论文标题
根据保利操作员的期望值引入量子纠缠措施
Introduction Of Quantum Entanglement Measure Based On The Expectation Values Of Pauli Operators
论文作者
论文摘要
在本文中，首先考虑到在可分离的状态下，一个粒子的测量对第二个粒子的测量没有影响，我们表明爱丽丝和鲍勃可以找到方向，在这些方向上，它们在粒子旋转上的测量结果始终最大化。换句话说，粒子的状态是朝着该方向应用的操作员的本征态，因此两个颗粒的自旋的总和可以具有最大值。我们将争辩说，在纠缠状态下，由于粒子测量结果彼此的影响，爱丽丝和鲍勃找不到所需的操作员。因此，在这样的测量中，颗粒的总自旋始终小于上述最大值。但是我们要求他们尝试衡量将获得最大价值的方向。由于该值是可分离状态的最大值，对于完全纠缠的状态，对于其余的状态，它将与两个最大值和最小值之间的纠缠程度成正比，我们将此参数设置为“可分离性指数”。然后，基于此指数，引入了纠缠的度量并将其扩展到具有较高维度的州。最后，研究了di-qutrit状态的示例，并研究了di-qudit状态，并通过示例结果证实了该措施的效率。考虑到在此度量中，根据期望值计算纠缠的值，我们可以在实验中衡量期望值，我们希望能更接近纠缠值的可检验性。
In this paper, firstly considering that in separable states, the measurement of one particle has no effect on the measurement of the second particle, we show that Alice and Bob can find directions in which the results of their measurements on the spin of the particle are always maximized. In other words, the state of the particle is an eigenstate for the operator that is applied in that direction, so the sum of the spins of two particles can have a maximum value. We will argue that in entangled states, due to the effect of particle measurement results on each other, Alice and Bob cannot find the desired operators. Therefore, in such measurements, the total spin of the particles will always be less than the mentioned maximum. But we ask them to try and measure in directions that will get the most value. Because this value is maximum for separable states and minimum for fully entangled states, and for the rest of the states, it will be proportional to the degree of entanglement between the two maximum and minimum values, we set this parameter as We are calling it the "separability index". Then, based on this index, the measure of entanglement was introduced and extended to states with higher dimensions. In the end, examples of di-qubit states di-qutrit states, and di-qudit states were investigated and the efficiency of the measure was confirmed by the results of the examples. Considering that in this measure, the values of entanglement are calculated based on the expectation values and we can measure the expectation values in the experiment, we hope to be one step closer to the testability of the entanglement value.
