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A mixed quantum state can be taken as capturing an unspecified form of ignorance; or as describing the lack of knowledge about the true pure state of the system ("proper mixture"); or as arising from entanglement with another system that has been disregarded ("improper mixture"). These different views yield identical density matrices and therefore identical predictions for future measurements. But when used as prior beliefs for inferring the past state from later observations ("retrodiction"), they lead to different updated beliefs. This is a purely quantum feature of Bayesian agency. Based on this observation, we establish a framework for retrodicting on any quantum belief and we prove a necessary and sufficient condition for the equivalence of beliefs. We also illustrate how these differences have operational consequences in quantum state recovery.

Building on the approach of stochastic thermodynamics, we define entropy production for arbitrary quantum processes, using Bayesian tools to capture the inherent subjective element. First, we show that the classical expression for average entropy production involves only comparisons of statistics at the input or output, and thus can be formally generalized by replacing probability distributions by quantum states. To go beyond the mere average, we construct an entropy production operator, that generalizes the value of entropy to the non-commutative case. The operator is Hermitian; its average is non-negative, so that the Second Law takes its usual form $\langle\Sigma\rangle\geq 0$; it formally satisfies the Jarzynski equality and the Crooks fluctuation theorem; and recovers the classical expression for classical processes. We also present features whose fully quantum version is not a straightforward translation of the classical one: these may point to the core difference between classical and quantum thermodynamics., Comment: 14 pages, 3 figures; added new result on Crooks fluctuation theorem and deleted an erroneous figure; comments are welcome

Despite the remarkable advancements in Visual Question Answering (VQA), the challenge of mitigating the language bias introduced by textual information remains unresolved. Previous approaches capture language bias from a coarse-grained perspective. However, the finer-grained information within a sentence, such as context and keywords, can result in different biases. Due to the ignorance of fine-grained information, most existing methods fail to sufficiently capture language bias. In this paper, we propose a novel causal intervention training scheme named CIBi to eliminate language bias from a finer-grained perspective. Specifically, we divide the language bias into context bias and keyword bias. We employ causal intervention and contrastive learning to eliminate context bias and improve the multi-modal representation. Additionally, we design a new question-only branch based on counterfactual generation to distill and eliminate keyword bias. Experimental results illustrate that CIBi is applicable to various VQA models, yielding competitive performance.

Bayes' rule, which is routinely used to update beliefs based on new evidence, arises from a principle of minimal change. This principle states that updated beliefs must be consistent with new data, while deviating minimally from the prior belief. Here, we introduce a quantum analog of the minimal change principle and use it to derive a quantum Bayes' rule by minimizing the change between two quantum input-output processes, not just their marginals. This is analogous to the classical case where Bayes' rule is obtained by minimizing the change between the joint input-output distributions. When the change is quantified by the fidelity, the quantum minimal change principle has a unique solution, and the resulting quantum Bayes' rule recovers the Petz transpose map., Comment: 10 pages, 1 figure, added clarifications and a figure; comments are welcome

The Petz map has been established as a quantum version of the Bayes' rule. It unifies the conceptual belief update rule of a quantum state observed after a forward quantum process, and the operational reverse process that brings the final state to a recovered state equal to the updated belief, counteracting the forward process. Here, we study a higher-order generalization of the quantum Bayes' rule by considering a quantum process undergoing a quantum supermap. For a few families of initial beliefs, we show that a similar unification is possible -- the rules to update the belief of quantum channels can be implemented via a "reverse" quantum supermap, which we call the retrodiction supermap, allowing for applications such as error correction in quantum cloud computing. Analytical solutions are provided for those families, while a recipe for arbitrary initial beliefs is yet to be found., Comment: 11 pages, 7 figures, 1 table, fixed typos and added a reference

