Pure steered states of Einstein-Podolsky-Rosen steering

Abstract

In the Einstein-Podolsky-Rosen experiment, when Alice makes a measurement on her part of a bipartite system, Bob's part is collapsed to, or steered to, a specific ensemble. Moreover, by reading her measurement outcome, Alice can specify which state in the ensemble Bob's system is steered to and with which probability. The possible states that Alice can steer Bob's system to are called steered states. In this work, we study the subset of steered states which are pure after normalization. We illustrate that these pure steered states, if they exist, often carry interesting information about the shared bipartite state. This information content becomes particularly clear when we study the purification of the shared state. Some applications are discussed. These include a generalization of the fundamental lemma in the so-called "all-versus-nothing proof of steerability" for systems of arbitrary dimension

EPR steering paradox ‘2 Q = (2−δ) C ’

“…And because ˜r n 0 2 and ˜r n 1 2 are mixed states, and the density matrices of a mixed state can be convexly combined in a number of different ways, there are an infinite number of states in { } r à x x , in addition to the two that must contain ˜r n 0 1 and ˜r n 1 1 . Then Bob's conditional state can be described as Summing over equation (23) and taking the trace, the quantum result on the left is '2 Q ', while the result of the LHS model on the right is '(…”

“…Similarly, inequality methods for EPR steering have been proposed, such as linear EPR steering inequality [19,20] and chained EPR steering inequality [21]. In addition, similar to the AVN argument for Bell nonlocality without inequalities, AVN proofs for EPR steering have been studied [22,23], among which, the EPR steering paradox [24,25] is also a very valuable method for studying EPR steering without inequalities, which reveals the steering nature of the quantum state through a logical contradiction between quantum mechanics and classical theory. However, previous studies on the EPR steering paradox were only for the case where the conditional states of the steered party, Bob, are pure states.…”

Quantum steering in tripartite quantum systems

“…Chen等人 [29] 证明了对于任何2-比特纠缠态, 如果存在投影测 量使Bob的规范化条件状态变成两个不同的纯态, 那么Alice可以控制Bob的状态. Nguyen等人 [30] 将文 献 [29]中的结果推广到高维系统. Wu等人 [31] 证明 了对于N-测量协议中任何给定的2-比特量子态, 如 果它有一个局部隐变量模型, 那么就有一个隐态 个数不大于2 N 的局部隐态模型.…”