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Foundations of Quantum Mechanics

INFORMATION FLOW IN QUANTUM MECHANICS: THE QUANTUM MAXWELL DEMON

George Chapline

Published Apr 1, 1992• 3 citations
Publisher

Abstract

Quantum information can be lost only when a quantum system is placed in contact with a heat bath, and then only in proportion to the entropy generated. Applied to the universe as a whole this suggests that the universe is in an algorithmically simple nearly pure quantum state. This could be verified by "squeezing'' the vacuum state, and it is quite plausible that this is exactly what is happening inside black holes.

DOI
10.1142/9789814436687_0031

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Quantum information can be lost only when a quantum system is placed in contact with a heat bath, and then only in proportion to the entropy generated. Applied to the universe as a whole this suggests that the universe is in an algorithmically simple nearly pure quantum state. This could be verified by "squeezing'' the vacuum state, and it is quite plausible that this is exactly what is happening inside black holes.
In 1976 Stephen Hawking proposed that information may be lost from our universe as a pure quantum state collapses gravitationally into a black hole, which then evaporates completely into a mixed state of thermal radiation. Although this proposal is controversial, it is tempting to consider analogous processes that might occur in certain theories of consciousness. For example, one might postulate that independent degrees of freedom be ascribed to the mental world to help explain the feeling of a correlation between one's desires and one's choice of actions. If so, one might ask whether information in the physical world can be lost to such postulated degrees of freedom in the mental world. Or, one might hypothesize that the mental world can affect the physical world by modifying the quantum action for the physical world in a coordinate-invariant way (analogous to the alpha parameters in wormhole theory).
The second law of classical equilibrium thermodynamics, based on the positivity of entropy production, asserts that any process occurs only in a direction that some information may be lost (flow out of the system) due to the irreversibility inside the system. However, any thermodynamic system can exhibit fluctuations in which negative entropy production may be observed. In particular, in stochastic quantum processes due to quantum correlations and also memory effects we may see the reversal energy flow (heat flow from the cold system to the hot system) and the backflow of information into the system that leads to the negativity of the entropy production which is an apparent violation of the Second Law. In order to resolve this apparent violation, we will try to properly extend the Second Law to quantum processes by incorporating information explicitly into the Second Law. We will also provide a thermodynamic operational meaning for the flow and backflow of information. Finally, it is shown that negative and positive entropy production can be described by a quantum thermodynamic force.
In apparent contradiction to the laws of thermodynamics, Maxwell's demon is able to cyclically extract work from a system in contact with a thermal bath, exploiting the information about its microstate. The resolution of this paradox required the insight that an intimate relationship exists between information and thermodynamics. Here, we realize a Maxwell demon experiment that tracks the state of each constituent in both the classical and quantum regimes. The demon is a microwave cavity that encodes quantum information about a superconducting qubit and converts information into work by powering up a propagating microwave pulse by stimulated emission. Thanks to the high level of control of superconducting circuits, we directly measure the extracted work and quantify the entropy remaining in the demon's memory. This experiment provides an enlightening illustration of the interplay of thermodynamics with quantum information.
In semiclassical gravity, the final state of black-hole evaporation cannot be described by a pure state. Nevertheless, we point out that the system can be described by a generalized pure state, which is not defined on a three-dimensional hypersurface but on the four-dimensional spacetime describing the whole Universe at all times. Unlike the conventional quantum state, such a generalized state treats time on an equal footing with space, which makes it well suited for systems that are both quantum and relativistic. In particular, such a generalized state contains a novel type of information encoded in the correlations between future and past, which avoids the black-hole information paradox.
With the approaching second quantum revolution, the study of quantum thermodynamics, particularly heat flow, has become even more relevant for two main reasons. First, understanding heat and other types of noise is essential for protecting quantum information and preventing decoherence. Second, the ability to manufacture and control quantum systems developed for the quantum computer allows for experimental study of quantum thermodynamics in entirely new settings. In this thesis, several systems involving quantum systems in contact with baths are studied theoretically in experimentally available settings. First, two rectification or diode setups for heat currents are proposed using a dark-state mechanism. In one system, the dark-state mechanism is imperfect but very robust. In the other system, the dark-state mechanism relies on quantum entanglement and is much better but more fragile towards decoherence. Next, a quantum version of the Wheatstone bridge is built using the same entanglement-powered dark state mechanism. After having studied several boundary-driven quantum systems, the lessons learned are generalized into resonance conditions using a general linear chain of weakly interacting chains of strongly interacting spins. The final two chapters focus on the ability to study statistical physics in realizable quantum systems. First, a Maxwell's demon setup is proposed. A demon-controlled qutrit is coupled to two non-Markovian baths. The information back-flow from the non-Markovian baths allows the demon to more effectively transfer heat from the cold bath to the hot bath. Second, the Mott insulator to superfluid phase transition in a lattice of transmons is examined. The ground state has a variable particle number and is prepared using adiabatic state preparation. This allows for the exploration of the entire phase diagram.
In this work, we describe optically inspired models for unitary black hole (BH) evaporation. The goal of these models are (i) to be operationally simple, (ii) approximately preserve the thermal nature of the emitted Hawking Radiation (HR), and (iii) attempt to reproduce the Page Curve that purports that information flows forth from the BH when it has evaporated to approximately half its initial mass. We concentrate on modeling the BH as a single mode squeezed state successively interacting, by means of beam splitters and squeezers, with vacuum modes near the horizon, giving rise to entangled pairs representing the external Hawking radiation and its partner particle inside the horizon. Since all states and operations are Gaussian throughout, we use a symplectic formalism to track the evolution of the composite system through the evolving means and variances of their quadrature operators. This allows us to easily compute correlations and entanglement between the BH and the HR, as well as calculate correlations between the BH at early and late times.