# Publications

**Authors: **Tamal Guha, Mir Alimuddin, Sumit Rout, Amit Mukherjee, Some Sankar Bhattacharya and Manik Banik

**Year:** 2020

Randomness appears both in classical stochastic physics and in quantum mechanics. A number of communication models and other information protocols entail sharing randomness among distant parties. Here we report a computational scenario of shared randomness processing where quantum sources manifest clear-cut precedence over the corresponding classical counterparts. The advantage is established in a resource theoretic set-up which we formalize in this work. The classical mutual information turns out to be a faithful resource quantifier of shared randomness although it does not sufficiently characterize all possible transitions among the resources. Quantum theory exhibits advantage in shared randomness processing in the sense that the set of resourceful states obtained under free operation from a bipartite quantum system is strictly larger than the set obtained from an analogous classical system. Interestingly, the quantum advantage can be manifested in the optimal payoff of a two players co-operative game — the `non-monopolize social subsidy’ game. We also show that the quantum states resulting to the desired advantage necessitates nonclassicality in the form of quantum discord. We then address the task of distributing shared randomness between two parties. Quite interestingly, it turns out that noisy quantum channel can exhibit advantage even when it has zero quantum capacity and classical capacity much less than the corresponding classical channel. The imperfect channel examples facilitates and welcomes experiment to achieve the reported quantum advantage with presently available quantum devices.

**Authors: **Xiaobin Zhao, Yuxiang Yang and Giulio Chiribella

**Year:** 2020

We address the study of quantum metrology enhanced by indefinite causal order, demonstrating a quadratic advantage in the estimation of the product of two average displacements in a continuous variable system. We prove that no setup where the displacements are probed in a fixed order can have root-mean-square error vanishing faster than the Heisenberg limit 1/N, where N is the number of displacements contributing to the average. In stark contrast, we show that a setup that probes the displacements in a superposition of two alternative orders yields a root-mean-square error vanishing with super-Heisenberg scaling 1/N^2. This result opens up the study of new measurement setups where quantum processes are probed in an indefinite order, and suggests enhanced tests of the canonical commutation relations, with potential applications to quantum gravity.

**Authors: **John Burniston, Michael Grabowecky, Carlo Maria Scandolo, Giulio Chiribella and Gilad Gour

**Year:** 2020

Quantum supermaps are a higher-order generalization of quantum maps, taking quantum maps to quantum maps. It is known that any completely positive, trace non-increasing (CPTNI) map can be performed as part of a quantum measurement. By providing an explicit counterexample we show that, instead, not every quantum supermap sending a quantum channel to a CPTNI map can be realized in a measurement on quantum channels. We find that the supermaps that can be implemented in this way are exactly those transforming quantum channels into CPTNI maps even when tensored with the identity supermap. We link this result to the fact that the principle of causality fails in the theory of quantum supermaps.

**Authors: **Ge Bai, Yuxiang Yang and Giulio Chiribella

**Year:** 2019

We design quantum compression algorithms for parametric families of tensor network states. We first establish an upper bound on the amount of memory needed to store an arbitrary state from a given state family. The bound is determined by the minimum cut of a suitable flow network, and is related to the flow of information from the manifold of parameters that specify the states to the physical systems in which the states are embodied. For given network topology and given edge dimensions, our upper bound is tight when all edge dimensions are powers of the same integer. When this condition is not met, the bound is optimal up to a multiplicative factor smaller than 1.585. We then provide a compression algorithm for general state families, and show that the algorithm runs in polynomial time for matrix product states.

**Authors: **Matt Wilson and Giulio Chiribella

**Year:** 2020

The quantum switch is a higher-order operation that takes as an input two quantum processes and combines them in a coherent superposition of two alternative orders. Here we provide an approach to the quantum switch based on the methods of categorical quantum mechanics. Specifically, we represent the quantum switch as a sum of diagrams in the category of finite dimensional Hilbert spaces, or, equivalently, as a sum of diagrams built from Selinger’s CPM construction. The sum-of diagrams picture provides intuition for the activation of classical capacity of completely depolarising channels (CDPCs) and allows for generalisation to N-channel switches. We demonstrate the use of these partially diagrammatic methods by deriving a permutation condition for computing the output of any N-channel switch of CDPCs, we then use that condition to prove that amongst all possible terms, the interference terms associated to cyclic permutations of the N channels are the information transmitting terms with maximum normalisation.

