arXiv subjects

Giulio Chiribella

Publications and source records attributed to Giulio Chiribella.

At least 73 records · Page 4Linked to original sources

arXiv2022

The nonequilibrium cost of accurate information processing

Accurate information processing is crucial both in technology and in nature. To achieve it, any information processing system needs an initial supply of resources away from thermal equilibrium. Here we establish a fundamental limit on the accuracy achievable with a given amount of nonequilibrium resources. The limit applies to arbitrary information processing tasks and arbitrary information processing systems subject to the laws of quantum mechanics. It is easily computable and is expressed in terms of an entropic quantity, which we name reverse entropy, associated to a time reversal of the information processing task under consideration. The limit is achievable for all deterministic classical computations and for all their quantum extensions. As an application, we establish the optimal tradeoff between nonequilibrium and accuracy for the fundamental tasks of storing, transmitting, cloning, and erasing information. Our results set a target for the design of new devices approaching the ultimate efficiency limit, and provide a framework for demonstrating thermodynamical advantages of quantum devices over their classical counterparts.

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arXiv2022

Compression for Qubit Clocks

Two-Ievel (qubit) clock systems are often used to perform precise measurement of time. In this work, we propose a compression protocol for $n$ identically prepared states of qubit clocks. The protocol faithfully encodes the states into $(1/2)\log n$ qubits and $(1/2)\log n$ classical bits and works even in the presence of noise. If the purity of the clock states is fixed, $(1/2)\log n$ qubits are sufficient. We also prove that this protocol requires the minimum amount of total memory among all protocols with vanishing error in the large $n$ limit.

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arXiv2022

Indefinite causal order enables perfect quantum communication with zero capacity channels

Quantum mechanics is compatible with scenarios where the relative order between two events can be indefinite. Here we show that two independent instances of a noisy process can behave as a perfect quantum communication channel when used in a coherent superposition of two alternative orders. This phenomenon occurs even if the original process has zero capacity to transmit quantum information. In contrast, perfect quantum communication does not occur when the message is sent directly from the sender to the receiver through a superposition of alternative paths, with an independent noise process acting on each path. The possibility of perfect quantum communication through independent noisy channels highlights a fundamental difference between the superposition of orders in time and the superposition of paths in space.

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arXiv2022

Resource theory of causal connection

The capacity of distant parties to send signals to one another is a fundamental requirement in many information-processing tasks. Such ability is determined by the causal structure connecting the parties, and more generally, by the intermediate processes carrying signals from one laboratory to another. Here we build a fully fledged resource theory of causal connection for all multi-party communication scenarios, encompassing those where the parties operate in a definite causal order and also where the order is indefinite. We define and characterize the set of free processes and three different sets of free transformations thereof, resulting in three distinct resource theories of causal connection. In the causally ordered setting, we identify the most resourceful processes in the bipartite and tripartite scenarios. In the general setting, instead, our results suggest that there is no global most valuable resource. We establish the signalling robustness as a resource monotone of causal connection and provide tight bounds on it for many pertinent sets of processes. Finally, we introduce a resource theory of causal non-separability, and show that it is -- in contrast to the case of causal connection -- unique. Together our results offer a flexible and comprehensive framework to quantify and transform general quantum processes, as well as insights into their multi-layered causal connection structures.

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arXiv2022

Flexible learning of quantum states with generative query neural networks

Deep neural networks are a powerful tool for the characterization of quantum states. Existing networks are typically trained with experimental data gathered from the specific quantum state that needs to be characterized. But is it possible to train a neural network offline and to make predictions about quantum states other than the ones used for the training? Here we introduce a model of network that can be trained with classically simulated data from a fiducial set of states and measurements, and can later be used to characterize quantum states that share structural similarities with the states in the fiducial set. With little guidance of quantum physics, the network builds its own data-driven representation of quantum states, and then uses it to predict the outcome statistics of quantum measurements that have not been performed yet. The state representation produced by the network can also be used for tasks beyond the prediction of outcome statistics, including clustering of quantum states and identification of different phases of matter. Our network model provides a flexible approach that can be applied to online learning scenarios, where predictions must be generated as soon as experimental data become available, and to blind learning scenarios where the learner has only access to an encrypted description of the quantum hardware.

