Abstract

When two or even more quantum systems are entangled a number of counter-intuitive phenomena arises [1]. A particular example of such multipartite entangled states are the W-class which in general form is a coherent superposition of N qubit states exhibiting equal probability amplitudes. They come along with the exceptional property that their entanglement is robust against decoherence [2]. To this date the photonic realization of W-states has entirely relied on bulk optics [3]. Implementing their generation in integrated-optical platforms which are beneficial regarding stability, robustness, and miniaturization one can tremendously increase their size (order) and generation efficiency. In our work, we experimentally realize high-order W-states by forcing single photons to exist in a uniform coherent superposition of N (= 16, 8, 4, 5, 2) spatial optical modes within an integrated multi-port system. Thus, they are in the state $|{\text{W}}_N〉=(1/\sqrt{N}){\displaystyle {\sum }_{n=1}^N{\text{e}}^{\text{i}{\varphi }_n}{\widehat{a}}_n^{†}|0〉}$,where ${\widehat{a}}_n^{†}$ denotes the bosonic creation operator in mode n, and ϕ_n represents an arbitrary relative phase. For this purpose, we have fabricated a discrete network of integrated 50/50 beam splitters as shown in Fig. 1 (left). As it is presented in Fig. 1 (right) a flat photon number probability distribution is observed for various orders of |W_N〉-states. Furthermore, we experimentally very the multipartite entanglement of the generated states by means of a verification device projecting W-states to single-photon Fock states and applying a fidelity criterion [4]. Interestingly, in the generated W-states, the probability for a single photon to emerge from any of the output ports is exactly the same. Based on that fact we have additionally developed a scheme to generate genuine random numbers, which is of great importance nowadays [5]. The authenticity of the random numbers is verified by applying the fifteen statistical tests suggested by National Institute of Standard Technology (NIST) [6].

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