What Information Theory Can Tell Us About Quantum Reality

Abstract

Abstract. An investigation of Einstein's "physical" reality and the concept of quantum reality in terms of information theory suggests a solution to quantum paradoxes such as the Einstein-Podolsky-Rosen (EPR) and the Schrödinger-cat paradoxes. Quantum reality, the picture based on unitarily evolving wavefunctions, is complete, but appears incomplete from the observer's point of view for fundamental reasons arising from the quantum information theory of measurement. Physical reality, the picture based on classically accessible observables is, in the worst case of EPR experiments, unrelated to the quantum reality it purports to reflect. Thus, quantum information theory implies that only correlations, not the correlata, are physically accessible: the mantra of the Ithaca interpretation of quantum mechanics.

Quantum information theory of the Bell-state quantum eraser

“…Still, neither of these states predict the quanton's state, which after all is neither here nor there. We are thus forced to admit that our classical devices do not (and cannot) reveal to us the quantum reality underlying our classical world [29]. However, experimental (and theoretical) ingenuity has allowed us to be aware of our classical device's deceptions, and shown us the path to perhaps design even more clever schemes to lift the veil from the underlying quantum reality.…”

Toward a Fully Relativistic Theory of Quantum Information

“…On the other hand, it is possible, armed with my measurement result, to make predictions about the state of other detectors measuring the same spin. And even though all these detectors will agree about their result, technically they agree about a random variable (the state of the measurement device), not the actual state of the spin they believe their measurement device to reflect [23]. Indeed, what else could they agree on, since the spin does not have a state?…”

“…Still, a resolution of the microscopic dynamics in black hole evaporation is needed. One possible approach is to use quantum information theory to characterize the relative states of the black hole, the stimulated radiation emitted during the formation of the black hole, and the Hawking radiation (spontaneous emission of radiation) created in the subsequent evaporation [23,58]. As we have lost track of the stimulated radiation, we must always average over it ("trace" it out), which (along with tracing out the causally disconnected region that lies beyond the Schwarzschild radius) creates the positive black hole entropy.…”

“…In the flat space-time treatment of Ref. [23], the entropy balance between the black hole and the Hawking radiation can be maintained because entanglement is spread between the stimulated radiation, Hawking radiation, and the black hole. While all three are strongly entangled, tracing over the stimulated radiation produces a state of no correlations between Hawking radiation and black hole, implying that the Hawking radiation appears purely thermal.…”

Quantum Computing

“…Nielsen [109] (Svozil [110,111], Holevo [112], Knill, Laflamme [113,114], and Ohya [115] develop a theory of quantum errorcorrecting codes and quantum information theory, e.g., they give the definition of quantum mutual entropy for an entangled state. Buhrman et al [116], and Adami, Cerf [117] contrast quantum information theory with classical information theory. Quantum channel capacity has been investigated for noisy channels (DiVincenzo, et al [118], Holevo [119], Barnum et al [120]), very noisy channels (Shor,Smolin [121]), and quantum erasure channels (Bennett et al [122]).…”