论文标题
关于一个纯转向状态的力量，用于用一对Qubit
On the power of one pure steered state for EPR-steering with a pair of qubits
论文作者
论文摘要
正如最初引入的那样，EPR现象是一个政党（爱丽丝）通过在两个测量设置之间进行选择的能力，即另一方的量子系统（BOB）成两个纯净状态的两个不同的集合。后来正式为量子信息任务，即使不同的合奏构成混合状态，也可以显示EPR-Steering。考虑爱丽丝和鲍勃各自具有量子的情况，爱丽丝执行二分法投影测量。在这种情况下，她可以在鲍勃（Bob）的布洛克（Bloch Ball）中指向椭圆形$ {\ cal e} $的合奏中的各州。此外，让转向椭圆形$ {\ cal e} $具有非零卷。以前已经表明，如果爱丽丝的第一个测量设置产生一个组成两个纯状态的集合，那么此，以及其他任何一个测量设置，都将证明EPR稳定。在这里，我们可以考虑如果爱丽丝的第一个设置中的合奏只包含一个纯状态$ \ mathsf {p} \ in {\ cal e} $，则在概率$ p_ \ m athsf {p} $中出现。使用投影性的几何形状，我们在分析上得出了必要和足够的条件，以使爱丽丝能够使用此情况和第二个设置来证明鲍勃状态的epr-steeering，当时这些之间的两个集合在给定的平面中。基于此，我们表明，对于给定的$ {\ cal e} $，如果$ p_ \ mathsf {p} $足够高[$ p _ {\ sf p}> p _ {\ rm max}^{\ rm max}^{\ cal e} {\ cal e} \ in [0,1）$ in [0,0,1）$，然后由Alice sovere a alice Exeply sovere Expection Exexplie Exexpeive e Prope fore epr-ste epr ste epr ste epr ste epr ste epr ste。同样，我们得出A $ p _ {\ rm min}^{\ cal e} $，这样$ p_ \ mathsf {p}> p _ {\ rm min}^{\ cal e} $对于爱丽丝仅使用首次设置和其他设置和其他设置和其他设置而言是必要的。此外，我们得出的表情很紧。对于球形转向椭圆形，边界重合：$ p _ {\ rm max}^{\ cal e} = p _ {\ rm min}^{\ cal e} $。
As originally introduced, the EPR phenomenon was the ability of one party (Alice) to steer, by her choice between two measurement settings, the quantum system of another party (Bob) into two distinct ensembles of pure states. As later formalized as a quantum information task, EPR-steering can be shown even when the distinct ensembles comprise mixed states. Consider the scenario where Alice and Bob each have a qubit and Alice performs dichotomic projective measurements. In this case, the states in the ensembles to which she can steer form the surface of an ellipsoid ${\cal E}$ in Bob's Bloch ball. Further, let the steering ellipsoid ${\cal E}$ have nonzero volume. It has previously been shown that if Alice's first measurement setting yields an ensemble comprising two pure states, then this, plus any one other measurement setting, will demonstrate EPR-steering. Here we consider what one can say if the ensemble from Alice's first setting contains only one pure state $\mathsf{p}\in{\cal E}$, occurring with probability $p_\mathsf{p}$. Using projective geometry, we derive the necessary and sufficient condition analytically for Alice to be able to demonstrate EPR-steering of Bob's state using this and some second setting, when the two ensembles from these lie in a given plane. Based on this, we show that, for a given ${\cal E}$, if $p_\mathsf{p}$ is high enough [$p_{\sf p} > p_{\rm max}^{\cal E} \in [0,1)$] then any distinct second setting by Alice is sufficient to demonstrate EPR-steering. Similarly we derive a $p_{\rm min}^{\cal E}$ such that $p_\mathsf{p}>p_{\rm min}^{\cal E}$ is necessary for Alice to demonstrate EPR-steering using only the first setting and some other setting. Moreover, the expressions we derive are tight; for spherical steering ellipsoids, the bounds coincide: $p_{\rm max}^{\cal E} = p_{\rm min}^{\cal E}$.
