My rule of thumb has always been, don't quote anything unless you are going to comment on the quotation. If all you are doing is citing an information source to support an assertion, make the assertion in your own words and cite the source in a footnote.
But a summary is not about proving or supporting anything. It is a statement of what the argument of the paper is. It is the job of the rest of the paper to support the conclusions. It is the job of the summary to briefly sketch the main argument and conclusion so that a reader can quickly tell if the paper is relevant to their own work. I can't see why you would quote or footnote anything in a summary.
In writing anything, you always have to keep in mind what the reader's purpose is in reading it. The reader's purpose in reading a research paper is twofold: to discover its conclusions, and to test its data and method to determine whether to accept its conclusions. For this second part, they need access to the research material via quotations or footnotes.
The reader's purpose in reading a summary of a research paper is simply and solely to determine if the paper is relevant to their work and therefore worth their time. They are not, at this stage questioning it conclusions, data, or method, only it relevance. So they don't need access to the supporting evidence, and so they don't need quotations or footnotes.
All that said, different institutions have different standards, not all of which make actual sense, but all of which you have to follow if you write for that institution. So look up what the standards and practices are for the institution you are writing for and follow them.