Lluis Masanes

From Bell's Theorem to Secure Quantum Key Distribution

The first step in any quantum key distribution (QKD) protocol consists of sequences of measurements that produce correlated classical data. We show that these correlation data must violate some Bell inequality in order to contain distillable secrecy, if not they could be produced by quantum measurements performed on a separable state of larger dimension. We introduce a new QKD protocol and prove its security against any individual attack by an adversary only limited by the no-signaling condition.

A Derivation of quantum theory from physical requirements

Quantum theory (QT) is usually formulated in terms of abstract mathematical postulates involving Hilbert spaces, state vectors and unitary operators. In this paper, we show that the full formalism of QT can instead be derived from five simple physical requirements, based on elementary assumptions regarding preparations, transformations and measurements. This is very similar to the usual formulation of special relativity, where two simple physical requirements—the principles of relativity and light speed invariance—are used to derive the mathematical structure of Minkowski space–time. Our derivation provides insights into the physical origin of the structure of quantum state spaces (including a group-theoretic explanation of the Bloch ball and its three dimensionality) and suggests several natural possibilities to construct consistent modifications of QT.

Secure device-independent quantum key distribution with causally independent measurement devices

Device-independent quantum key distribution (QKD) aims to provide key distribution schemes, the security of which is based on the laws of quantum physics, but which does not require any assumptions about the internal working of the devices used in the protocol. This strong form of security is possible only when using correlations that violate a Bell inequality. Here, we provide a general security proof for a large class of protocols in a model in which the raw key is generated by independent measurements. This independence condition may be justifiable in several implementations and is necessarily satisfied when the raw key is generated by N separate pairs of devices. Our work shows that device-independent QKD is possible with key rates comparable to those of standard schemes.

Universally composable privacy amplification from causality constraints.

We consider schemes for secret key distribution which use as a resource correlations that violate Bell inequalities. We provide the first security proof for such schemes, according to the strongest notion of security, the so-called universally composable security. Our security proof does not rely on the validity of quantum mechanics, it solely relies on the impossibility of arbitrarily fast signaling between separate physical systems. This allows for secret communication in situations where the participants distrust their quantum devices.

All bipartite entangled states are useful for information processing.

The question of whether all entangled states can be used as a nonclassical resource has remained open so far. Here we provide a conclusive answer to this problem for the case of systems shared by two parties. We show that any entangled state can enhance the teleportation power of some other state. This holds even if the state is bound entangled.

Full randomness from arbitrarily deterministic events

Do completely unpredictable events exist? Classical physics excludes fundamental randomness. Although quantum theory makes probabilistic predictions, this does not imply that nature is random, as randomness should be certified without relying on the complete structure of the theory being used. Bell tests approach the question from this perspective. However, they require prior perfect randomness, falling into a circular reasoning. A Bell test that generates perfect random bits from bits possessing high-but less than perfect-randomness has recently been obtained. Yet, the main question remained open: does any initial randomness suffice to certify perfect randomness? Here we show that this is indeed the case. We provide a Bell test that uses arbitrarily imperfect random bits to produce bits that are, under the non-signalling principle assumption, perfectly random. This provides the first protocol attaining full randomness amplification. Our results have strong implications onto the debate of whether there exist events that are fully random.

Existence of an information unit as a postulate of quantum theory

Significance Despite the enormous success of quantum theory, its significance and meaning are still being debated. In particular, the standard postulates of quantum theory are abstract mathematical statements in terms of complex vectors, self-adjoint operators, etc., and as such they lack a clear physical interpretation. For this reason, it is difficult to assess what they say about the structure of the physical world. In this article, we prove that quantum theory can be formulated through four very simple postulates, each having a direct physical and intuitive meaning. Also, our postulates unveil some connections between physics and information that remain hidden in the standard postulates, thus supporting Wheeler’s hypothesis “it from bit.” Does information play a significant role in the foundations of physics? Information is the abstraction that allows us to refer to the states of systems when we choose to ignore the systems themselves. This is only possible in very particular frameworks, like in classical or quantum theory, or more generally, whenever there exists an information unit such that the state of any system can be reversibly encoded in a sufficient number of such units. In this work, we show how the abstract formalism of quantum theory can be deduced solely from the existence of an information unit with suitable properties, together with two further natural assumptions: the continuity and reversibility of dynamics, and the possibility of characterizing the state of a composite system by local measurements. This constitutes a set of postulates for quantum theory with a simple and direct physical meaning, like the ones of special relativity or thermodynamics, and it articulates a strong connection between physics and information.

Storing quantum dynamics in quantum states: A stochastic programmable gate

We show how to encode quantum dynamics in the state of a quantum system, in such a way that the system can be used to stochastically perform, at a later time, the stored transformation on some other quantum system. The probability of failure decreases exponentially with the number of qubits that store the transformation. We discuss optimality of this scheme, whose applications include viability of a (stochastic) programmable quantum gate and the teleportation of quantum transformations using entanglement and unidirectional classical communication.

Asymptotic Violation of Bell Inequalities and Distillability

A multipartite quantum state violates a Bell inequality asymptotically if, after jointly processing by general local operations an arbitrarily large number of copies of it, the result violates the inequality. In the bipartite case we show that asymptotic violation of the Clauser-Horne-Shimony-Holt inequality is equivalent to distillability. Hence, bound entangled states do not violate it. In the multipartite case we consider the complete set of full-correlation Bell inequalities with two dichotomic observables per site. We show that asymptotic violation of any of these inequalities by a multipartite state implies that pure-state entanglement can be distilled from it, although the corresponding distillation protocol may require that some of the parties join into several groups. We also obtain the extreme points of the set of distributions generated by measuring N quantum systems with two dichotomic observables per site.

Thermalization and Canonical Typicality in Translation-Invariant Quantum Lattice Systems

It has previously been suggested that small subsystems of closed quantum systems thermalize under some assumptions; however, this has been rigorously shown so far only for systems with very weak interaction between subsystems. In this work, we give rigorous analytic results on thermalization for translation-invariant quantum lattice systems with finite-range interaction of arbitrary strength, in all cases where there is a unique equilibrium state at the corresponding temperature. We clarify the physical picture by showing that subsystems relax towards the reduction of the global Gibbs state, not the local Gibbs state, if the initial state has close to maximal population entropy and certain non-degeneracy conditions on the spectrumare satisfied.Moreover,we showthat almost all pure states with support on a small energy window are locally thermal in the sense of canonical typicality. We derive our results from a statement on equivalence of ensembles, generalizing earlier results by Lima, and give numerical and analytic finite size bounds, relating the Ising model to the finite de Finetti theorem. Furthermore, we prove that global energy eigenstates are locally close to diagonal in the local energy eigenbasis, which constitutes a part of the eigenstate thermalization hypothesis that is valid regardless of the integrability of the model.