~C$ steering is discussed. Firstly, we give some relationships between the $AB\\rightarrow~C$ steering of $\\rho^{ABC}$ and $A\\rightarrow~C$ steering of the reduced state $\\rho^{AC}$ as well as $B\\rightarrow~C$ steering of the reduced state $\\rho^{BC}$ based ontheir definitions. Secondly, by deducing an inequality (called an steering inequality) for $AB\\rightarrow~C$ unsteerable states, a necessary condition for a quantum state to be $AB\\rightarrow~C$ unsteerable is obtained. Furthermore, the steering radius $S(\\rho)$ of a state $\\rho$ is defined and it is proved that when $\\rho$ is $AB\\rightarrow~C$ unsteerable, $S(\\rho)\\le1$ and that when $S(\\rho)>1$, $t\\rho+(1-t)\\eta$ is $AB\\rightarrow~C$ steerable for each $t_0<t\\le1$ and for each $AB\\rightarrow~C$ unsteerable state $\\eta$ where $t_0=\\frac{2}{S(\\rho)+1}$.Finally, $AB\\rightarrow~C$ steerability of the “partial convex combinations of the GHZ state, generalized GHZ state and the W-state with a $AB\\rightarrow~C$ unsteerable state are detected, respectively by using the obtained steering inequality.

Zhongguo kexue. Wulixue Lixue TianwenxueNov 7, 20192 citations

Several kinds of Gaussian quantum channels related to Einstein-Podolsky-Rosen steering

Ruifen Ma, Yanjing Sun, Xiaofei Qi

Quantum steering is a crucial quantum resource that lies intermediate between entanglement and Bell nonlocality. Gaussian channels, meanwhile, play a foundational role in diverse quantum protocols, secure communication, and related fields. In this paper, we focus on several classes of Gaussian channels associated with quantum steering: Gaussian steering-annihilating channels, Gaussian steering-breaking channels, Gaussian unsteerable channels, and maximal Gaussian unsteerable channels. We give the concepts of these channels, derive the necessary and sufficient conditions for a Gaussian channel to belong to each class, and explore the intrinsic relationships among them. Additionally, since quantifying the steering capability of Gaussian channels in continuous-variable systems requires an understanding of the structure of free superchannels, we also provide a detailed characterization of Gaussian unsteerable superchannels and maximal Gaussian unsteerable superchannels.Quantum steering is a crucial quantum resource that lies intermediate between entanglement and Bell nonlocality. Gaussian channels, meanwhile, play a foundational role in diverse quantum protocols, secure communication, and related fields. In this paper, we focus on several classes of Gaussian channels associated with quantum steering: Gaussian steering-annihilating channels, Gaussian steering-breaking channels, Gaussian unsteerable channels, and maximal Gaussian unsteerable channels. We give the concepts of these channels, derive the necessary and sufficient conditions for a Gaussian channel to belong to each class, and explore the intrinsic relationships among them. Additionally, since quantifying the steering capability of Gaussian channels in continuous-variable systems requires an understanding of the structure of free superchannels, we also provide a detailed characterization of Gaussian unsteerable superchannels and maximal Gaussian unsteerable superchannels.

quant-pharXiv:2511.05003Nov 10, 20250 citations

Some New Properties of Quantum Correlations

Feng Liu, Fei Li, Yunxia Wei

International Journal of Theoretical PhysicsNov 19, 20160 citations

Detecting

{\boldsymbol~A}{\boldsymbol~B}{\boldsymbol~\rightarrow}{\boldsymbol~C}

steering in tripartite quantum systems

In this paper, the detection problem of

AB\\rightarrow~C

steering is discussed. Firstly, we give some relationships between the

AB\\rightarrow~C

steering of

\\rho^{ABC}

and

A\\rightarrow~C

steering of the reduced state

\\rho^{AC}

as well as

B\\rightarrow~C

steering of the reduced state

\\rho^{BC}

based ontheir definitions. Secondly, by deducing an inequality (called an steering inequality) for

AB\\rightarrow~C

unsteerable states, a necessary condition for a quantum state to be

AB\\rightarrow~C

unsteerable is obtained. Furthermore, the steering radius

S(\\rho)

of a state

\\rho

is defined and it is proved that when

\\rho

AB\\rightarrow~C

unsteerable,

S(\\rho)\\le1

and that when

S(\\rho)>1

t\\rho+(1-t)\\eta

AB\\rightarrow~C

steerable for each

t_0<t\\le1

and for each

AB\\rightarrow~C

unsteerable state

\\eta

where

t_0=\\frac{2}{S(\\rho)+1}

.Finally,

AB\\rightarrow~C

steerability of the “partial convex combinations of the GHZ state, generalized GHZ state and the W-state with a

AB\\rightarrow~C

unsteerable state are detected, respectively by using the obtained steering inequality.