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If each bitcoin has a ledger (Peer to Peer) and contains all the transaction history since it was mined, then how come it can be stolen? For example, Bitcoins were stolen by hackers from Mt. Gox. If the Bitcoins each have a ledger it would show its owner and the Mt. Gox account. So it would be traceable and hard to trade if stolen. Maybe I am not fully clear, would appreciate clarification - thanks!

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I believe the large threat of theft of Bitcoin or digital assets is through hacking into your account located on an exchange or possibly your wallet. I do not believe you find theft at this point in time elsewhere. In the future we may see qubits or quantum computing being able to conquer the blockchains security. But as of now I believe it is through people hacking your accounts.

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Bitcoin is never technically stolen, it is the private keys used for signing transactions which are.

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Firstly, there is no "each Bitcoin". On a technical level, there is no such an object as "a Bitcoin". Rather it is a ledger of transactions, and the Bitcoin that people own are entries on that ledger.

When Bitcoin is stolen, an additional transaction is added to the ledger that says that the Bitcoin is transferred from the original owner to the thief. This transaction is exactly the same as any other Bitcoin transaction; it says money is sent from person A to person B.

In the case of a theft, the thief has gained access to the private keys necessary to send the Bitcoin elsewhere (i.e. create a valid transaction). Using those keys, the thief created such a transaction and sen the coins to himself.

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