透過共享一對最大糾纏態,理想的量子傳態可以將一未知的d維量子態從一處完整的遙傳至另一處,若Alice和Bob只共享了古典資源,則傳態的保真度,即,Alice欲傳的態和Bob拿到的態兩者的最大平均保真度為fc=2/(d+1),這個值對應到了單態比Fc=1/d。如果Alice和Bob共享了一對傳態保真度f<fc(F<Fc)的糾纏態ρ,但在局域性篩選器成功的作用之後,傳態保真度f>fc(F>Fc),則我們說量子糾纏態ρ具有潛在的傳態能力。在這份研究工作內,我們探究:(1)有一個參數、兩個d維量子位元族的量子糾纏態以及Werner state的潛在傳態能力,(2)局域性篩選器成功的機率以及有多少傳態保真度可以藉由局域性篩選器來增加,兩者之間的關係,(3)將我們得到的結果和Rains的半定程式做比較,其考慮所有跡數保持的正局部轉置操作來最大化傳態保真度,(4)直接最大化單態比和最大化整體傳態保真度之間的差異,(5)給予一個如何用Mach-Zehnder干涉儀來測量兩個未知量子態的光子的例子。

An ideal quantum teleportation transfers an unknown d-dimensional quantum state intact from one party to another via the use of a maximally entangled state. If Alice and Bob only share a classical resource, the teleportation fidelity, i.e., the maximal average fidelity between the state to be teleported and the state received is at most fc=2/(d+1), which corresponds to singlet fraction Fc=1/d. If they share an entangled state ρ with teleportation fidelity f<fc (so equivalent to F<Fc) and upon successful local filtering, the teleportation fidelity becomes larger than fc (or F>Fc), we say that ρ has hidden teleportation power. Here, we investigate (1) the hidden teleportation power of a one-parameter family of entangled states and Werner state, (2) the trade-off between the success probability of local filtering and the extent to which the teleportation fidelity can be increased by this means,(3) the upper bound obtained by Rains’s semidefinite program [13], (4) difference between maximizing the singlet fraction after local filtering and maximizing cost function, (5) we also give an example of Mach-Zehnder interferometer to show how to measure the fidelity [5] of two photons in unknown states.

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