Long-context capabilities are essential for large language models (LLMs) to tackle complex and long-input tasks. Despite numerous efforts made to optimize LLMs for long contexts, challenges persist in robustly processing long inputs. In this paper, we introduce GraphReader, a graph-based agent system designed to handle long texts by structuring them into a graph and employing an agent to explore this graph autonomously. Upon receiving a question, the agent first undertakes a step-by-step analysis and devises a rational plan. It then invokes a set of predefined functions to read node content and neighbors, facilitating a coarse-to-fine exploration of the graph. Throughout the exploration, the agent continuously records new insights and reflects on current circumstances to optimize the process until it has gathered sufficient information to generate an answer. Experimental results on the LV-Eval dataset reveal that GraphReader, using a 4k context window, consistently outperforms GPT-4-128k across context lengths from 16k to 256k by a large margin. Additionally, our approach demonstrates superior performance on four challenging single-hop and multi-hop benchmarks., Comment: [EMNLP 2024] The first four authors contributed equally, 29 pages

Predicting unseen relations that cannot be observed during the training phase is a challenging task in relation extraction. Previous works have made progress by matching the semantics between input instances and label descriptions. However, fine-grained matching often requires laborious manual annotation, and rich interactions between instances and label descriptions come with significant computational overhead. In this work, we propose an efficient multi-grained matching approach that uses virtual entity matching to reduce manual annotation cost, and fuses coarse-grained recall and fine-grained classification for rich interactions with guaranteed inference speed. Experimental results show that our approach outperforms the previous State Of The Art (SOTA) methods, and achieves a balance between inference efficiency and prediction accuracy in zero-shot relation extraction tasks. Our code is available at https://github.com/longls777/EMMA., Comment: Accepted to the main conference of NAACL2024

The advent of Large Language Models (LLMs) has drastically enhanced dialogue systems. However, comprehensively evaluating the dialogue abilities of LLMs remains a challenge. Previous benchmarks have primarily focused on single-turn dialogues or provided coarse-grained and incomplete assessments of multi-turn dialogues, overlooking the complexity and fine-grained nuances of real-life dialogues. To address this issue, we introduce MT-Bench-101, specifically designed to evaluate the fine-grained abilities of LLMs in multi-turn dialogues. By conducting a detailed analysis of real multi-turn dialogue data, we construct a three-tier hierarchical ability taxonomy comprising 4208 turns across 1388 multi-turn dialogues in 13 distinct tasks. We then evaluate 21 popular LLMs based on MT-Bench-101, conducting comprehensive analyses from both ability and task perspectives and observing differing trends in LLMs performance across dialogue turns within various tasks. Further analysis indicates that neither utilizing common alignment techniques nor chat-specific designs has led to obvious enhancements in the multi-turn abilities of LLMs. Extensive case studies suggest that our designed tasks accurately assess the corresponding multi-turn abilities. The data and code are available at \url{https://github.com/mtbench101/mt-bench-101}., Comment: [ACL 2024] The first three authors contribute equally, 34 pages, repo at https://github.com/mtbench101/mt-bench-101

We study quantum circuits constructed from $\sqrt{iSWAP}$ gates and, more generally, from the entangling gates that can be realized with the XX+YY interaction alone. Such gates preserve the Hamming weight of states in the computational basis, which means they respect the global U(1) symmetry corresponding to rotations around the z axis. Equivalently, assuming that the intrinsic Hamiltonian of each qubit in the system is the Pauli Z operator, they conserve the total energy of the system. We develop efficient methods for synthesizing circuits realizing any desired energy-conserving unitary using XX+YY interaction with or without single-qubit rotations around the z-axis. Interestingly, implementing generic energy-conserving unitaries, such as CCZ and Fredkin gates, with 2-local energy-conserving gates requires the use of ancilla qubits. When single-qubit rotations around the z-axis are permitted, our scheme requires only a single ancilla qubit, whereas with the XX+YY interaction alone, it requires 2 ancilla qubits. In addition to exact realizations, we also consider approximate realizations and show how a general energy-conserving unitary can be synthesized using only a sequence of $\sqrt{iSWAP}$ gates and 2 ancillary qubits, with arbitrarily small error, which can be bounded via the Solovay-Kitaev theorem. Our methods are also applicable for synthesizing energy-conserving unitaries when, rather than the XX+YY interaction, one has access to any other energy-conserving 2-body interaction that is not diagonal in the computational basis, such as the Heisenberg exchange interaction. We briefly discuss the applications of these circuits in the context of quantum computing, quantum thermodynamics, and quantum clocks., Comment: V3: Typos corrected. Published version

