arXiv subjects

Xiangjing Liu

Publications and source records attributed to Xiangjing Liu.

At least 19 recordsLinked to original sources

arXiv2026

Generalised Probabilistic Theories

We give an introduction to research associated with the generalised probabilistic theories framework, also known as the convex framework. States are real vectors representing lists of probabilities of measurement outcomes. Convex combinations of the vectors represent probabilistic combinations of different state preparations. Transformations are real matrices. Measurement outcomes are represented by functionals of the states, inner products of the state with a real vector, whose values are the probability of the measurement outcome in question. The framework generalises quantum theory. We describe the operational meaning of the framework, and how the concepts can be defined in terms of cones of states and measurement outcome vectors. We describe how the classical and quantum probability theories are represented in the framework. We describe Bell non-locality and the theory with super-quantum non-locality known as box world. We discuss generalised Hamiltonian mechanics in the discrete case and in continuous phase space, including the role of negativity of the phase space density in contextuality and tunnelling.

quant-ph↗

arXiv2026

Reversing Heat Flow by Coherence in a Multipartite Quantum System

The second law of thermodynamics dictates that heat flows spontaneously from a high-temperature entity to a lower-temperature one. Yet, recent advances have demonstrated that quantum correlations between a system and its thermal environment can induce a reversal of heat flow, challenging classical thermodynamic expectations. Here, we experimentally demonstrate that internal quantum coherence in a multipartite spin system can also reverse heat flow, without relying on initial correlations with the environment. Under the collision model with cascade interaction, we verify that both the strength and the phase of the coherence term determine the direction and magnitude of energy transfer. These results enable precise control of heat flow using only local quantum properties.

quant-ph↗

arXiv2025

Spatial Incompatibility Witnesses for Quantum Temporal Correlations

We introduce a witness-based framework for certifying quantum temporal correlations via the pseudo-density matrix (PDM) formalism, which is a spatiotemporal generalization of the density matrix. We define spatial incompatibility (SI) as the minimum distance between a PDM and valid density matrices. For trace-norm distance, we show that this reduces to the PDM's negativity, enabling the construction of experimentally accessible SI witnesses. We derive a tight bound on SI for quantum channels and analyze the respective roles of state and channel coherence in witnessing SI. Our approach, unlike the LG framework, exploits measurements that generate coherence through state disturbance. We further show that channels satisfying the LG inequality for incoherent states can still exhibit detectable SI, demonstrating that measurement disturbance enhances the certification of temporal correlations.

quant-ph↗

arXiv2025

No Practical Quantum Broadcasting: Even Virtually

Quantum information cannot be broadcast -- an intrinsic limitation imposed by quantum mechanics. However, recent advances in virtual operations offer new insights into the no-broadcasting theorem. Here, we focus on the practical utility and introduce sample efficiency as a fundamental constraint, requiring any practical broadcasting protocol perform no worse than the naïve approach of direct preparation and distribution. We prove that no linear process -- whether quantum or beyond -- can simultaneously uphold sample efficiency, unitary covariance, permutation invariance, and classical consistency. This leads to a no-practical-broadcasting theorem, which places strict limits on the practical distribution of quantum information. By applying Schur-Weyl duality, we establish the uniqueness of the canonical 1-to-$N$ virtual broadcasting map that satisfies the latter three conditions, provide its construction, and determine its sample complexity through semidefinite programming. Finally, we explore the interplay between virtual broadcasting and a quantum spacetime framework, known as the pseudo-density operator, showing that their correspondence holds only in the 1-to-2 case, underscoring the fundamental asymmetry between spatial and temporal statistics in the quantum world.

