For some time after Bell showed that entanglement had experimentally testable consequences, it was still viewed as a qualitative property, chiefly useful for establishing the validity of quantum mechanics in contrast to rival explanations. Sandu Popescu was among the first to view entanglement instead as resource to quantified, husbanded and used. In the early 1990's he devised, and later with Branca et al carried out, an early form of teleportation, "remote state preparation" in which an arbitrary quantum state, known to the sender, is exactly transmitted to a receiver using only entanglement and a two-bit classical message. In the mid 1990s he and his collaborators devised the techniques of entanglement concentration and distillation, allowing low quality entanglement to be converted into useful form, by means of local operations and classical communication (LOCC). Both these techniques and the LOCC paradigm become central to the burgeoning fields of quantum error correction and fault tolerance, as well as to the theory of quantum channels and security proofs for quantum cryptography. His early discovery, with Lo, that unlike entanglement concentration, entanglement dilution requires a significant (O(sqrt(N)) amount of classical communication led to understanding the impossibility of coherently destroying entanglement.

Since his grad student days under Yakir Aharonov, Popescu has been attracted to the most counterintuitive manifestations of quantum mechanics, hoping that by understanding these the paradoxes could be dispelled, the surprises would end, and the subject would begin to seem as natural and harmonious as, say, classical mechanics or special relativity. Considerable progress has been made, by Popescu and others, toward this goal of what might be called a mature quantum intuition, although the surprises have been numerous and multifarious. Among them was Popescu's discovery, with Gisin, that two antiparallel spins convey more information about their direction than two parallel spins. The physical inequivalence of these two seemingly equivalent forms of information reflects the antiunitarity of spin inversion and highlights the subtlety of boundary between abstract mathematical information, even quantum information, and its physical embodiment. More recently, with Collins et al, Popescu introduced "quantum gloves"---pairs of rotationally invariant quantum states that convey complete information about the chirality of a 3-dimensional reference frame but no information about its orientation.

An early and continuing hope of quantum foundations researchers has been to derive the mathematical formalism of quantum mechanics from a few simple physical principles such as the impossibility of cloning, or faster-than-light communication. One of these hopes was dashed in an interesting way by Popescu and Rohrlich's discovery of stronger-than quantum, but still non-signaling correlations. Much research ensued on these so-called nonlocal PR boxes, and non-signaling correlations in general. Despite their hypothetical nature, they have practical applications, for example allowing the security of quantum cryptography to be proved without assuming the validity of quantum mechanics, based solely on the extent of violation of Bell inequalities. Popescu used entanglement theory to answer a purely local question about classical computation: how many 3-bit reversible gates (Toffoli gates) are needed to implement a given reversible classical function. The need for such gates had traditionally been explained by saying that since one- and two-bit reversible gates are all linear, 3-bit gates are needed to provide nonlinearity; but there was no evident way to quantify the nonlinearity. However, by mapping the reversible classical function onto a manipulation of separated pairs of qubits, Popescu, Groisman and Massar showed that the number of Toffolis in the local classical computation is given by the amount of initial entanglement needed to perform the corresponding bi-local quantum computation by local operations and classical communication, a well-studied problem.

A recent thrust of Popescu's work, also recognized by this Bell Prize, has been the application of entanglement and quantum theory to thermodynamics. This includes the elegant derivation, with Short and Winter, of statistical mechanical ensembles, traditionally explained as averages over time or initial conditions, instead as snapshots (partial traces, mathematically speaking) of an overwhelmingly likely entangled pure state between a system and its environment. Quite recently Popescu and collaborators have applied quantum techniques to the oldest part of thermodynamics, the theory of refrigerators and heat engines, showing that even the smallest quantum engines can attain the efficiency limits derived nearly two centuries ago by Sadi Carnot for macroscopic classical engines.

### Citations to the work for which the prize is awarded

Barrett, Linden, Massar, Pironio, Popescu, and Roberts, Non-local correlations as an information theoretic resource, Phys. Rev. A 71, 022101 (2005)

Popescu, Short, and Winter, Entanglement and the Foundations of Statistical Mechanics, Nature Physics 2, 754 (2006).

Linden, Popescu, Short, and Winter, Quantum nonlocality and beyond: Limits from nonlocal computation, Phys. Rev. Lett. 99, 180502 (2007)

Linden, Popescu, Short, and Winter, Quantum mechanical evolution towards thermal equilibrium, Phys. Rev E 79, 061103 (2009)

Linden, Popescu, and Skrzypczyk, How small can thermal machines be? The smallest possible refrigerator Phys. Rev. Lett.105, 130401 (2010).

### Further related reading

Popescu & Rohrlich, Quantum non-locality as an axiom, Found. Phys. 24, 379 (1994)

Boschi, Branca, De Martini, Hardy, and Popescu, Experimental Realization of Teleporting an Unknown Pure Quantum State via Dual Classical and Einstein-Podolsky-Rosen Channels, Phys. Rev. Lett. 80, 1121 (1998)