Freiburg 2019 – scientific programme

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FM: Fall Meeting

FM 58: Quantum Information Concepts in Thermodynamics

FM 58.3: Talk

Wednesday, September 25, 2019, 14:45–15:00, 3042

Von Neumann entropy from unitarity — Paul Boes¹, Jens Eisert¹, Rodrigo Gallego¹, Markus P. Müller^2,3, and •Henrik Wilming⁴ — ¹Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany — ²Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria — ³Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5, Canada — ⁴Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland

The von Neumann entropy is a key quantity in quantum information theory. It quantifies the amount of quantum information contained in a state when many identical and independent (i.i.d.) copies are available. We provide a new operational characterization of the von Neumann entropy which neither requires an i.i.d. limit nor any explicit randomness. We do so by showing that the von Neumann entropy fully characterizes single-shot state transitions in unitary quantum mechanics, as long as one has access to a suitable ancillary system whose reduced state remains invariant in the transition and an environment which has the effect of dephasing in an arbitrary preferred basis. Furthermore we formulate and provide evidence for the catalytic entropy conjecture, which states that the above holds true even in the absence of a decohering environment. If true, it would prove an intimate connection between single-shot state transitions in unitary quantum mechanics and the von Neumann entropy. We also discuss implications of these insights to thermodynamics.