![]() The entity that tells us what Bob's probabilities to measure certain results are is a density matrix $\rho_B$ that is obtained from the full Alice Bob state $\rho_$ via a partial trace, and this partial trace is the same no matter what Alice does.Īnd sure, if you're looking to experimentally test this, you can always claim that only yields "statistical proof" (the test would have to be that Bob cannot, on average (an inherently statistical notion!), do better than random chance in trying to guess what Alice did) - maybe next time Bob can suddenly communicate with Alice and quantum mechanics as we understand it has stopped working. The claim that "faster-than-light communication via entanglement is impossible" is precisely that the answer to this is "No." - Bob cannot perform any measurement that would allow him any sort of inference about what Alice did, neither a certain nor a statistical one. Can Bob say anything about what Alice did? Note: Not just "Can Bob receive a specifically coded message Alice is trying to send him?", but whether he can say anything at all, with any degree of certainty. However, I am not comfortable with counterfactual thinking, and I don't really see how it makes things more formal.Īt least in the context of things like the no-communication theorem, the technical meaning of "no communication" is very clear:Īlice and Bob have coordinated to perform measurements on two halves of an entangled state at spacelike separation. In fact, the only definition I can think of is a counterfactual one: "Bob receives exactly the message Alice was supposed to send him, and it would have been the case even if I had asked Alice to send any other message". What do sentences like "such theory forbids faster-than-light communication" precisely mean? Moreover, if we repeat such experiments a certain number of times and Alice and Bob always succeed, I don't think I can gain more than a statistical proof of their power, but not an absolute one. This story surely sounds extraordinary but I don't see which rule of physics would forbid it to happen: would some force forbid Bob to articulate the precise words Alice was supposed to send him? Point in space-time where we have all four agreed to meet, and myįriend tells me that Bob "received" exactly the lines of the poem. Her head and looks concentrated, says "it's done", and we reach the ![]() ![]() Poem, and ask Alice to send these sentences to Bob then she touches Last moment, I think of something, let's say, the first lines of a My friend has to recordĮverything Bob would have claimed to "receive" from Alice. Space-time that are space-like separated. Alice and I travel very far away, while myįriend and Bob stay together here, and each group reaches points in I often read sentences like "relativity forbid faster-than-light communication" or "quantum entanglement cannot be used to convey information faster than light", but it seems to me that the formalization of "faster-than-light communication is not possible" is harder than it might look.Īssume that me and a friend, the "skeptics", want to investigate ifĪlice and Bob can transmit information faster than light, as theyĬlaim they're able to do. ![]()
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