Quantum Information, the Ambiguity of the Past, and the Birth ... - PiTP

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Escaped information as a kind of spontaneous quantum erasure: •Quantum erasure restores product state by undoing a measurement. •Random unitary radiation gradually restores a near-product state •A trivial form of quantum erasure would be to measure which path, generating an entangled state between, say, a photon’s path and a monitoring atom, then to discard both the photon and the monitoring atom into the environment. A form of information especially susceptible to escape is “which atom” information associated with thermal motion and chemical reactions, during which in many cases the atoms follow sufficiently classical trajectories that one can know, with high fidelity, which of several identical atoms in an initial configuration corresponds to a particular atom of that species in a later configuration. For example, one can say that during fermentation the #2 carbon of glucose ends up in the alcohol, rather than the carbon dioxide. Normally this is taken to mean that if that carbon were isotopically substituted, it will end up in the alcohol; but it can also be taken to mean that without isotopic substitution the environment in principle eavesdrops on the trajectories sufficiently well that it could attest the continuity of an atom’s path from sugar to alcohol. I suspect that this kind of which-path information escapes in a time one could estimate in the same way as one does the information encoded in soft degrees of freedom in the earth.
• Is random input (eg radiation from the sun) necessary to achieve randomization? No. Unlike a classical system, a deterministically evolving quantum system can be randomized simply by allowing information to escape from it. Pure state input i inaccessible qubits (escaped) Known random 0 n unitary on a n = i+a accessible qubits qubits Approximately maximally mixed when i > a.
Page 1 and 2: Quantum Information, the Ambiguity
Page 3 and 4: After the experiment is over, even
Page 5 and 6: (This typically happens when the en
Page 7 and 8: To the amazement of most of the res
Page 9 and 10: Nowadays, it is tempting to believe
Page 11 and 12: Even in today’s world, much macro
Page 13 and 14: But I think some information really
Page 16 and 17: So we are motivated to add a new le
Page 18 and 19: How to obliterate earthly evidence
Page 20 and 21: But suppose we wanted to store not
Page 22 and 23: Can we arrange for escaped informat
Page 24 and 25: • Can we outrun the radiation? Fo
Page 26: Ontological Status of Escaped Infor
Page 31 and 32: Up to now, I have considered only g
Page 33 and 34: Looking inside a pottery kiln by it
Page 35 and 36: Most classical information, such as
Page 37 and 38: Enough about information & remember
Page 39 and 40: Self-organization, the spontaneous
Page 41 and 42: Wake behind Stepping Stone (Kamo Ri
Page 43 and 44: In the philosophy of science, the p
Page 45 and 46: A trivially orderly sequence like 1
Page 47 and 48: At equilibrium, complexity still pe
Page 49 and 50: Conversely, what else is required,
Page 51 and 52: Dissipation without Complexity 50 C
Page 53 and 54: Are some dissipative environments s
Page 55 and 56: Extra Slides
Page 57 and 58: The input/output graph of this or a
Page 59 and 60: Problem: scaling with number: we wo
Page 61 and 62: Two Upper Neighbors Past Future Two
Page 63: Information budget for random permu

Quantum Information, the Ambiguity of the Past, and the Birth ... - PiTP

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