Seminars

Abstract: The amplification of light in quantum theory has a long history, with research devoted mostly to the linear (i.e. one-photon) regime due to its simplicity [1]. However, nonlinear amplification has also received some interest since the 1960s. One obvious generalisation of linear/one-photon amplification is to allow for two photons (and only two) to be emitted or lost during amplification [2,3]. It was shown in the early days of amplifier research that such a two-photon device contained an operating regime where one-photon amplification was seemingly possible despite being prohibited at the outset by the model [2]. This apparent paradox has remained unresolved till now [4].

In this talk I will show how this apparent contradiction can be resolved and what the resolution implies for the physics of linear amplifiers. In particular, we will see how additive noise and multiplicative noise in a linear amplifier can be understood in terms of elementary atom-photon interactions. This understanding of amplifier noise also sheds light on the status of the parametric amplifier where it has been claimed to be a universal model for any phase-preserving linear amplifier [1,4].

I will try to explain my results with minimal background knowledge in amplifiers and theoretical techniques with emphasis on the physics and concepts.

[1] C. Caves+, Quantum limits on phase-preserving linear amplifiers, Physical Review A, 2012.
[2] P. Lambropoulos, Quantum statistics of a two-photon amplifier, Physical Review, 1967.
[3] K. J. McNeil and D. F. Walls, A master equation approach to nonlinear optics, Journal of Physics A, 1974.
[4] A. Chia+, Phase-preserving linear amplifiers not simulable by the parametric amplifier, Physical Review Letters, 2020.

While the standard formulation of quantum theory relies on a fixed background causal structure, one can consider a more general framework – based on quantum theory – where the causal structure is indefinite (the “process matrix formalism”). Interestingly, the tools introduced to identify causal indefiniteness – causal non-separability and causal inequalities – have been developed by analogy with quantum entanglement and Bell inequalities. An explicit example of a physical process with indefinite causal structure is the so-called ‘quantum switch’.
In this work, we take a bottom-up approach. We identify two new types of circuits that naturally generalise the fixed-order case which we fully characterise. We first introduce “quantum circuits with classical control of causal order ”, in which the order of operations is still well-defined, but not necessarily fixed in advance: it can in particular be established dynamically, in a classically-controlled manner, as the circuit is being used. We then consider “ quantum circuits with quantum control of causal order ”, in which the order of operations is controlled coherently. The latter encompasses all known examples of physically realisable processes with indefinite causal order, including the celebrated quantum switch. Interestingly, it also contains new examples arising from the combination of dynamical and coherent control of causal order, and we detail explicitly one such process. Nevertheless, we show that quantum circuits with quantum control of causal order can only generate “causal” correlations, compatible with a well-defined causal order. We furthermore extend our considerations to probabilistic circuits that produce also classical outcomes, and we demonstrate by an example how the characterisations derived in this work allow us to identify new advantages for quantum information processing tasks that could be demonstrated in practice.

We discuss schemes to certify local quantum systems via self-testing and dimension witnessing. This work leverages the graph-theoretic framework for contextuality introduced by Cabello, Severini, and Winter, combined with tools from combinatorial optimisation that guarantee the unicity of optimal solutions. We first show that the celebrated Klyachko-Can-Binicioglu-Shumovsky inequality and its generalisation to contextuality scenarios with odd cycle compatibility relations admit robust self-testing. We extend this robust self-testing result to the class of contextuality scenarios with odd anti-cycle compatibility structure which enables us to self-test arbitrary high dimensional quantum systems. Dimension witnessing is another tool for device certification where the goal is to certify the underlying dimensions of the quantum systems just from the measurement statistics. We present the concepts and tools needed for graph-theoretic quantum dimension witnessing and illustrate their use by identifying quantum dimension witnesses, including a family that can certify arbitrarily high quantum dimensions with few events.

Bell’s theorem is supposed to exclude all local hidden-variable models of quantum correlations. However, an explicit counterexample shows that a new class of local realistic models, based on generalized arithmetic and calculus, can exactly reconstruct rotationally symmetric quantum probabilities typical of two-electron singlet states. Observable probabilities are consistent with the usual arithmetic employed by macroscopic observers, but counterfactual aspects of Bell’s theorem are sensitive to the choice of hidden-variable arithmetic and calculus. The model is classical in the sense of Einstein, Podolsky, Rosen, and Bell: elements of reality exist and probabilities are modeled by integrals of hidden-variable probability densities. Probability densities have a Clauser-Horne product form typical of local realistic theories. However, neither the product nor the integral nor the representation of rotations are the usual ones. The integral has all the standard properties but only with respect to the arithmetic that defines the product. Certain formal transformations of integral expressions one finds in the usual proofs à la Bell do not work, so standard Bell-type inequalities cannot be proved. The system we consider is deterministic, local-realistic, rotationally invariant, observers have free will, detectors are perfect, so is free of all the canonical loopholes discussed in the literature.