quant-ph↗

arXiv2025

Experimental Virtual Quantum Broadcasting

The quantum no-broadcasting theorem states that it is fundamentally impossible to perfectly replicate an arbitrary quantum state, even if correlations between the copies are allowed. While quantum broadcasting cannot occur through any physical process, it can be achieved via postprocessing of experimental data using a process called virtual quantum broadcasting (VQB). In this work, we report the experimental implementation of a quantum circuit based on the linear combination of unitaries, integrated with a post-processing protocol, to realize VQB in a nuclear magnetic resonance system. VQB can be expressed as a linear combination of two channels: the universal cloner, which broadcasts the target quantum state, and the universal antisymmetrizer, which reduces broadcasting error. We implement both channels within the same circuit and demonstrate that the universal cloner is the closest physical map to VQB. In addition, we show how the universal antisymmetrizer can be utilized to mitigate imperfections in the cloner, enabling near-ideal fidelity. Our method is applicable to broadcasting quantum systems of any dimension.

quant-ph↗

arXiv2025

Quantum Causal Inference with Extremely Light Touch

We give a causal inference scheme using quantum observations alone for a case with both temporal and spatial correlations: a bipartite quantum system with measurements at two times. The protocol determines compatibility with 5 causal structures distinguished by the direction of causal influence and whether there are initial correlations. We derive and exploit a closed-form expression for the space-time pseudo-density matrix (PDM) for many times and qubits. This PDM can be determined by light-touch coarse-grained measurements alone. We prove that if there is no signalling between two subsystems, the reduced state of the PDM cannot have negativity, regardless of initial spatial correlations. In addition, the protocol exploits the time asymmetry of the PDM to determine the temporal order. The protocol succeeds for a state with coherence undergoing a fully decohering channel. Thus coherence in the channel is not necessary for the quantum advantage of causal inference from observations alone.

quant-ph↗

arXiv2024

Experimental demonstration of quantum causal inference via noninvasive measurements

We probe the foundations of causal structure inference experimentally. The causal structure concerns which events influence other events. We probe whether causal structure can be determined without intervention in quantum systems. Intervention is commonly used to determine causal structure in classical scenarios, but in the more fundamental quantum theory, there is evidence that measurements alone, even coarse-grained measurements, can suffice. We demonstrate the experimental discrimination between several possible causal structures for a bipartite quantum system at two times, solely via coarse-grained projective measurements. The measurements are implemented by an approach known as scattering circuits in a nuclear magnetic resonance platform. Using recent analytical methods the data thus gathered is sufficient to determine the causal structure. Coarse-grained projective measurements disturb the quantum state less than fine-grained projective measurements and much less than interventions that reset the system to a fixed state.

quant-ph↗

arXiv2024

Quantum causal inference via scattering circuits in NMR

We report NMR scattering circuit experiments that reveal causal structure. The scattering circuit involves interacting a probe qubit with the system of interest and finally measuring the probe qubit. The scattering circuit thereby implements a coarse-grained projective measurement. Causal structure refers to which events influence others and in the quantum case corresponds to different quantum circuit structures. In classical scenarios, intervention is commonly used to infer causal structure. In this quantum scenario of a bipartite system at two times, we demonstrate via scattering circuit experiments that coarse-grained measurements alone suffice for determining the causal structure. The experiment is undertaken by manipulating the nuclear spins of four Carbon-13 atoms in crotonic acid. The data analysis determines the compatibility of the data with given causal structures via representing the data as a pseudo density matrix (PDM) and analysing properties of the PDM. We demonstrate the successful identification of the causal structure for partial swap channels and fully decohering channels.

quant-ph↗

arXiv2024

Certifying Quantum Temporal Correlation via Randomized Measurements: Theory and Experiment

We consider the certification of temporal quantum correlations using the pseudo-density matrix (PDM), an extension of the density matrix to the time domain, where negative eigenvalues are key indicators of temporal correlations. Conventional methods for detecting these correlations rely on PDM tomography, which often involves excessive redundant information and requires exponential resources. In this work, we develop an efficient protocol for temporal correlation detection by virtually preparing the PDM within a single time slice and estimating its second-order moments using randomized measurements. Through sample complexity analysis, we demonstrate that our protocol requires only a constant number of measurement bases, making it particularly advantageous for systems utilizing ensemble average measurements, as it maintains constant runtime complexity regardless of the number of qubits. We experimentally validate our protocol on a nuclear magnetic resonance platform, a typical thermodynamic quantum system, where the experimental results closely align with theoretical predictions, confirming the effectiveness of our protocol.

