arXiv subjects

Giulio Chiribella

Publications and source records attributed to Giulio Chiribella.

At least 109 records · Page 6Linked to original sources

arXiv2019

Quantum-enhanced learning of rotations about an unknown direction

We design machines that learn how to rotate a quantum bit about an initially unknown direction, encoded in the state of a spin-j particle. We show that a machine equipped with a quantum memory of O(log j) qubits can outperform all machines with purely classical memory, even if the size of their memory is arbitrarily large. The advantage is present for every finite j and persists as long as the quantum memory is accessed for no more than O(j) times. We establish these results by deriving the ultimate performance achievable with purely classical memories, thus providing a benchmark that can be used to experimentally demonstrate the implementation of quantum-enhanced learning.

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arXiv2019

Quantum Shannon theory with superpositions of trajectories

Shannon's theory of information was built on the assumption that the information carriers were classical systems. Its quantum counterpart, quantum Shannon theory, explores the new possibilities arising when the information carriers are quantum systems. Traditionally, quantum Shannon theory has focussed on scenarios where the internal state of the information carriers is quantum, while their trajectory is classical. Here we propose a second level of quantisation where both the information and its propagation in spacetime is treated quantum mechanically. The framework is illustrated with a number of examples, showcasing some of the counterintuitive phenomena taking place when information travels simultaneously through multiple transmission lines.

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arXiv2019

Attaining the ultimate precision limit in quantum state estimation

We derive a bound on the precision of state estimation for finite dimensional quantum systems and prove its attainability in the generic case where the spectrum is non-degenerate. Our results hold under an assumption called local asymptotic covariance, which is weaker than unbiasedness or local unbiasedness. The derivation is based on an analysis of the limiting distribution of the estimator's deviation from the true value of the parameter, and takes advantage of quantum local asymptotic normality, a useful asymptotic characterization of identically prepared states in terms of Gaussian states. We first prove our results for the mean square error of a special class of models, called D-invariant, and then extend the results to arbitrary models, generic cost functions, and global state estimation, where the unknown parameter is not restricted to a local neighbourhood of the true value. The extension includes a treatment of nuisance parameters, i.e. parameters that are not of interest to the experimenter but nevertheless affect the precision of the estimation. As an illustration of the general approach, we provide the optimal estimation strategies for the joint measurement of two qubit observables, for the estimation of qubit states in the presence of amplitude damping noise, and for noisy multiphase estimation.

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arXiv2019

Quantum speedup in the identification of cause-effect relations

The ability to identify cause-effect relations is an essential component of the scientific method. The identification of causal relations is generally accomplished through statistical trials where alternative hypotheses are tested against each other. Traditionally, such trials have been based on classical statistics. However, classical statistics becomes inadequate at the quantum scale, where a richer spectrum of causal relations is accessible. Here we show that quantum strategies can greatly speed up the identification of causal relations. We analyse the task of identifying the effect of a given variable, and we show that the optimal quantum strategy beats all classical strategies by running multiple equivalent tests in a quantum superposition. The same working principle leads to advantages in the detection of a causal link between two variables, and in the identification of the cause of a given variable.

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arXiv2019

Proceedings of the 15th International Conference on Quantum Physics and Logic

Quantum Physics and Logic is an annual conference that brings together researchers working on mathematical foundations of quantum physics, quantum computing, and related areas, with a focus on structural perspectives and the use of logical tools, ordered algebraic and category-theoretic structures, formal languages, semantical methods, and other computer science techniques applied to the study of physical behaviour in general. Work that applies structures and methods inspired by quantum theory to other fields (including computer science) is also welcome.

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arXiv2019

Quantum Stopwatch: How To Store Time in a Quantum Memory

Quantum mechanics imposes a fundamental tradeoff between the accuracy of time measurements and the size of the systems used as clocks. When the measurements of different time intervals are combined, the errors due to the finite clock size accumulate, resulting in an overall inaccuracy that grows with the complexity of the setup. Here we introduce a method that in principle eludes the accumulation of errors by coherently transferring information from a quantum clock to a quantum memory of the smallest possible size. Our method could be used to measure the total duration of a sequence of events with enhanced accuracy, and to reduce the amount of quantum communication needed to stabilize clocks in a quantum network.

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arXiv2019

Compression for quantum population coding

We study the compression of n quantum systems, each prepared in the same state belonging to a given parametric family of quantum states. For a family of states with f independent parameters, we devise an asymptotically faithful protocol that requires a hybrid memory of size (f/2)log(n), including both quantum and classical bits. Our construction uses a quantum version of local asymptotic normality and, as an intermediate step, solves the problem of compressing displaced thermal states of n identically prepared modes. In both cases, we show that (f/2)log(n) is the minimum amount of memory needed to achieve asymptotic faithfulness. In addition, we analyze how much of the memory needs to be quantum. We find that the ratio between quantum and classical bits can be made arbitrarily small, but cannot reach zero: unless all the quantum states in the family commute, no protocol using only classical bits can be faithful, even if it uses an arbitrarily large number of classical bits.

