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Discriminating States: the quantum Chernoff bound.
TLDR
The problem of discriminating two different quantum states in the setting of asymptotically many copies is considered, and the minimal probability of error is determined, leading to the identification of the quantum Chernoff bound, thereby solving a long-standing open problem.
Evenly distributed unitaries: On the structure of unitary designs
We clarify the mathematical structure underlying unitary t-designs. These are sets of unitary matrices, evenly distributed in the sense that the average of any tth order polynomial over the design
Subadditivity of q-entropies for q>1
I prove a basic inequality for Schatten q-norms of quantum states on a finite-dimensional bipartite Hilbert space H1⊗H2: 1+∥ρ∥q⩾∥Tr1ρ∥q+∥Tr2ρ∥q. This leads to a proof—in the finite-dimensional
On Strong Superadditivity of the Entanglement of Formation
We employ a basic formalism from convex analysis to show a simple relation between the entanglement of formation EF and the conjugate function E* of the entanglement function E(ρ)=S(TrAρ). We then
A high-resolution sensor based on tri-aural perception
TLDR
A high-resolution sensor composed of three ultrasonic sensors, one transmitter/receiver and two extra receivers, which allows a significant improvement in the information-extraction process and is impervious to measurement variations common to all three receivers.
α-z-Rényi relative entropies
TLDR
A two-parameter family of Renyi relative entropies Dα,z(ρ ∥ σ) that are quantum generalisations of the classical Renyi divergence Dα(p ∥ q) are considered, obtaining explicit formulas for each one of them.
Asymptotic Error Rates in Quantum Hypothesis Testing
We consider the problem of discriminating between two different states of a finite quantum system in the setting of large numbers of copies, and find a closed form expression for the asymptotic
Symmetric squares of graphs
A sharp continuity estimate for the von Neumann entropy
We derive an inequality relating the entropy difference between two quantum states to their trace norm distance, sharpening a well-known inequality due to Fannes. In our inequality, equality can be
Entanglement cost under positive-partial-transpose-preserving operations.
TLDR
It is proved that for the antisymmetric Werner state PPT cost and PPT entanglement of distillation coincide, which is the first example of a truly mixed state for whichEntanglement manipulation is asymptotically reversible, which points towards a unique entanglements measure under PPT operations.
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