If I purchase Monero with Bitcoin, then purchase Bitcoin with Monero, can the two Bitcoin ledgers be linked?

Here's a hypothetical scenario I've been pondering.

John Doe has 10 Bitcoin that is being closely monitored by a large organization. No matter how many times John Doe tumbles and splits his Bitcoin, the large organization has the computing power to trace all 10 of the Bitcoin back to John Doe.

John Doe decides that he still wants to own Bitcoin, but he wants to own his Bitcoin anonymously where the large organization cannot find trace it. John Doe converts the 10 Bitcoin he owns into 1440 Monero on an exchange using a burner account that requires no personal information to create. Then, after several days, John Doe converts the 1440 Monero on the exchange back to 10 Bitcoin.

Finally, John Doe then transfers the 10 Bitcoin off the exchange to a cold storage wallet where only he can access it.

At the end of this hypothetical scenario, is the 10 Bitcoin stored in John Doe's cold storage wallet completely anonymous and untraceable by the large organization?

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from Bitcoin - The Currency of the Internet https://ift.tt/2mMDQXF

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