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arXiv2018

Quantum communication in a superposition of causal orders

Quantum mechanics allows for situations where the relative order between two processes is entangled with a quantum degree of freedom. Here we show that such entanglement can enhance the ability to transmit quantum information over noisy communication channels. We consider two completely dephasing channels, which in normal conditions are unable to transmit any quantum information. We show that, when the two channels are traversed in an indefinite order, a quantum bit sent through them has a 25% probability to reach the receiver without any error. For partially dephasing channels, a similar advantage takes place deterministically: the amount of quantum information that can travel through two channels in a superposition of orders can be larger than the amount of quantum information that can travel through each channel individually.

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arXiv2018

Agents, subsystems, and the conservation of information

Dividing the world into subsystems is an important component of the scientific method. The choice of subsystems, however, is not defined a priori. Typically, it is dictated by experimental capabilities, which may be different for different agents. Here we propose a way to define subsystems in general physical theories, including theories beyond quantum and classical mechanics. Our construction associates every agent A with a subsystem SA, equipped with its set of states and its set of transformations. In quantum theory, this construction accommodates the notion of subsystems as factors of a tensor product Hilbert space, as well as the notion of subsystems associated to a subalgebra of operators. Classical systems can be interpreted as subsystems of quantum systems in different ways, by applying our construction to agents who have access to different sets of operations, including multiphase covariant channels and certain sets of free operations arising in the resource theory of quantum coherence. After illustrating the basic definitions, we restrict our attention to closed systems, that is, systems where all physical transformations act invertibly and where all states can be generated from a fixed initial state. For closed systems, we propose a dynamical definition of pure states, and show that all the states of all subsystems admit a canonical purification. This result extends the purification principle to a broader setting, in which coherent superpositions can be interpreted as purifications of incoherent mixtures.

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arXiv2018

Enhanced communication with the assistance of indefinite causal order

In quantum Shannon theory, the way information is encoded and decoded takes advantage of the laws of quantum mechanics, while the way communication channels are interlinked is assumed to be classical. In this Letter we relax the assumption that quantum channels are combined classically, showing that a quantum communication network where quantum channels are combined in a superposition of different orders can achieve tasks that are impossible in conventional quantum Shannon theory. In particular, we show that two identical copies of a completely depolarizing channel become able to transmit information when they are combined in a quantum superposition of two alternative orders. This finding runs counter to the intuition that if two communication channels are identical, using them in different orders should not make any difference. The failure of such intuition stems from the fact that a single noisy channel can be a random mixture of elementary, non-commuting processes, whose order (or lack thereof) can affect the ability to transmit information.

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arXiv2018

Microcanonical thermodynamics in general physical theories

Microcanonical thermodynamics studies the operations that can be performed on systems with well-defined energy. So far, this approach has been applied to classical and quantum systems. Here we extend it to arbitrary physical theories, proposing two requirements for the development of a general microcanonical framework. We then formulate three resource theories, corresponding to three different sets of basic operations: i) random reversible operations, resulting from reversible dynamics with fluctuating parameters, ii) noisy operations, generated by the interaction with ancillas in the microcanonical state, and iii) unital operations, defined as the operations that preserve the microcanonical state. We focus our attention on a class of physical theories, called sharp theories with purification, where these three sets of operations exhibit remarkable properties. Firstly, each set is contained into the next. Secondly, the convertibility of states by unital operations is completely characterised by a majorisation criterion. Thirdly, the three sets are equivalent in terms of state convertibility if and only if the dynamics allowed by theory satisfy a suitable condition, which we call unrestricted reversibility. Under this condition, we derive a duality between the resource theory of microcanonical thermodynamics and the resource theory of pure bipartite entanglement.

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arXiv2017

Entanglement, non-Markovianity, and causal non-separability

Quantum mechanics, in principle, allows for processes with indefinite causal order. However, most of these causal anomalies have not yet been detected experimentally. We show that every such process can be simulated experimentally by means of non-Markovian dynamics with a measurement on additional degrees of freedom. Explicitly, we provide a constructive scheme to implement arbitrary acausal processes. Furthermore, we give necessary and sufficient conditions for open system dynamics with measurement to yield processes that respect causality locally, and find that tripartite entanglement and nonlocal unitary transformations are crucial requirements for the simulation of causally indefinite processes. These results show a direct connection between three counter-intuitive concepts: non-Markovianity, entanglement, and causal indefiniteness.