quant-ph↗

arXiv2024

Quantum harvester enables energy transfer without randomness transfer or dissipation

We consider a foundational question in energy harvesting: given a partly random energy source, is it possible to extract the energy without also transferring randomness or accepting another thermodynamical cost? We answer this in the positive, describing scenarios and protocols where in principle energy is extracted from a field with randomness but without any randomness being transferred, and without energy dissipation. Such protocols fundamentally outperform existing methods of rectification which dissipate power, or feedback demon-like protocols which transfer randomness to the feedback system. The protocols exploit the possibility of the harvesting system taking several trajectories that lead to the same final state at a given time. We explain why these protocols do not violate basic physical principles. A key example involves the experimentally well-established phenomenon of Rabi oscillations between energy levels, exploiting the multitude of rotation axes in the state space that take the lower energy state to the excited state. The quantum system is deterministically excited to the highest energy level after interacting with the source for a fixed amount of time, irrespective of the random initial phase of the external potential.

quant-ph↗

arXiv2024

Experimental Validation of Enhanced Information Capacity by Quantum Switch in Accordance with Thermodynamic Laws

We experimentally probe the interplay of the quantum switch with the laws of thermodynamics. The quantum switch places two channels in a superposition of orders and may be applied to thermalizing channels. Quantum-switching thermal channels has been shown to give apparent violations of the second law. Central to these apparent violations is how quantum switching channels can increase the capacity to communicate information. We experimentally show this increase and how it is consistent with the laws of thermodynamics, demonstrating how thermodynamic resources are consumed. We use a nuclear magnetic resonance approach with coherently controlled interactions of nuclear spin qubits. We verify an analytical upper bound on the increase in capacity for channels that preserve energy and thermal states, and demonstrate that the bound can be exceeded for an energy-altering channel. We show that the switch can be used to take a thermal state to a state that is not thermal, whilst consuming free energy associated with the coherence of a control system. The results show how the switch can be incorporated into quantum thermodynamics experiments as an additional resource.

quant-ph↗

arXiv2024

Inferring the arrow of time in quantum spatiotemporal correlations

We consider how to tell the time-ordering associated with measurement data from quantum experiments at two times and any number of qubits. We define an arrow of time inference problem. We consider conditions on the initial and final states that are symmetric or asymmetric under time reversal. We represent the spatiotemporal measurement data via the pseudo density matrix space-time state. There is a forward process which is CPTP and a reverse process which is obtained via a novel recovery map based on inverting unitary dilations. For asymmetric conditions, the protocol determines whether the data is consistent with the unitary dilation recovery map or the CPTP map. For symmetric conditions, the recovery map yields a valid CPTP map and the experiment may have taken place in either direction. We also discuss adapting the approach to the Leifer-Spekkens or Process matrix space-time states.

quant-ph↗

arXiv2024

Unification of spatiotemporal quantum formalisms: mapping between process and pseudo-density matrices via multiple-time states

We consider the relation between three different approaches to defining quantum states across several times and locations: the pseudo-density matrix (PDM), the process matrix, and the multiple-time state approaches. Previous studies have shown that bipartite two-time states can reproduce the statistics of bipartite process matrices. Here, we show that the operational scenarios underlying two-time states can be represented as PDMs, and thereby construct a mapping from process matrices with measurements to PDMs. The existence of this mapping implies that PDMs can, like the process matrix, model processes with indefinite causal orders. The results contribute to the unification of quantum models of spatiotemporal states.

quant-ph↗

arXiv2023

Conformally Invariant Brans-Dicke Loop Quantum Cosmology: A Quantum Geometric Model of Linking Theory

