![]() ![]() We discuss implications of these insights to readings of the third law of quantum thermodynamics and hint at potentially profound implications to holography. Our results add significant support to recent insights that, contrary to common wisdom, the standard von Neumann entropy also characterizes single-shot situations and opens up the possibility for operational single-shot interpretations of other standard entropic quantities. ![]() If true, this would prove an intimate connection between single-shot state transitions in unitary quantum mechanics and the von Neumann entropy. Building upon these insights, we formulate and provide evidence for the catalytic entropy conjecture, which states that the above result holds true even in the absence of decoherence. This is not the most general state we can think of. Von Neumanns gedanken experiment is repeated, which led him to the formula of thermodynamic entropy of a statistical operator. This paper is an introduction to the von Neumann entropy in a historic approach. 1 Mixed Quantum State So far we have dealt with pure quantum states yi axxi. Entropy, von Neumann and the von Neumann entropy. If the state is expressed as a quantum density matrix, then this. In particular, we will discuss mixed quantum states, density matrices, von Neumann entropy and the trace distance between mixed quantum states. 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 catalyst-an ancillary system that can be reused after the transition-and an environment which has the effect of dephasing in a preferred basis. Von-neumann-entropy definition: (quantum mechanics) The entropy of a quantum state. In this Letter, we provide a new operational characterization of the von Neumann entropy which neither requires an i.i.d. The von Neumann entropy is a key quantity in quantum information theory and, roughly speaking, quantifies the amount of quantum information contained in a state when many identical and independent (i.i.d.) copies of the state are available, in a regime that is often referred to as being asymptotic. ![]()
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