Quantum Darwinism posits that the emergence of a classical reality relies on the spreading of classical information from a quantum system to many parts of its environment. But what are the essential physical principles of quantum theory that make this mechanism possible? We address this question by formulating the simplest instance of Darwinism — CNOT-like fan-out interactions — in a class of probabilistic theories that contain classical and quantum theory as special cases. We determine necessary and sufficient conditions for any theory to admit such interactions. We find that every non-classical theory that admits this spreading of classical information must have both entangled states and entangled measurements. Furthermore, we show that Spekkens’ toy theory admits this form of Darwinism, and so do all probabilistic theories that satisfy principles like strong symmetry, or contain a certain type of decoherence processes. Our result suggests the counterintuitive general principle that in the presence of local non-classicality, a classical world can only emerge if this non-classicality can be “amplified” to a form of entanglement.

Nonlocality, as demonstrated by the violation of Bell inequalities, enables device-independent cryptographic tasks that do not require users to trust their apparatus. In this presentation, we consider devices whose inputs are spatiotemporal degrees of freedom, e.g. orientations or time durations. Without assuming the validity of quantum theory, we prove that the devices’ statistical response must respect their input’s symmetries, with profound foundational and technological implications. We exactly characterize the bipartite binary quantum correlations in terms of local symmetries, indicating a fundamental relation between spacetime and quantum theory. For Bell experiments characterized by two input angles, we show that the correlations are accounted for by a local hidden variable model if they contain enough noise, but conversely must be nonlocal if they are pure enough. This allows us to construct a “Bell witness” that certifies nonlocality with fewer measurements than possible without such spatiotemporal symmetries, suggesting a new class of semi-device-independent protocols for quantum technologies.

With the study of ever decreasing systems, it’s paramount to understand thermodynamic phenomena in ultra-small scales, where quantum phenomena live. This gave origin to the flourishing research field known as quantum thermodynamics. One of its main branches, which deals with quantum systems undergoing thermodynamic cycles, is called quantum heat engines (QHEs). These are assembled to convert one kind of energy into another, namely heat into work, in the quantum domain. The idea of converting heat into work has been intensively explored since the First Industrial Revolution, but it gains new direction with the many possibilities brought by quantum theory resources, such as coherence and entanglement. For optimizing the output power of these QHEs, one must consider finite-time operation. In this seminar, I will present a new model of finite-time QHEs. By means of using collisional models, a cyclic sequence of pure heat and pure work strokes are applied to a generic quantum chain. This gives rise to a stroboscopic evolution of the state of the quantum chain, which presents a transient regime as well as a limit cycle. Once reached the limit cycle, the results show that the heat exchanged with the heat baths depends solely on the boundary sites of the quantum chain. The model is proved useful for the optimization of the output power of stroke-based QHEs both analytically and numerically. One curious feature of this framework is that, for a given family of models containing a specific kind of internal interactions, there is a universal efficiency value, the Otto efficiency, which remains the same for any cycle period.

We present a framework in which unique games are represented in the form of edge-labelings of graphs. We define an equivalence relation which preserves both classical and quantum values of games. We also show how the classical value of the game depends on the properties of the cycles within the labeled graph. In particular, we relate the problem of computing the classical value of single-party anti-correlation XOR games to finding the edge bipartization number of a graph, and connect the computation of the classical value of XOR-d games to the identification of specific cycles in the graph. In some specific cases this approach allows us to calculate the classical values of games.

A standardly adopted notion of classicality is the following: a system is deemed classical if its set of states is a simplex. Also, it is traditionally excluded that a classical theory may admit of entangled states. This is of course the case for classical theory (CT). An operational probabilistic theory where all systems are classical, and all pure states of composite systems are entangled, will be presented. The theory, called bilocal classical theory (BCT), is endowed with a rule for composing an arbitrary number of systems, and with a nontrivial set of transformations. Moreover, BCT is proved to be well-posed using an exhaustive procedure to construct generic theories, along with a sufficient set of conditions to verify their consistency. Hence, BCT demonstrates that the presence of entanglement is independent of the existence of incompatible measurements. Some phenomena occurring in the theory are compatible with CT or quantum theory (QT)—such as the existence of a universal processor, cloning, entanglement swapping, dense coding, additivity of classical capacities—while others contradict both CT and QT, including: non-monogamous entanglement and hypersignaling. The theory is causal and satisfies the no-restriction hypothesis. At the same time, it violates a number of information-theoretic principles enjoyed by QT, most notably: local discriminability, purity of parallel composition of states, and purification. Some open problems raised by BCT will be pointed out. In particular, a no-go conjecture for the existence of a local-realistic ontological model associated with BCT will be formulated.

REFERENCES
—Classical theories with entanglement. Giacomo Mauro D’Ariano, Marco Erba, and Paolo Perinotti, Phys. Rev. A 101, 042118
—Classicality without local discriminability: Decoupling entanglement and complementarity. Giacomo Mauro D’Ariano, Marco Erba, and Paolo Perinotti, Phys. Rev. A 102, 052216

Because of the approaching deadline of 15/12/2020 for many NCN grant applications, the Director, himself a member of NCN and a co-author in many of its projects, will share his expertise in writing them.