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arXiv2017

Units of rotational information

Entanglement in angular momentum degrees of freedom is a precious resource for quantum metrology and control. Here we study the conversions of this resource, focusing on Bell pairs of spin-J particles, where one particle is used to probe unknown rotations and the other particle is used as reference. When a large number of pairs are given, we show that every rotated spin-J Bell state can be reversibly converted into an equivalent number of rotated spin one-half Bell states, at a rate determined by the quantum Fisher information. This result provides the foundation for the definition of an elementary unit of information about rotations in space, which we call the Cartesian refbit. In the finite copy scenario, we design machines that approximately break down Bell states of higher spins into Cartesian refbits, as well as machines that approximately implement the inverse process. In addition, we establish a quantitative link between the conversion of Bell states and the simulation of unitary gates, showing that the fidelity of probabilistic state conversion provides upper and lower bounds on the fidelity of deterministic gate simulation. The result holds not only for rotation gates, but also to all sets of gates that form finite-dimensional representations of compact groups. For rotation gates, we show how rotations on a system of given spin can simulate rotations on a system of different spin.

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arXiv2017

Optimal quantum operations at zero energy cost

Quantum technologies are developing powerful tools to generate and manipulate coherent superpositions of different energy levels. Envisaging a new generation of energy-efficient quantum devices, here we explore how coherence can be manipulated without exchanging energy with the surrounding environment. We start from the task of converting a coherent superposition of energy eigenstates into another. We identify the optimal energy-preserving operations, both in the deterministic and in the probabilistic scenario. We then design a recursive protocol, wherein a branching sequence of energy-preserving filters increases the probability of success while reaching maximum fidelity at each iteration. Building on the recursive protocol, we construct efficient approximations of the optimal fidelity-probability trade-off, by taking coherent superpositions of the different branches generated by probabilistic filtering. The benefits of this construction are illustrated in applications to quantum metrology, quantum cloning, coherent state amplification, and ancilla-driven computation. Finally, we extend our results to transitions where the input state is generally mixed and we apply our findings to the task of purifying quantum coherence.

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arXiv2017

Certifying quantumness: Benchmarks for the optimal processing of generalized coherent and squeezed states

Quantum technology promises revolutionary advantages in information processing and transmission compared to classical technology; however, determining which specific resources are needed to surpass the capabilities of classical machines often remains a nontrivial problem. To address such a problem, one first needs to establish the best classical solutions, which set benchmarks that must be beaten by any implementation claiming to harness quantum features for an enhanced performance. Here we introduce and develop a self-contained formalism to obtain the ultimate, generally probabilistic benchmarks for quantum information protocols including teleportation and approximate cloning, with arbitrary ensembles of input states generated by a group action, so-called Gilmore-Perelomov coherent states. This allows us to construct explicit fidelity thresholds for the transmission of multimode Gaussian and non-Gaussian states of continuous variable systems, as well as qubit and qudit pure states drawn according to nonuniform distributions on the Bloch hypersphere, which accurately model the current laboratory facilities. The performance of deterministic classical procedures such as square-root measurement strategies is further compared with the optimal probabilistic benchmarks, and the state-of-the-art performance of experimental quantum implementations against our newly derived thresholds is discussed. This work provides a comprehensive collection of directly useful criteria for the reliable certification of quantum communication technologies.

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arXiv2017

Incompatible measurements on quantum causal networks

The existence of incompatible measurements, epitomized by Heisenberg's uncertainty principle, is one of the distinctive features of quantum theory. So far, quantum incompatibility has been studied for measurements that test the preparation of physical systems. Here we extend the notion to measurements that test dynamical processes, possibly consisting of multiple time steps. Such measurements are known as testers and are implemented by interacting with the tested process through a sequence of state preparations, interactions, and measurements. Our first result is a characterization of the incompatibility of quantum testers, for which we provide necessary and sufficient conditions. Then, we propose a quantitative measure of incompatibility. We call this measure the robustness of incompatibility and define it as the minimum amount of noise that has to be added to a set of testers in order to make them compatible. We show that (i) the robustness is lower bounded by the distinguishability of the sequence of interactions used by the tester and (ii) maximum robustness is attained when the interactions are perfectly distinguishable. The general results are illustrated in the concrete example of binary testers probing the time-evolution of a single-photon polarization.

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arXiv2017

Quantum amplification and purification of noisy coherent states

Quantum-limited amplifiers increase the amplitude of quantum signals at the price of introducing additional noise. Quantum purification protocols operate in the reverse way, by reducing the noise while attenuating the signal. Here we investigate a scenario that interpolates between these two extremes. We search for the optimal physical process that generates $M$ approximate copies of pure and amplified coherent state, starting from $N$ copies of a noisy coherent state with Gaussian modulation. We prove that the optimal deterministic processes are always Gaussian, whereas non-Gaussianity powers up probabilistic advantages in suitable parameter regimes. The optimal processes are experimentally feasible, both in the deterministic and in the probabilistic scenario. In view of this fact, we provide benchmarks that can be used to certify the experimental demonstration of the quantum-enhanced amplification and purification of coherent states.

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arXiv2017

Optimal quantum tomography

The present short review article illustrates the latest theoretical developments on quantum tomography, regarding general optimization methods for both data-processing and setup. The basic theoretical tool is the informationally complete measurement. The optimization theory for the setup is based on the new theoretical approach of quantum combs.

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