**Authors: **Yu Guo, Xiao-Min Hu, Zhi-Bo Hou, Huan Cao, Jin-Ming Cui, Bi-Heng Liu, Yun-Feng Huang, Chuan-Feng Li, Guang-Can Guo and Giulio Chiribella

**Year:** 2020

Communication in a network generally takes place through a sequence of intermediate nodes connected by communication channels. In the standard theory of communication, it is assumed that the communication network is embedded in a classical spacetime, where the relative order of different nodes is well defined. In principle, a quantum theory of spacetime could allow the order of the intermediate points between sender and receiver to be in a coherent superposition. Here we experimentally realize a tabletop simulation of this exotic possibility on a photonic system, demonstrating high-fidelity transmission of quantum information over two noisy channels arranged in a superposition of two alternative causal orders.

**Authors:**Giulio Chiribella, Erik Aurell and Karol Życzkowski

**Year:**2021 A cornerstone of quantum mechanics is the characterisation of symmetries provided by Wigner’s theorem. Wigner’s theorem establishes that every symmetry of the quantum state space must be either a unitary transformation, or an antiunitary transformation. Here we extend Wigner’s theorem from quantum states to quantum evolutions, including both the deterministic evolution associated to the dynamics of closed systems, and the stochastic evolutions associated to the outcomes of quantum measurements. We prove that every symmetry of the space of quantum evolutions can be decomposed into two state space symmetries that are either both unitary or both antiunitary. Building on this result, we show that it is impossible to extend the time reversal symmetry of unitary quantum dynamics to a symmetry of the full set of quantum evolutions. Our no-go theorem implies that any time symmetric formulation of quantum theory must either restrict the set of the allowed evolutions, or modify the operational interpretation of quantum states and processes. Here we propose a time symmetric formulation of quantum theory where the allowed quantum evolutions are restricted to a suitable set, which includes both unitary evolution and projective measurements, but excludes the deterministic preparation of pure states. The standard operational formulation of quantum theory can be retrieved from this time symmetric version by introducing an operation of conditioning on the outcomes of past experiments.

**Authors:**Some Sankar Bhattacharya, Ananda G. Maity, Tamal Guha, Giulio Chiribella and Manik Banik

**Year:**2020 We introduce the task of random-receiver quantum communication, in which a sender transmits a quantum message to a receiver chosen from a list of n spatially separated parties. The choice of receiver is unknown to the sender, but is known by the n parties, who coordinate their actions by exchanging classical messages. In normal conditions, random-receiver quantum communication requires a noiseless quantum communication channel from the sender to each of the n receivers. In contrast, we show that random-receiver quantum communication can take place through entanglement-breaking channels if the order of such channels is controlled by a quantum bit that is accessible through quantum measurements. Notably, this phenomenon cannot be mimicked by allowing free quantum communication between the sender and any subset of k

**Authors: **Giulio Chiribella and Zixuan Liu

**Year:** 2021

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 in principle possible to probe a quantum dynamics in the backward direction, or in more general combinations of the forward and the backward direction. To answer this question, we characterise all possible time-reversals that satisfy four natural requirements and we identify the largest set of quantum processes that can in principle be probed in both time directions. Then, we show that quantum theory is compatible with the existence of a new kind of operations where the arrow of time is indefinite. We explicitly construct one such operation, called the quantum time flip, and show that it cannot be realised by any quantum circuit with a definite direction of time. The quantum time flip offers an advantage in a game where a referee challenges a player to identify a hidden relation between two gates, and can be experimentally simulated with photonic systems, shedding light on the information-processing capabilities of exotic scenarios in which the arrow of time is in a quantum superposition.

**Authors: **Ge Bai, Ya-Dong Wu, Yan Zhu, Masahito Hayashi and Giulio Chiribella

**Year:** 2020

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.

**Authors: **Richard Howl and Ivette Fuentes

**Year:** 2021

We introduce a quantum interferometric scheme that uses states that are sharp in frequency and delocalized in position. The states are frequency modes of a quantum field that is trapped at all times in a finite volume potential, such as a small box potential. This allows for significant miniaturization of interferometric devices. Since the modes are in contact at all times, it is possible to estimate physical parameters of global multi-mode channels. As an example, we introduce a three-mode scheme and calculate precision bounds in the estimation of parameters of two-mode Gaussian channels. This scheme can be implemented in several systems, including superconducting circuits, cavity-QED and cold atoms. We consider a concrete implementation using the ground state and two phononic modes of a trapped Bose-Einstein condensate. We apply this to show that frequency interferometry can improve the sensitivity of phononic gravitational waves detectors by several orders of magnitude, even in the case that squeezing is much smaller than assumed previously and that the system suffers from short phononic lifetimes. Other applications range from magnetometry, gravimetry and gradiometry to dark matter/energy searches.

