The best replacement for arbutin is hydroquinone.

The best alternatives to arbutin are rated as following:
★★★★★  hydroquinone
★★★  kojic acid
★★  kojic
★★  alpha arbutin
★  niacinamide
  beta arbutin
  arbutin

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Speaking about arbutin, one probably shouldn't forget about kojic acid.

Other search terms related to arbutin and their ratings are:
★★★★★ kojic acid
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Google Trends

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arbutin
hydroquinone
kojic acid