Francesco Buscemi

Departing from the usual paradigm of local operations and classical communication adopted in entanglement theory, we study here the interconversion of quantum states by means of local operations and shared randomness. A set of necessary and sufficient conditions for the existence of such a transformation between two given quantum states is given in terms of the payoff they yield in a suitable class of nonlocal games. It is shown that, as a consequence of our result, such a class of nonlocal game

We study optimal rates for quantum communication over a single use of a channel, which itself can correspond to a finite number of uses of a channel with arbitrarily correlated noise. The corresponding capacity is often referred to as the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">one-shot</i> quantum capacity. In this paper, we prove bounds on the one-shot quantum capacity of an arbitrary channel. This allows us to compute the quantum capacity o

We introduce information-theoretic definitions for noise and disturbance in quantum measurements and prove a state-independent noise-disturbance tradeoff relation that these quantities have to satisfy in any conceivable setup. Contrary to previous approaches, the information-theoretic quantities we define are invariant under the relabelling of outcomes and allow for the possibility of using quantum or classical operations to "correct" for the disturbance. We also show how our bound implies stron

We show that complete positivity is not only sufficient but also necessary for the validity of the quantum data-processing inequality. As a consequence, the reduced dynamics of a quantum system are completely positive, even in the presence of initial correlations with its surrounding environment, if and only if such correlations do not allow any anomalous backward flow of information from the environment to the system. Our approach provides an intuitive information-theoretic framework to unify a

In quantum mechanics the statistics of the outcomes of a measuring apparatus is described by a positive operator valued measure (POVM). A quantum channel transforms POVMs into POVMs, generally irreversibly, thus losing some of the information retrieved from the measurement. This poses the problem of which POVMs are “undisturbed,” i.e., they are not irreversibly connected to another POVM. We will call such POVMs clean. In a sense, the clean POVMs would be “perfect,” since they would not have any

We derive the optimal $N\ensuremath{\rightarrow}M$ phase-covariant quantum cloning for equatorial states in dimension $d$ with $M=kd+N$, $k$ integer. The cloning maps are optimal for both global and single-qudit fidelity. The map is achieved by an ``economical'' cloning machine, which works without ancilla.

We perform an information-theoretical analysis of quantum measurement processes and obtain the global information balance in quantum measurements, in the form of a closed chain equation for quantum mutual entropies. Our balance provides a tight and general entropic information-disturbance trade-off, and explains the physical mechanism underlying it. Finally, the single-outcome case, that is, the case of measurements with posts election, is briefly discussed.

The crucial feature of a memoryless stochastic process is that any information about its state can only decrease as the system evolves. Here we show that such a decrease of information is equivalent to the underlying stochastic evolution being divisible. The main result, which holds independently of the model of the microscopic interaction and is valid for both classical and quantum stochastic processes, relies on a quantum version of the so-called Blackwell-Sherman-Stein theorem in classical st

Measurement incompatibility describes two or more quantum measurements whose expected joint outcome on a given system cannot be defined. This purely nonclassical phenomenon provides a necessary ingredient in many quantum information tasks such as violating a Bell inequality or nonlocally steering part of an entangled state. In this Letter, we characterize incompatibility in terms of programmable measurement devices and the general notion of quantum programmability. This refers to the temporal fr

Winter's measurement compression theorem stands as one of the most penetrating insights of quantum information theory (QIT). In addition to making an original and profound statement about measurement in quantum theory, it also underlies several other general protocols in QIT. In this paper, we provide a full review of Winter's measurement compression theorem, detailing the information processing task, giving examples for understanding it, reviewing Winter's achievability proof, and detailing a n

We show that for qubits and qutrits it is always possible to perfectly recover quantum coherence by performing a measurement only on the environment, whereas for dimension d >3 there are situations where recovery is impossible, even with complete access to the environment. For qubits, the minimal amount of classical information to be extracted from the environment equals the entropy exchange.

We obtain the general formula for the optimal rate at which singlets can be distilled from any given noisy and arbitrarily correlated entanglement resource by means of local operations and classical communication (LOCC). Our formula, obtained by employing the quantum information spectrum method, reduces to that derived by Devetak and Winter [Proc. R. Soc. London, Ser. A 461, 207 (2005)], in the special case of an independent and identically distributed resource. The proofs rely on a one-shot ver

There are several inequalities in physics which limit how well we can process physical systems to achieve some intended goal, including the second law of thermodynamics, entropy bounds in quantum information theory, and the uncertainty principle of quantum mechanics. Recent results provide physically meaningful enhancements of these limiting statements, determining how well one can attempt to reverse an irreversible process. In this paper, we apply and extend these results to give strong enhance

The theory of majorization and its variants, including thermomajorization, have been found to play a central role in the formulation of many physical resource theories, ranging from entanglement theory to quantum thermodynamics. Here we formulate the framework of quantum relative Lorenz curves, and show how it is able to unify majorization, thermomajorization, and their noncommutative analogs. In doing so, we define the family of Hilbert $\ensuremath{\alpha}$ divergences and show how it relates