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arXiv2022

Detecting Quantum Capacities of Continuous-Variable Quantum Channels

Quantum communication channels and quantum memories are the fundamental building blocks of large-scale quantum communication networks. Estimating their capacity to transmit and store quantum information is crucial in order to assess the performance of quantum communication systems, and to detect useful communication paths among the nodes of future quantum networks. However, the estimation of quantum capacities is a challenging task for continuous variable systems, such as the radiation field, for which a complete characterization via quantum tomography is practically unfeasible. Here we introduce a method for detecting the quantum capacity of continuous variable communication channels and memories without performing a full process tomography. Our method works in the general scenario where the devices are used a finite number of times, can exhibit correlations across multiple uses, and can change dynamically under the control of a malicious adversary. The method is experimentally friendly and can be implemented using only finitely-squeezed states and homodyne measurements.

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arXiv2022

Quantum Causal Unravelling

Complex processes often arise from sequences of simpler interactions involving a few particles at a time. These interactions, however, may not be directly accessible to experiments. Here we develop the first efficient method for unravelling the causal structure of the interactions in a multipartite quantum process, under the assumption that the process has bounded information loss and induces causal dependencies whose strength is above a fixed (but otherwise arbitrary) threshold. Our method is based on a quantum algorithm whose complexity scales polynomially in the total number of input/output systems, in the dimension of the systems involved in each interaction, and in the inverse of the chosen threshold for the strength of the causal dependencies. Under additional assumptions, we also provide a second algorithm that has lower complexity and requires only local state preparation and local measurements. Our algorithms can be used to identify processes that can be characterized efficiently with the technique of quantum process tomography. Similarly, they can be used to identify useful communication channels in quantum networks, and to test the internal structure of uncharacterized quantum circuits.

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arXiv2022

Quantum networks boosted by entanglement with a control system

Networks of quantum devices with coherent control over their configuration offer promising advantages in quantum information processing. So far, the investigation of these advantages assumed that the control system was initially uncorrelated with the data processed by the network. Here, we explore the power of quantum correlations between data and control, showing two communication tasks that can be accomplished with information-erasing channels if and only if the sender shares prior entanglement with a third party (the ``controller'') controlling the network configuration. The first task is to transmit classical messages without leaking information to the controller. The second task is to establish bipartite entanglement with a receiver, or, more generally, to establish multipartite entanglement with a number of spatially separated receivers.

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arXiv2022

Heisenberg-limited metrology with coherent control on the probes' configuration

A central feature of quantum metrology is the possibility of Heisenberg scaling, a quadratic improvement over the limits of classical statistics. This scaling, however, is notoriously fragile to noise. While for some noise types it can be restored through error correction, for other important types, such as dephasing, the Heisenberg scaling appears to be irremediably lost. Here we show that this limitation can sometimes be lifted if the experimenter has the ability to probe physical processes in a coherent superposition of alternative configurations. As a concrete example, we consider the problem of phase estimation in the presence of a random phase kick, which in normal conditions is known to prevent the Heisenberg scaling. We provide a parallel protocol that achieves Heisenberg scaling with respect to the probes' energy, as well as a sequential protocol that achieves Heisenberg scaling with respect to the total probing time. In addition, we show that Heisenberg scaling can also be achieved for frequency estimation in the presence of continuous-time dephasing noise, by combining the superposition of paths with fast control operations.

