# Can quantum money be reliably "burned?"

One of the novel features of Bitcoin and other cryptocurrencies is that coins can be irrefutably "burned" or destroyed, by creating a transaction to send the money to a junk burn address.

Thinking similarly about quantum money - from knots, or hidden subspaces, Wiesner's currency, BBBW, etc. - has an "obvious" way to be destroyed. For example, given a legitimate Wiesner coin, by measuring in the "wrong" basis, the currency would be destroyed.

But it's not clear how to irrefutably prove that the coin was destroyed.

For example, if I have a Wiesner coin, and I tell the world that I've burned it, is there a way that I can do it so that others will believe me? Even if I'm the bank?

Edit

I think I first heard of this question in a fascinating and stimulating lecture by Or Sattath - https://www.youtube.com/watch?v=Zd5tDyPXsIM - at around 59:20.

As Meowwzz suggests, clearly measuring a coin in a burn basis will burn it. That burn basis can even be orthogonal to the valid basis, maximally destroying the coin, I think.

Another option that comes to mind is for the bank to publish and broadcast, on a public classical channel, the correct basis for a serial number $s$. Thus, the secret is released, enabling anyone to clone the coin at will, and effectively destroying the unclonability, and hence uniqueness and value, of the coin.

Such an option (on a classical channel) is viable for Wiesner's coin, and the Hidden Subspaces coin, but I don't think for the Quantum Knots coin - there's no secret to be released on the Knots coin.

However, such an option can only be done by the bank or whoever knows the classical secret, whereas I think Meowzz's approach can be done by anyone, including the holder of the coin of interest.

If each coin is entangled w/ the ledger, burning a coin via measuring it in the 'burn' (or 'wrong') basis would create an update in the ledger which could then be verified by anyone who had access to the ledger.

See this paper: Quantum Blockchain using entanglement in time for more info on one approach.

I also posted a question about time entangled blockchains which includes a couple links:

1. Quantum Secured Blockchain

2. Quantum Bitcoin: An Anonymous and Distributed Currency Secured by the No-Cloning Theorem of Quantum Mechanics

• What does "entangled with the ledger" mean? What does "burn" basis mean? Jul 3 '18 at 6:57
• @Blue Are you asking what a ledger is or how one might actually go about creating entanglement in a blockchain? Also, added clarification on burn basis. Jul 3 '18 at 7:09
• Yes. It's not clear to me which source you're getting the terms in the first paragraph from - "ledger", "burn basis", etc and their meaning isn't clear to me either. It would be nice if you can add a source/reference for your first paragraph. Jul 3 '18 at 7:14
• Blockchains are often referred to as ledgers (see link). The burn basis is an arbitrary named basis [ the OP stated 'wrong' basis ] named by me. The source or reference for the 1st paragraph is me. If you need a citation, see here Jul 3 '18 at 7:23
• I think you could find out more on proving destruction of quantum states in papers by Anne Broadbent.
– holl
Aug 4 '21 at 6:27