Conservation laws and the foundations of quantum mechanics.

In a recent paper, [Y. Aharonov, S. Popescu, D.

A dynamical quantum Cheshire Cat effect and implications for counterfactual communication.

Here we report a type of dynamic effect that is at the core of the so called "counterfactual computation" and especially "counterfactual communication" quantum effects that have generated a lot of interest recently. The basic feature of these counterfactual setups is the fact that particles seem to be affected by actions that take place in locations where they never (more precisely, only with infinitesimally small probability) enter. Specifically, the communication/computation takes place without the quantum particles that are supposed to be the information carriers travelling through the communication channel or entering the logic gates of the computer.

On conservation laws in quantum mechanics.

We raise fundamental questions about the very meaning of conservation laws in quantum mechanics, and we argue that the standard way of defining conservation laws, while perfectly valid as far as it goes, misses essential features of nature and has to be revisited and extended.

Reference Frames Which Separately Store Noncommuting Conserved Quantities.

Even in the presence of conservation laws, one can perform arbitrary transformations on a system if given access to a suitable reference frame, since conserved quantities may be exchanged between the system and the frame. Here we explore whether these quantities can be separated into different parts of the reference frame, with each part acting as a "battery" for a distinct quantity. For systems composed of spin-1/2 particles, we show that the components of angular momentum S_{x}, S_{y}, and S_{z} (noncommuting conserved quantities) may be separated in this way, and also provide several extensions of this result.

Constraints on nonlocality in networks from no-signaling and independence.

The possibility of Bell inequality violations in quantum theory had a profound impact on our understanding of the correlations that can be shared by distant parties. Generalizing the concept of Bell nonlocality to networks leads to novel forms of correlations, the characterization of which is, however, challenging. Here, we investigate constraints on correlations in networks under the natural assumptions of no-signaling and independence of the sources.

Quantum reference frames and their applications to thermodynamics.

We construct a quantum reference frame, which can be used to approximately implement arbitrary unitary transformations on a system in the presence of any number of extensive conserved quantities, by absorbing any back action provided by the conservation laws. Thus, the reference frame at the same time acts as a battery for the conserved quantities. Our construction features a physically intuitive, clear and implementation-friendly realization.

Thermodynamics of quantum systems with multiple conserved quantities.

Recently, there has been much progress in understanding the thermodynamics of quantum systems, even for small individual systems. Most of this work has focused on the standard case where energy is the only conserved quantity. Here we consider a generalization of this work to deal with multiple conserved quantities.

Quantum violation of the pigeonhole principle and the nature of quantum correlations.

The pigeonhole principle: "If you put three pigeons in two pigeonholes, at least two of the pigeons end up in the same hole," is an obvious yet fundamental principle of nature as it captures the very essence of counting. Here however we show that in quantum mechanics this is not true! We find instances when three quantum particles are put in two boxes, yet no two particles are in the same box. Furthermore, we show that the above "quantum pigeonhole principle" is only one of a host of related quantum effects, and points to a very interesting structure of quantum mechanics that was hitherto unnoticed.

Multiple Observers Can Share the Nonlocality of Half of an Entangled Pair by Using Optimal Weak Measurements.

We investigate the trade-off between information gain and disturbance for von Neumann measurements on spin-1/2 particles, and derive the measurement pointer state that saturates this trade-off, which turns out to be highly unusual. We apply this result to the question of whether the nonlocality of a single particle from an entangled pair can be shared among multiple observers that act sequentially and independently of each other, and show that an arbitrarily long sequence of such observers can all violate the Clauser-Horne-Shimony-Holt-Bell inequality.

Work extraction and thermodynamics for individual quantum systems.

Thermodynamics is traditionally concerned with systems comprised of a large number of particles. Here we present a framework for extending thermodynamics to individual quantum systems, including explicitly a thermal bath and work-storage device (essentially a 'weight' that can be raised or lowered). We prove that the second law of thermodynamics holds in our framework, and gives a simple protocol to extract the optimal amount of work from the system, equal to its change in free energy.

How energy conservation limits our measurements.

Observations in quantum mechanics are subject to complex restrictions arising from the principle of energy conservation. Determining such restrictions, however, has been so far an elusive task, and only partial results are known. In this Letter, we discuss how constraints on the energy spectrum of a measurement device translate into limitations on the measurements which we can effect on a target system with a nonconstant energy operator.

Entanglement enhances cooling in microscopic quantum refrigerators.

Small self-contained quantum thermal machines function without external source of work or control but using only incoherent interactions with thermal baths. Here we investigate the role of entanglement in a small self-contained quantum refrigerator. We first show that entanglement is detrimental as far as efficiency is concerned-fridges operating at efficiencies close to the Carnot limit do not feature any entanglement.

