The certification of entanglement dimensionality is of great importance in characterizing quantum systems. Recently, it was pointed out that quantum correlation of high-dimensional states can be simulated with a sequence of lower-dimensional states. Such a problem may render existing characterization protocols unreliable—the observed entanglement may not be a truly high-dimensional one. Here, we introduce the notion of irreducible entanglement to capture its dimensionality that is indecomposable in terms of a sequence of lower-dimensional entangled systems. We prove this new feature can be detected in a measurement-device-independent manner with an entanglement witness protocol. To demonstrate the practicability of this technique, we experimentally apply it on a 3-dimensional bipartite state, and the result certifies the existence of irreducible (at least) 3-dimensional entanglement.

纠缠维数的证明对于表征量子系统非常重要。最近，有人指出可以用一系列低维态来模拟高维态的量子相关性。这样的问题可能会使现有的表征协议不可靠-观察到的纠缠可能不是真正的高维纠缠。在这里，我们引入不可约纠缠的概念来捕获其维数，该维数在一系列低维纠缠系统中是不可分解的。我们证明可以使用纠缠见证协议以独立于测量设备的方式检测到此新功能。为了证明该技术的实用性，我们通过实验将其应用于3维二分态，