Conservation laws and the foundations of quantum mechanics.

In a recent paper, [Y. Aharonov, S. Popescu, D. Rohrlich, Proc. Natl. Acad. Sci. U.S.A.118 e1921529118 (2021)], it was argued that while the standard definition of conservation laws in quantum mechanics, which is of a statistical character, is perfectly valid, it misses essential features of nature and it can and must be revisited to address the issue of conservation/nonconservation in individual cases. Specifically, in the above paper, an experiment was presented in which it can be proven that in some individual cases, energy is not conserved, despite being conserved statistically. It was felt however that this is worrisome and that something must be wrong if there are individual instances in which conservation does not hold, even though this is not required by the standard conservation law. Here, we revisit that experiment and show that although its results are correct, there is a way to circumvent them and ensure individual case conservation in that situation. The solution is however quite unusual, challenging one of the basic assumptions of quantum mechanics, namely that any quantum state can be prepared, and it involves a time-holistic, double nonconservation effect. Our results bring light on the role of the preparation stage of the initial state of a particle and on the interplay of conservation laws and frames of reference. We also conjecture that when such a full analysis of any conservation experiment is performed, conservation is obeyed in every individual case.

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. Here we show that something far more subtle is taking place: It is not necessary for the particle to enter the region where the controlling action takes place; it is enough for the controlled property of the particle, (i.e., the property that is being controlled by actions in the control region), to enter that region. The presence of the controlled property, without the particle itself, is possible via a quantum Cheshire Cat type effect in which a property can be disembodied from the particle that possesses it. At the same time, we generalize the quantum Cheshire Cat effect to dynamical settings, in which the property that is "disembodied" from the particle possessing it propagates in space, and leads to a flux of "disembodied" conserved quantities.

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. These results also play a key role in the quantum thermodynamics of noncommuting conserved quantities.

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. We consider the triangle network with binary outputs, and derive strong constraints on correlations even though the parties receive no input, i.e., each party performs a fixed measurement. We show that some of these constraints are tight, by constructing explicit local models (i.e. where sources distribute classical variables) that can saturate them. However, we also observe that other constraints can apparently not be saturated by local models, which opens the possibility of having nonlocal (but non-signaling) correlations in the triangle network with binary outputs.

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. Indeed, the reference system is composed of the same types of subsystems as the original system and is finite for any desired accuracy. In addition, the interaction with the reference frame can be broken down into two-body terms coupling the system to one of the reference frame subsystems at a time. We apply this construction to quantum thermodynamic set-ups with multiple, possibly non-commuting conserved quantities, which allows for the definition of explicit batteries in such cases.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'.

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. Each conserved quantity, which, importantly, need not commute with the rest, can be extracted and stored in its own battery. Unlike the standard case, in which the amount of extractable energy is constrained, here there is no limit on how much of any individual conserved quantity can be extracted. However, other conserved quantities must be supplied, and the second law constrains the combination of extractable quantities and the trade-offs between them. We present explicit protocols that allow us to perform arbitrarily good trade-offs and extract arbitrarily good combinations of conserved quantities from individual quantum systems.

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. Our results shed new light on the very notions of separability and correlations in quantum mechanics and on the nature of interactions. It also presents a new role for entanglement, complementary to the usual one. Finally, interferometric experiments that illustrate our effects are proposed.

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. Our results apply to any quantum system in an arbitrary initial state, in particular including non-equilibrium situations. The optimal protocol is essentially reversible, similar to classical Carnot cycles, and indeed, we show that it can be used to construct a quantum Carnot engine.

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. Moving away from the Carnot regime, we show that entanglement can enhance cooling and energy transport. Hence, a truly quantum refrigerator can outperform a classical one. Furthermore, the amount of entanglement alone quantifies the enhancement in cooling.

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. We provide efficient algorithms to characterize such limitations and, in case the target is a two-level quantum system, we quantify them exactly. Our Letter, thus, identifies the boundaries between what is possible or impossible to measure, i.e., between what we can see or not, when energy conservation is at stake.

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. Here, we report on a quantum delayed-choice experiment in which both particle and wave behaviors are investigated simultaneously. The genuinely quantum nature of the photon's behavior is certified via nonlocality, which here replaces the delayed choice of the observer in the original experiment. We observed strong nonlocal correlations, which show that the photon must simultaneously behave both as a particle and as a wave.

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. We demonstrate these claims by studying the smallest thermal machines. We show further that this perspective provides a powerful way to view thermodynamics, by analyzing a number of phenomena. This includes approaching Carnot efficiency (where we find that all machines do so essentially by becoming equivalent to the smallest thermal machines), entropy production in irreversible machines, and a way to view work in terms of negative temperature and population inversion. Moreover we introduce the idea of "genuine" thermal machines and are led to considering the concept of "strength" of work.

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. Furthermore, we also argue that, even if entanglement does exist, it is purely incidental and seems to play no essential role for the transport efficiency. We emphasize that our paper is not a proof that entanglement does not exist in light-harvesting complexes-this would require a knowledge of the system and its parameters well beyond the state of the art. Rather, we present a counter-example to the recent claims of entanglement, showing that the arguments, as they stand at the moment, are not sufficiently justified and hence cannot be taken as a proof for the existence of entanglement, let alone of its essential role, in the excitation transport.

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. As a building block, the present simple mechanism supports the perspective that entanglement can exist also in systems which are exposed to a hot environment and to high levels of decoherence, which we expect, e.g., for biological systems. Our results also suggest that entanglement plays a role in the heat exchange between molecular machines and environment. Experimental simulation of our model with trapped ions is within reach of the current state-of-the-art quantum technologies.

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., not requiring external sources of work) consisting of only a small number of qubits and/or qutrits. We present three different models, consisting of two qubits, a qubit and a qutrit with nearest-neighbor interactions, and a single qutrit, respectively. We then investigate the fundamental limits to their performance; in particular, we show that it is possible to cool towards absolute zero.

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. We prove, with virtually full generality, that reaching equilibrium is a universal property of quantum systems: almost any subsystem in interaction with a large enough bath will reach an equilibrium state and remain close to it for almost all times. We also prove several general results about other aspects of thermalization besides equilibration, for example, that the equilibrium state does not depend on the detailed microstate of the bath.

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. In particular, we present the coupler, a device enabling nonlocality swapping, the analogue of quantum entanglement swapping, as well as teleportation. Remarkably, part of the boundary between quantum and post-quantum correlations emerges in our study.