This is a broad question underlying the analysis of any proprietary issues of cryptocurrencies and other assets on blockchains, since they may be seen as nothing but information (data) whose value is acknowledged by the market or specific parties involved in a transaction.
Information cannot be an object of legal rights in Japanese law (a position presumably shared by many legal systems), a major exception being intellectual properties. Thus, if a disc containing valuable information is stolen, a criminal charge cannot be brought against the theft of the information but only against the theft of the disc (See e.g. Tokyo District Court judgment on 7 July 1998). The rationale is that if otherwise, a conduct like browsing at a bookshop could be a criminal offense, which would seem counter-intuitive.
This general position may need to be reviewed with the proliferation of financially valuable information such as big data in the society. Emissions quota may be regarded as another example. I have previously considered the issues of conflict of laws in emissions trading on the assumption that emissions quotas can be an object of ownership. That assumption conjures up the image of ownership of atmosphere and has been met with occasional scepticisms but it is now widely accepted. Cryptocurrencies and other assets on blockchains, too, would pose a challenge to the conventional thinking and I think that they should be treated as being capable of becoming objects of legal rights at least for the sake of conflict-of-law analysis.