Observational entropy captures both the intrinsic uncertainty of a thermodynamic state and the lack of knowledge due to coarse-graining. We demonstrate two interpretations of observational entropy, one as the statistical deficiency resulting from a measurement, the other as the difficulty of inferring the input state from the measurement statistics by quantum Bayesian retrodiction. These interpretations show that the observational entropy implicitly includes a uniform reference prior. Since the uniform prior cannot be used when the system is infinite-dimensional or otherwise energy-constrained, we propose generalizations by replacing the uniform prior with arbitrary quantum states that may not even commute with the state of the system. We propose three candidates for this generalization, discuss their properties, and show that one of them gives a unified expression that relates both interpretations., Comment: 17 pages, no figure, 1 table. Reformatted to published version

Unextendible product bases (UPBs) play a key role in the study of quantum entanglement and nonlocality. A famous open question is whether there exist genuinely unextendible product bases (GUPBs), namely multipartite product bases that are unextendible with respect to every possible bipartition. Here we shed light on this question by providing a characterization of UPBs and GUPBs in terms of orthogonality graphs. Building on this connection, we develop a method for constructing UPBs in low dimensions, and we derive a lower bound on the size of any GUPB, significantly improving over the state of the art. Moreover, we show that every minimal GUPB saturating our bound must be associated to regular graphs. Finally, we discuss a possible path towards the construction of a minimal GUPB in a tripartite system of minimal local dimension.

The task of testing whether two uncharacterized quantum devices behave in the same way is crucial for benchmarking near-term quantum computers and quantum simulators, but has so far remained open for continuous-variable quantum systems. In this Letter, we develop a machine learning algorithm for comparing unknown continuous variable states using limited and noisy data. The algorithm works on non-Gaussian quantum states for which similarity testing could not be achieved with previous techniques. Our approach is based on a convolutional neural network that assesses the similarity of quantum states based on a lower-dimensional state representation built from measurement data. The network can be trained offline with classically simulated data from a fiducial set of states sharing structural similarities with the states to be tested, or with experimental data generated by measurements on the fiducial states, or with a combination of simulated and experimental data. We test the performance of the model on noisy cat states and states generated by arbitrary selective number-dependent phase gates. Our network can also be applied to the problem of comparing continuous variable states across different experimental platforms, with different sets of achievable measurements, and to the problem of experimentally testing whether two states are equivalent up to Gaussian unitary transformations.

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., Comment: Major improvements in the presentation; new numerical experiments that illustrate the applicability of our neural network to various types of states

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.

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., Comment: 43 pages, 5 figures. Modified to match the published version. This version supercedes arXiv:2012.01731

Continuous-variable quantum information, encoded into infinite-dimensional quantum systems, is a promising platform for the realization of many quantum information protocols, including quantum computation, quantum metrology, quantum cryptography, and quantum communication. To successfully demonstrate these protocols, an essential step is the certification of multimode continuous-variable quantum states and quantum devices. This problem is well studied under the assumption that multiple uses of the same device result into identical and independently distributed (i.i.d.) operations. However, in realistic scenarios, identical and independent state preparation and calls to the quantum devices cannot be generally guaranteed. Important instances include adversarial scenarios and instances of time-dependent and correlated noise. In this paper, we propose the first set of reliable protocols for verifying multimode continuous-variable entangled states and devices in these non-i.i.d scenarios. Although not fully universal, these protocols are applicable to Gaussian quantum states, non-Gaussian hypergraph states, as well as amplification, attenuation, and purification of noisy coherent states.

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., Comment: 21 pages, 4 figures. Unchanged from previous version. Superceded by arXiv:2109.13166