In free probability, Voiculescu's free entropy counts matrix microstates that approximate an operator. It is a non-commutative analog of the Shannon entropy, distinct from any quantum entropy of a density operator, but it has had no physical meaning in quantum theory. We define a finite-dimensional physical free entropy at finite resolution and show that it directly characterizes, up to an explicit constant, the minimal quantum memory needed to program many copies of a state with known eigenvalues and unknown eigenbasis. This task is a variant of Schumacher compression, and we call its optimal cost the quantum minimum description length. We briefly discuss how free entropy differs from quantum entropies and its potential applications in quantum physics.
We study a variant of Schumacher compression. The task asks for the minimal memory cost for compressing many copies of a density matrix with known spectrum and unknown eigenbasis, without preserving its purification. For fixed dimension and distinct positive eigenvalues, we obtain the cost through its additive constant...
Patrick M. Hayden, Alexander Maloney, Jin-Zhao Wang et al.· 1 citation
Von Neumann proposed two quantum entropies, one in 1927 and the other in 1929. He intended to define thermodynamic entropy for quantum states in both cases. The 1927 entropy is the well-known von Neumann entropy, which is zero for all pure states. The 1929 entropy, which is nonzero for almost all pure states, has large...
Distinguishability is a central concept in information theory and extends naturally to quantum systems. This work shows that, for any two finite-dimensional memoryless quantum channels, parallel, adaptive and general testing strategies achieve the same Stein exponent at every fixed type-I error tolerance $\epsilon\in(0...
We study disorder-free localization in a spin-coupled quantum walk on the hypercube within the quantum Bernoulli noises framework. We derive a general criterion for disorder-free localization: it occurs if and only if some spectral subspace of a reduced unitary evolution contains a vector whose position marginal probab...
We show that the emergence of a ``magic barrier'', characterized by a transient maximum of nonstabilizerness during rapid entanglement growth, is a universal feature of thermalization within quantum ergodic theories, which is intimately connected to random matrix spectral properties. Starting from a pure product state,...
J. Minár, Andreas Schafer, Leonhard Schmotzer et al.· 1 citation
Entanglement Distance (ED) was originally proposed as a geometric measure of entanglement derived from the Fubini-Study metric on the projective Hilbert space. Independently, the Meyer-Wallach and Scott measures quantify multipartite entanglement via linear entropy. In this work, we demonstrate that these two seemingly...
Lorenzo Capra, Lucio De Simone, Roberto Franzosi· 0 citations
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