论文标题
为$ 2 \ otimes d $ Quantum System构建一个可分离和绝对可分离状态的球
Constructing a ball of separable and absolutely separable states for $2\otimes d$ quantum system
论文作者
论文摘要
绝对可分离状态是一种可分离的状态，在任何全球统一转型的作用下都可以分离。这些状态可能具有量子相关性，也可能没有量子相关性，这些相关性可以通过量子不一致来衡量。我们发现绝对可分离态在量子计算中也有用，即使它包含无限的量子相关性。因此，要搜索具有零和零不和谐的两量Qubit的绝对可分离状态的类别，我们为$ tr（\ varrho^{2}）$得出了上限，其中$ \ varrho $表示所有零和不和谐状态。通常，上限取决于所考虑的状态，但是如果该状态属于某些特定类别的零不一调状态，那么我们发现上限是独立的。后来，可以表明，在这些特定类别的零不和状态中，存在绝对可分离的子类。此外，我们为给定量子问题状态的可分离性提供了必要条件。然后，我们使用派生条件以$ 2 \ otime d $ d $量子系统构造球，由$ tr（ρ^{2}）\ leq tr（x^{2}）+2tr（xz）+tr（xz）+tr（z^{2}）$，$ 2 \ otime d $ Quantum System the $ $ $ $ $ $ s y y $ $ s y y $ $ s $ $ s $ $ s $ $ pe $ x，z \ geq 0 $。特别是，对于Qubit-Qubit System，我们表明，与$ TR（ρ^{2}）所描述的球相比，新构造的球包含较大的绝对可分离状态，\ leq \ leq \ frac {1} {3} $。最后，我们从纯度方面得出了必要的条件，以实现正在研究的量子问题的绝对可分离性。
Absolute separable states is a kind of separable state that remain separable under the action of any global unitary transformation. These states may or may not have quantum correlation and these correlations can be measured by quantum discord. We find that the absolute separable states are useful in quantum computation even if it contains infinitesimal quantum correlation in it. Thus to search for the class of two-qubit absolute separable states with zero discord, we have derived an upper bound for $Tr(\varrho^{2})$, where $\varrho$ denoting all zero discord states. In general, the upper bound depends on the state under consideration but if the state belong to some particular class of zero discord states then we found that the upper bound is state independent. Later, it is shown that among these particular classes of zero discord states, there exist sub-classes which are absolutely separable. Furthermore, we have derived necessary conditions for the separability of a given qubit-qudit states. Then we used the derived conditions to construct a ball for $2\otimes d$ quantum system described by $Tr(ρ^{2})\leq Tr(X^{2})+2Tr(XZ)+Tr(Z^{2})$, where the $2\otimes d$ quantum system is described by the density operator $ρ$ which can be expressed by block matrices $X,Y$ and $Z$ with $X,Z\geq 0$. In particular, for qubit-qubit system, we show that the newly constructed ball contain larger class of absolute separable states compared to the ball described by $Tr(ρ^{2})\leq \frac{1}{3}$. Lastly, we have derived the necessary condition in terms of purity for the absolute separability of a qubit-qudit system under investigation.