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arXiv2022

Quantum operations with indefinite time direction

The fundamental dynamics of quantum particles is neutral with respect to the arrow of time. And yet, our experiments are not: we observe quantum systems evolving from the past to the future, but not the other way round. A fundamental question is whether it is possible to conceive a broader set of operations that probe quantum processes in the backward direction, from the future to the past, or more generally, in a combination of the forward and backward directions. Here we introduce a mathematical framework for these operations, showing that some of them cannot be interpreted as random mixtures of operations that probe processes in a definite direction. As a concrete example, we construct an operation, called the quantum time flip, that probes an unknown dynamics in a quantum superposition of the forward and backward directions. This operation exhibits an information-theoretic advantage over all operations with definite direction. It can be realised probabilistically using quantum teleportation, and can be reproduced experimentally with photonic systems. More generally, we introduce a set of multipartite operations that include indefinite time direction as well as indefinite causal order, providing a framework for potential extensions of quantum theory.

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arXiv2022

Counterexamples to the extendibility of positive unital norm-one maps

Arveson's extension theorem guarantees that every completely positive map defined on an operator system can be extended to a completely positive map defined on the whole C*-algebra containing it. An analogous statement where complete positivity is replaced by positivity is known to be false. A natural question is whether extendibility could still hold for positive maps satisfying stronger conditions, such as being unital and norm 1. Here we provide three counterexamples showing that positive norm-one unital maps defined on an operator subsystem of a matrix algebra cannot be extended to a positive map on the full matrix algebra. The first counterexample is an unextendible positive unital map with unit norm, the second counterexample is an unextendible positive unital isometry on a real operator space, and the third counterexample is an unextendible positive unital isometry on a complex operator space.

math.OA↗

arXiv2021

Quantum autoencoders for communication-efficient quantum cloud computing

In the model of quantum cloud computing, the server executes a computation on the quantum data provided by the client. In this scenario, it is important to reduce the amount of quantum communication between the client and the server. A possible approach is to transform the desired computation into a compressed version that acts on a smaller number of qubits, thereby reducing the amount of data exchanged between the client and the server. Here we propose quantum autoencoders for quantum gates (QAEGate) as a method for compressing quantum computations. We illustrate it in concrete scenarios of single-round and multi-round communication and validate it through numerical experiments. A bonus of our method is it does not reveal any information about the server's computation other than the information present in the output.

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arXiv2021

Optimal Universal Quantum Error Correction via Bounded Reference Frames

Error correcting codes with a universal set of transversal gates are a desideratum for quantum computing. Such codes, however, are ruled out by the Eastin-Knill theorem. Moreover, the theorem also rules out codes which are covariant with respect to the action of transversal unitary operations forming continuous symmetries. In this work, starting from an arbitrary code, we construct approximate codes which are covariant with respect to the entire group of local unitary gates in dimension $d$, using quantum reference frames. We show that our codes are capable of efficiently correcting different types of erasure errors. When only a small fraction of the $n$ qudits upon which the code is built are erased, our covariant code has an error that scales as $1/n^2$, which is reminiscent of the Heisenberg limit of quantum metrology. When every qudit has a chance of being erased, our covariant code has an error that scales as $1/n$. We show that the error scaling is optimal in both cases. Our approach has implications for fault-tolerant quantum computing, reference frame error correction, and the AdS-CFT duality.

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arXiv2021

Universal control of quantum processes using sector-preserving channels

No quantum circuit can turn a completely unknown unitary gate into its coherently controlled version. Yet, coherent control of unknown gates has been realised in experiments, making use of a different type of initial resources. Here, we formalise the task achieved by these experiments, extending it to the control of arbitrary noisy channels, and to more general types of control involving higher dimensional control systems. For the standard notion of coherent control, we identify the information-theoretic resource for controlling an arbitrary quantum channel on a $d$-dimensional system: specifically, the resource is an extended quantum channel acting as the original channel on a $d$-dimensional sector of a $(d+1)$-dimensional system. Using this resource, arbitrary controlled channels can be built with a universal circuit architecture. We then extend the standard notion of control to more general notions, including control of multiple channels with possibly different input and output systems. Finally, we develop a theoretical framework, called supermaps on routed channels, which provides a compact representation of coherent control as an operation performed on the extended channels, and highlights the way the operation acts on different sectors.