**Authors: **Richard Howl, Vlatko Vedral, Devang Naik, Marios Christodoulou, Carlo Rovelli, and Aditya Iyer **Year:** 2021

Tabletop tests of quantum gravity (QG) have long been thought to be practically impossible. However, remarkably, because of rapid progress in quantum information science (QIS), such tests may soon be achievable. Here we uncover an exciting new theoretical link between QG and QIS that also leads to a radical new way of testing QG with QIS experiments. Specifically, we find that only a quantum, not classical, theory of gravity can create non-Gaussianity, a QIS resource that is necessary for universal quantum computation, in the quantum field state of matter. This allows tests based on QIS in which non-Gaussianity in matter is used as a signature of QG. In comparison with previous studies testing QG with QIS where entanglement is used to witness QG when all other quantum interactions are excluded, our non-Gaussianity witness cannot be created by direct classical gravity interactions, facilitating tests that are not constrained by the existence of such processes. Our new signature of QG also enables tests that are based on just a single quantum system rather than a multipartite quantum system, simplifying previously considered experimental setups. We describe a tabletop test of QG that uses our non-Gaussianity signature and that is based on just a single quantum system, a Bose-Einstein condensate, in a single location. In contrast to proposals based on optomechanical setups, Bose-Einstein condensates have already been manipulated into massive nonclassical states, aiding the prospect of testing QG soon.

**Authors:**Ge Bai, Ya-Dong Wu, Yan Zhu, Masahito Hayashi, Giulio Chiribella

**Year:**2021 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, using only access to its input and output systems. Our method is based on a quantum algorithm whose complexity scales polynomially for all processes with bounded information loss. 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 a quantum networks, and to test the structure of uncharacterized quantum circuits.

**Authors: **Giulio Chiribella

**Year:** 2021

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. 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 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.

**Authors: **Ya-Dong Wu, Giulio Chiribella

**Year:** 2021

Transmission and storage of quantum information are the fundamental building blocks for large-scale quantum communication networks. Reliable certification of quantum communication channels and quantum memories requires the estimation of their capacities to transmit and store quantum information. This problem is challenging for continuous variable systems, such as the radiation field, for which a complete characterization of processes via quantum tomography is practically unfeasible. Here we develop protocols for detecting lower bounds to the quantum capacity of continuous variable communication channels and memories. Our protocols work in the general scenario where the devices are used a finite number of times, can exhibit correlations across multiple uses, and can be under the control of an adversary. Our protocols are experimentally friendly and can be implemented using Gaussian input states (single-mode squeezed or coherent) and Gaussian quantum measurements (homodyne or heterodyne). These schemes can be used to certify the transmission and storage of continuous variable quantum information, and to detect communication paths in quantum networks.

**Authors: ** Simon Milz, Jessica Bavaresco, Giulio Chiribella

**Year:** 2021

The capacity of distant parties to send one another signals 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 for two- and three-party scenarios. In contrast, our results suggest that in the general setting there is no global most valuable resource. We derive all monotones of causal connection, and for an important one amongst them, the signalling robustness, we provide tight bounds for many pertinent sets of processes. Finally, we demonstrate that a natural monotone of the resource theory of causal non-separability is also a monotone of causal connection, and elucidate the connection between the two theories. 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 structure.

**Authors: ** Giulio Chiribella, Matt Wilson, H. F. Chau

**Year:** 2021

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.

**Authors: ** Yan Zhu, Ya-Dong Wu, Ge Bai, Yuexuan Wang, Giulio Chiribella

**Year:** 2022

Deep neural networks are a powerful tool for characterizing quantum states. In this task, neural networks are typically trained with measurement data gathered from the quantum state to be characterized. But is it possible to train a neural network in a general-purpose way, which makes it applicable to multiple unknown quantum states? Here we show that learning across multiple quantum states and different measurement settings can be achieved by a generative query neural network, a type of neural network originally used in the classical domain for learning 3D scenes from 2D pictures. Our network can be trained offline with classically simulated data, and later be used to characterize unknown quantum states from real experimental data. 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 probabilities of requested quantum measurements on the states of interest. This approach can be applied to state learning scenarios where quantum measurement settings are not informationally complete and predictions must be given in real time, as experimental data become available, as well as to adversarial scenarios where measurement choices and prediction requests are designed to expose learning inaccuracies. The internal representation produced by the network can be used for other tasks beyond state characterization, including clustering of states and prediction of physical properties. The features of our method are illustrated on many-qubit ground states of Ising model and continuous-variable non-Gaussian states.

**Authors: ** Giulio Chiribella and Xiaobin Zhao

**Year:** 2022

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.

**Authors: ** Tamal Guha, Saptarshi Roy, Giulio Chiribella

**Year:** 2022

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.