A quantum delayed-choice experiment.

Quantum systems exhibit particle- or wavelike behavior depending on the experimental apparatus they are confronted by. This wave-particle duality is at the heart of quantum mechanics. Its paradoxical nature is best captured in the delayed-choice thought experiment, in which a photon is forced to choose a behavior before the observer decides what to measure.

Virtual qubits, virtual temperatures, and the foundations of thermodynamics.

We argue that thermal machines can be understood from the perspective of "virtual qubits" at "virtual temperatures": The relevant way to view the two heat baths which drive a thermal machine is as a composite system. Virtual qubits are two-level subsystems of this composite, and their virtual temperatures can take on any value, positive or negative. Thermal machines act upon an external system by placing it in thermal contact with a well-selected range of virtual qubits and temperatures.

A critical view on transport and entanglement in models of photosynthesis.

We revisit critically the recent claims, inspired by quantum optics and quantum information, that there is entanglement in the biological pigment-protein complexes, and that it is responsible for the high transport efficiency. While unexpectedly long coherence times were experimentally demonstrated, the existence of entanglement is, at the moment, a purely theoretical conjecture; it is this conjecture that we analyse. As demonstrated by a toy model, a similar transport phenomenology can be obtained without generating entanglement.

How small can thermal machines be? The smallest possible refrigerator.

We investigate the fundamental dimensional limits to thermodynamic machines. In particular, we show that it is possible to construct self-contained refrigerators (i.e.

Dynamic entanglement in oscillating molecules and potential biological implications.

We demonstrate that entanglement can persistently recur in an oscillating two-spin molecule that is coupled to a hot and noisy environment, in which no static entanglement can survive. The system represents a nonequilibrium quantum system which, driven through the oscillatory motion, is prevented from reaching its (separable) thermal equilibrium state. Environmental noise, together with the driven motion, plays a constructive role by periodically resetting the system, even though it will destroy entanglement as usual.

Quantum mechanical evolution towards thermal equilibrium.

The circumstances under which a system reaches thermal equilibrium, and how to derive this from basic dynamical laws, has been a major question from the very beginning of thermodynamics and statistical mechanics. Despite considerable progress, it remains an open problem. Motivated by this issue, we address the more general question of equilibration.

Emergence of quantum correlations from nonlocality swapping.

By studying generalized nonsignaling theories, the hope is to find out what makes quantum mechanics so special. In the present Letter, we revisit the paradigmatic model of nonsignaling boxes and introduce the concept of a genuine box. This will allow us to present the first generalized nonsignaling model featuring quantumlike dynamics.

Knill-laflamme-milburn linear optics quantum computation as a measurement-based computation.

We show that the Knill Lafllame Milburn method of quantum computation with linear optics gates can be interpreted as a one-way, measurement-based quantum computation of the type introduced by Briegel and Raussendorf. We also show that the permanent state of n n-dimensional systems is a universal state for quantum computation.

Quantum nonlocality and beyond: limits from nonlocal computation.

We address the problem of "nonlocal computation," in which separated parties must compute a function without any individual learning anything about the inputs. Surprisingly, entanglement provides no benefit over local classical strategies for such tasks, yet stronger nonlocal correlations allow perfect success. This provides intriguing insights into the limits of quantum information processing, the nature of quantum nonlocality, and the differences between quantum and stronger-than-quantum nonlocal correlations.

Knill-Laflamme-Milburn quantum computation with bosonic atoms.

A Knill-Laflamme-Milburn (KLM) type quantum computation with bosonic neutral atoms or bosonic ions is suggested. Crucially, as opposite to other quantum computation schemes involving atoms (ions), no controlled interactions between atoms (ions) involving their internal levels are required. Versus photonic KLM computation, this scheme has the advantage that single-atom (ion) sources are more natural than single-photon sources, and single-atom (ion) detectors are far more efficient than single-photon ones.

Entanglement of superpositions.

Given a bipartite quantum state (in arbitrary dimension) and a decomposition of it as a superposition of two others, we find bounds on the entanglement of the superposition state in terms of the entanglement of the states being superposed. In the case that the two states being superposed are biorthogonal, the answer is simple, and, for example, the entanglement of the superposition cannot be more than one ebit more than the average of the entanglement of the two states being superposed. However, for more general states, the situation is very different.

Lower bound on the number of Toffoli gates in a classical reversible circuit through quantum information concepts.

The question of finding a lower bound on the number of Toffoli gates in a classical reversible circuit is addressed. A method based on quantum information concepts is proposed. The method involves solely concepts from quantum information--there is no need for an actual physical quantum computer.