quant-ph↗

arXiv2021

Witnessing latent time correlations with a single quantum particle

When a noisy communication channel is used multiple times, the errors occurring at different times generally exhibit correlations. Classically, these correlations do not affect the evolution of individual particles: a single classical particle can only traverse the channel at a definite moment of time, and its evolution is insensitive to the correlations between subsequent uses of the channel. In stark contrast, here we show that a single quantum particle can sense the correlations between multiple uses of a channel at different moments of time. In an extreme example, we show that a channel that outputs white noise when the particle is sent at a definite time can exhibit correlations that enable a perfect transmission of classical bits when the particle is sent at a superposition of two times. In contrast, we show that, in the lack of correlations, a single particle sent at a superposition of two times undergoes an effective channel with classical capacity of at most 0.16 bits. When multiple transmission lines are available, time correlations can be used to simulate the application of quantum channels in a coherent superposition of alternative causal orders, and even to provide communication advantages that are not accessible through the superposition of causal orders.

quant-ph↗

arXiv2021

Process tomography in general physical theories

Process tomography, the experimental characterization of physical processes, is a central task in science and engineering. Here we investigate the axiomatic requirements that guarantee the in-principle feasibility of process tomography in general physical theories. Specifically, we explore the requirement that process tomography should be achievable with a finite number of auxiliary systems and with a finite number of input states. We show that this requirement is satisfied in every theory equipped with universal extensions, that is, correlated states from which all other correlations can be generated locally with non-zero probability. We show that universal extensions are guaranteed to exist in two cases: (1) theories permitting conclusive state teleportation, and (2) theories satisfying three properties of Causality, Pure Product States, and Purification. In case (2), the existence of universal extensions follows from a symmetry property of Purification, whereby all pure bipartite states with the same marginal on one system are locally interconvertible. Crucially, our results hold even in theories that do not satisfy Local Tomography, the property that the state of any composite system can be identified from the correlations of local measurements. Summarizing, the existence of universal extensions, without any additional requirement of Local Tomography, is a sufficient guarantee for the characterizability of physical processes using a finite number of auxiliary systems.

quant-ph↗

arXiv2021

Quantum and Classical Data Transmission through Completely Depolarising Channels in a Superposition of Cyclic Orders

Completely depolarising channels are often regarded as the prototype of physical processes that are useless for communication: any message that passes through them along a well-defined trajectory is completely erased. When two such channels are used in a quantum superposition of two alternative orders, they become able to transmit some amount of classical information, but still no quantum information can pass through them. Here we show that the ability to place N completely depolarising channels in a superposition of N alternative causal orders enables a high-fidelity, heralded transmission of quantum information with error vanishing as 1/N. This phenomenon highlights a fundamental difference with the N = 2 case, where completely depolarising channels are unable to transmit quantum data, even when placed in a superposition of causal orders. The ability to place quantum channels in a superposition of orders also leads to an increase of the classical communication capacity with N, which we rigorously prove by deriving an exact single-letter expression. Our results highlight the more complex patterns of correlations arising from multiple causal orders, which are similar to the more complex patterns of entanglement arising in multipartite quantum systems.

quant-ph↗

arXiv2021

Efficient Algorithms for Causal Order Discovery in Quantum Networks

Given black-box access to the input and output systems, we develop the first efficient quantum causal order discovery algorithm with polynomial query complexity with respect to the number of systems. We model the causal order with quantum combs, and our algorithms output the order of inputs and outputs that the given process is compatible with. Our algorithm searches for the last input and the last output in the causal order, removes them, and iteratively repeats the above procedure until we get the order of all inputs and outputs. Our method guarantees a polynomial running time for quantum combs with a low Kraus rank, namely processes with low noise and little information loss. For special cases where the causal order can be inferred from local observations, we also propose algorithms that have lower query complexity and only require local state preparation and local measurements. Our algorithms will provide efficient ways to detect and optimize available transmission paths in quantum communication networks, as well as methods to verify quantum circuits and to discover the latent structure of multipartite quantum systems.

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