We present a protocol for transferring arbitrary continuous-variable quantum states into a few discrete-variable qubits and back. The protocol is deterministic and utilizes only two-mode Rabi-type interactions which are readily available in trapped-i
on and superconducting circuit platforms. The inevitable errors caused by transferring an infinite-dimensional state into a finite-dimensional register are suppressed exponentially with the number of qubits. Furthermore, the encoded states exhibit robustness against noise, such as dephasing and amplitude damping, acting on the qubits. Our protocol thus provides a powerful and flexible tool for discrete-continuous hybrid quantum systems.
Thermal machines exploit interactions with multiple heat baths to perform useful tasks, such as work production and refrigeration. In the quantum regime, tasks with no classical counterpart become possible. Here, we explore the fundamental resources
needed to generate operationally useful entanglement. We focus on the minimal setting for quantum thermal machines, namely two-qubit autonomous thermal machines that use only incoherent interactions with their environment. Considering the paradigmatic tasks of Einstein-Podolsky-Rosen steering, quantum teleportation and Bell nonlocality, we investigate the trade-off between operational nonclassicality and the resources made available to the machine. For the resources, we consider bosonic and fermionic baths, with and without populations inversion, and with and without local filtering. We provide both constructive examples and no-go results demonstrating when each of the three tasks are possible or impossible. Our results identify fundamental limitations to autonomous entanglement generation and open up a path toward producing increasingly powerful quantum correlations from thermal resources.
Gaussian quantum states of bosonic systems are an important class of states. In particular, they play a key role in quantum optics as all processes generated by Hamiltonians up to second order in the field operators (i.e. linear optics and quadrature
squeezing) preserve Gaussianity. A powerful approach to calculations and analysis of Gaussian states is using phase-space variables and symplectic transformations. The purpose of this note is to serve as a concise reference for performing phase-space calculations on Gaussian states. In particular, we list symplectic transformations for commonly used optical operations (displacements, beam splitters, squeezing), and formulae for tracing out modes, treating homodyne measurements, and computing fidelities.
Quantum computing potentially offers exponential speed-ups over classical computing for certain tasks. A central, outstanding challenge to making quantum computing practical is to achieve fault tolerance, meaning that computations of any length or si
ze can be realised in the presence of noise. The Gottesman-Kitaev-Preskill code is a promising approach towards fault-tolerant quantum computing, encoding logical qubits into grid states of harmonic oscillators. However, for the code to be fault tolerant, the quality of the grid states has to be extremely high. Approximate grid states have recently been realized experimentally, but their quality is still insufficient for fault tolerance. Current implementable protocols for generating grid states rely on measurements of ancillary qubits combined with either postselection or feed forward. Implementing such measurements take up significant time during which the states decohere, thus limiting their quality. Here we propose a measurement-free preparation protocol which deterministically prepares arbitrary logical grid states with a rectangular or hexagonal lattice. The protocol can be readily implemented in trapped-ion or superconducting-circuit platforms to generate high-quality grid states using only a few interactions, even with the noise levels found in current systems.
Quantum communication leads to strong correlations, that can outperform classical ones. Complementary to previous works in this area, we investigate correlations in prepare-and-measure scenarios assuming a bound on the information content of the quan
tum communication, rather than on its Hilbert-space dimension. Specifically, we explore the extent of classical and quantum correlations given an upper bound on the one-shot accessible information. We provide a characterisation of the set of classical correlations and show that quantum correlations are stronger than classical ones. We also show that limiting information rather than dimension leads to stronger quantum correlations. Moreover, we present device-independent tests for placing lower bounds on the information given observed correlations. Finally, we show that quantum communication carrying $log d$ bits of information is at least as strong a resource as $d$-dimensional classical communication assisted by pre-shared entanglement.
Cooperative behaviour constitutes a key aspect of both human society and non-human animal systems, but explaining how cooperation evolves represents a major scientific challenge. It is now well established that social network structure plays a centra
l role for the viability of cooperation. However, not much is known about the importance of the positions of cooperators in the networks for the evolution of cooperation. Here, we investigate how cooperation is affected by correlations between cooperativeness and individual social connectedness. Using simulation models, we find that the effect of correlation between cooperativeness and connectedness (degree) depends on the social network structure, with positive effect in standard scale-free networks and no effect in standard Poisson networks. Furthermore, when degree assortativity is increased such that individuals cluster with others of similar social connectedness, we find that bridge areas between social clusters can act as barriers to the spread of defection, leading to strong enhancement of cooperation in particular in Poisson networks. But this effect is sensitive to the presence of Trojan horses (defectors placed within cooperator clusters). The study provides new knowledge about the conditions under which cooperation may evolve and persist, and the results are also relevant to consider in regard to human cooperation experiments.
Recently, a novel framework for semi-device-independent quantum prepare-and-measure protocols has been proposed, based on the assumption of a limited distinguishability between the prepared quantum states. Here, we discuss the problem of characterizi
ng an unknown quantum measurement device in this setting. We present several methods to attack this problem. Considering the simplest scenario of two preparations with lower bounded overlap, we show that genuine 3-outcome POVMs can be certified, even in the presence of noise. Moreover, we show that the optimal POVM for performing unambiguous state discrimination can be self-tested.
Quantum theory allows for randomness generation in a device-independent setting, where no detailed description of the experimental device is required. Here we derive a general upper bound on the amount of randomness that can be generated in such a se
tting. Our bound applies to any black-box scenario, thus covering a wide range of scenarios from partially characterised to completely uncharacterised devices. Specifically, we prove that the number of random bits that can be generated is limited by the number of different input states that enter the measurement device. We show explicitly that our bound is tight in the simplest case. More generally, our work indicates that the prospects of generating a large amount of randomness by using high-dimensional (or even continuous variable) systems will be extremely challenging in practice.
The causal structure of any experiment implies restrictions on the observable correlations between measurement outcomes, which are different for experiments exploiting classical, quantum, or post-quantum resources. In the study of Bell nonlocality, t
hese differences have been explored in great detail for more and more involved causal structures. Here, we go in the opposite direction and identify the simplest causal structure which exhibits a separation between classical, quantum, and post-quantum correlations. It arises in the so-called Instrumental scenario, known from classical causal models. We derive inequalities for this scenario and show that they are closely related to well-known Bell inequalities, such as the Clauser-Horne-Shimony-Holt inequality, which enables us to easily identify their classical, quantum, and post-quantum bounds as well as strategies violating the first two. The relations that we uncover imply that the quantum or post-quantum advantages witnessed by the violation of our Instrumental inequalities are not fundamentally different from those witnessed by the violations of standard inequalities in the usual Bell scenario. However, non-classical tests in the Instrumental scenario require fewer input choices than their Bell scenario counterpart, which may have potential implications for device-independent protocols.
We study the entanglement generated in the steady state of two interacting qubits coupled to thermal reservoirs. We show that the amount of steady-state entanglement can be enhanced by the presence of a third thermal reservoir which is common to both
qubits. Specifically, we find that entanglement can be enhanced as long as the temperature of the common reservoir is below the thermalisation temperature of the qubits, whenever a single temperature can be assigned to the steady state of the qubits in the absence of the common reservoir. Moreover, the amount of entanglement generated with the common reservoir present can be significantly larger than that which can be obtained without it for any temperature of the individual reservoirs. From the perspective of thermodynamics, we find that enhancement of entanglement is associated with heat absorption by the common reservoir. We propose a possible implementation of our scheme in superconducting circuits and find that a significant enhancement of steady-state entanglement should be observable under experimentally realistic conditions.