The loop quantization of the conformal Brans-Dicke cosmology is explored in the spatially flat and Bianchi-I setting. The scalar and conformal constraints governing the canonical model are quantized using the loop techniques. The physical Hilbert space of quantum spacetimes satisfying both quantum constraints is then obtained by incorporating the quantum geometric features. The Schrödinger cosmic evolutions are derived with the relational Heisenberg observables describing the dynamical degrees of freedom with respect to the chosen reference degrees of freedom, with the latter providing the physical coordinates for the spatial hypersurfaces and the conformal scales. We show that the emerging Schrödinger theories contain not only the loop quantum cosmology of GR, but also that of the so-called shape dynamics. The exact dictionary between the two theories is achieved via the underlying physical Hilbert space possessing the additional (loop-corrected) conformal symmetry.

gr-qc↗

arXiv2023

Bound on annealing performance from stochastic thermodynamics, with application to simulated annealing

Annealing is the process of gradually lowering the temperature of a system to guide it towards its lowest energy states. In an accompanying paper [Luo et al. Phys. Rev. E 108, L052105 (2023)], we derived a general bound on annealing performance by connecting annealing with stochastic thermodynamics tools, including a speed-limit on state transformation from entropy production. We here describe the derivation of the general bound in detail. In addition, we analyze the case of simulated annealing with Glauber dynamics in depth. We show how to bound the two case-specific quantities appearing in the bound, namely the activity, a measure of the number of microstate jumps, and the change in relative entropy between the state and the instantaneous thermal state, which is due to temperature variation. We exemplify the arguments by numerical simulations on the SK model of spin-glasses.

cond-mat.stat-mech↗

arXiv2023

General limit to thermodynamic annealing performance

Annealing has proven highly successful in finding minima in a cost landscape. Yet, depending on the landscape, systems often converge towards local minima rather than global ones. In this Letter, we analyse the conditions for which annealing is approximately successful in finite time. We connect annealing to stochastic thermodynamics to derive a general bound on the distance between the system state at the end of the annealing and the ground state of the landscape. This distance depends on the amount of state updates of the system and the accumulation of non-equilibrium energy, two protocol and energy landscape dependent quantities which we show are in a trade-off relation. We describe how to bound the two quantities both analytically and physically. This offers a general approach to assess the performance of annealing from accessible parameters, both for simulated and physical implementations.

cond-mat.stat-mech↗

arXiv2023

Thermodynamics of quantum switch information capacity activation

We address a new setting where the second law is under question: thermalizations in a quantum superposition of causal orders, enacted by the so-called quantum switch. This superposition has been shown to be associated with an increase in the communication capacity of the channels, yielding an apparent violation of the data-processing inequality and a possibility to separate hot from cold. We analyze the thermodynamics of this information capacity increasing process. We show how the information capacity increase is compatible with thermodynamics. We show that there may indeed be an information capacity increase for consecutive thermalizations obeying the first and second laws of thermodynamics if these are placed in an indefinite order and moreover that only a significantly bounded increase is possible. The increase comes at the cost of consuming a thermodynamic resource, the free energy of coherence associated with the switch.

quant-ph↗

arXiv2020

Circuit complexity for generalised coherent states in thermal field dynamics

In this work, we study the circuit complexity for generalized coherent states in thermal systems by adopting the covariance matrix approach. We focus on the coherent thermal (CT) state, which is non-Gaussian and has a nonvanishing one-point function. We find that even though the CT state cannot be fully determined by the symmetric two-point function, the circuit complexity can still be computed in the framework of the covariance matrix formalism by properly enlarging the covariance matrix. Now the group generated by the unitary is the semiproduct of translation and the symplectic group. If the reference state is Gaussian, the optimal geodesic is still be generated by a horizontal generator such that the circuit complexity can be read from the generalized covariance matrix associated to the target state by taking the cost function to be $F_2$. For a single harmonic oscillator, we discuss carefully the complexity and its formation in the cases that the reference states are Gaussian and the target space is excited by a single mode or double modes. We show that the study can be extended to the free scalar field theory.

hep-th↗