Composite Quantum Systems Research Articles

Fast generation of entanglement between coupled spins using optimization and deep learning methods

Coupled spins form composite quantum systems which play an important role in many quantum technology applications, with an essential task often being the efficient generation of entanglement between two constituent qubits. The simplest such system is a pair of spins-1/2 coupled with Ising interaction, and in previous works various quantum control methods such as adiabatic processes, shortcuts to adiabaticity and optimal control have been employed to quickly generate there one of the maximally entangled Bell states. In this study, we use machine learning and optimization methods to produce maximally entangled states in minimum time, with the Rabi frequency and the detuning used as bounded control functions. We do not target a specific maximally entangled state, like the preceding studies, but rather find the controls which maximize the concurrence, leading thus automatically the system to the closest such state in shorter time. By increasing the bounds of the control functions we observe that the corresponding optimally selected maximally entangled state also changes and the necessary time to reach it is reduced. The present work demonstrates also that machine learning and optimization offer efficient and flexible techniques for the fast generation of entanglement in coupled spin systems, and we plan to extent it to systems involving more spins, for example spin chains.

Quantum nonlocality of density operators and their corresponding density matrices

Quantum nonlocality represents correlations between subsystems of a composite quantum system, usually including Bell nonlocality, steerability, and entanglement. According to the hypothesis of quantum mechanics, states of a quantum system Q described by a d-dimensional Hilbert space are denoted by density operators acting on . Under a basis e for the Hilbert space , every abstract density operator ρ of the system AB corresponds to a density matrix ρ e , which is a state of the complex Hilbert space . In this work, we discuss the consistency of quantum nonlocality of density operators ρ and their corresponding density matrices ρ e under the chosen basis e. It is proved that only when a basis e is a product one, a density operator ρ is entangled (respectively, Bell nonlocal, steerable) if and only if its density matrix ρ e is entangled (respectively, Bell nonlocal, steerable).

Moment expansion method for composite open quantum systems including a damped oscillator mode

Moment expansion method for composite open quantum systems including a damped oscillator mode

Adiabatic elimination for composite open quantum systems: Reduced-model formulation and numerical simulations

Adiabatic elimination for composite open quantum systems: Reduced-model formulation and numerical simulations

Extracting Bayesian networks from multiple copies of a quantum system

Despite their theoretical importance, dynamic Bayesian networks associated with quantum processes are currently not accessible experimentally. We here describe a general scheme to determine the multi-time path probability of a Bayesian network based on local measurements on independent copies of a composite quantum system combined with postselection. We further show that this protocol corresponds to a nonprojective measurement. It thus allows the investigation of the multi-time properties of a given local observable while fully preserving all its quantum features.

Entangling capacity of operators

Given a unitary operator U acting on a composite quantum system what is the entangling capacity of U? This question is investigated using a geometric approach. The entangling capacity, defined via metrics on the unitary groups, leads to a minimax problem. The dual, a maximin problem, is investigated in parallel and yields some familiar entanglement measures. A class of entangling operators, called generalized control operators is defined. The entangling capacities and other properties for this class of operators is studied.

Indistinguishable entangled fermions: basics and future challenges.

The study of entanglement in systems composed of identical particles raises interesting challenges with far-reaching implications in both, our fundamental understanding of the physics of composite quantum systems, and our capability of exploiting quantum indistinguishability as a resource in quantum information theory. Impressive theoretical and experimental advances have been made in the last decades that bring us closer to a deeper comprehension and to a better control of entanglement. Yet, when it involves composites of indistinguishable quantum systems, the very meaning of entanglement, and hence its characterization, still finds controversy and lacks a widely accepted definition. The aim of the present paper is to introduce, within an accessible and self-contained exposition, the basic ideas behind one of the approaches advanced towards the construction of a coherent definition of entanglement in systems of indistinguishable particles, with focus on fermionic systems. We also inquire whether the corresponding tools developed for studying entanglement in identical-fermion systems can be exploited when analysing correlations in distinguishable-party systems, in which the complete information of the individual parts is not available. Further, we open the discussion on the broader problem of constructing a suitable framework that accommodates entanglement in the presence of generalized statistics. This article is part of the theme issue 'Identity, individuality and indistinguishability in physics and mathematics'.

Certifying genuine multipartite nonlocality without inequality in quantum networks

Genuine multipartite nonlocality constitutes the strongest form of nonlocality, which is a key resource for many quantum communication and computational tasks. Standard methods for certifying nonlocality often require accessing contradictions in paradoxes or violations of Bell inequalities for composite quantum systems. However, the existing approaches become infeasible and cannot be adopted straightforwardly for a quantum network scenario, which usually possesses complex topological structure and many independent quantum sources. We have developed a simple and customizable strategy to achieve scalable, efficient, and flexible characterizations for various typical quantum network scenarios. The subtle something-versus-nothing contradiction in Hardy-type paradoxes without inequality allows us to substantiate genuine multipartite nonlocality in general quantum networks. Examples range from chain-type network to star-type network, with source connections of any pure entangled permutation symmetric multiqubit states, entangled two-qubit states, etc. The tools extend significantly our ability to certify genuine multipartite nonlocality in state-of-the-art network situations, and make a prominent step forward toward deeper understanding and practical depiction of quantum networks.

A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature

This paper establishes new connections between many-body quantum systems, One-body Reduced Density Matrices Functional Theory (1RDMFT) and Optimal Transport (OT), by interpreting the problem of computing the ground-state energy of a finite-dimensional composite quantum system at positive temperature as a non-commutative entropy regularized Optimal Transport problem. We develop a new approach to fully characterize the dual-primal solutions in such non-commutative setting. The mathematical formalism is particularly relevant in quantum chemistry: numerical realizations of the many-electron ground-state energy can be computed via a non-commutative version of Sinkhorn algorithm. Our approach allows to prove convergence and robustness of this algorithm, which, to our best knowledge, were unknown even in the two marginal case. Our methods are based on a priori estimates in the dual problem, which we believe to be of independent interest. Finally, the above results are extended in 1RDMFT setting, where bosonic or fermionic symmetry conditions are enforced on the problem.

Principle of Information Causality Rationalizes Quantum Composition.

The principle of information causality, proposed as a generalization of no signaling principle, has efficiently been applied to outcast beyond quantum correlations as unphysical. In this Letter, we show that this principle, when utilized properly, can provide physical rationale toward structural derivation of multipartite quantum systems. In accordance with the no signaling condition, the state and effect spaces of a composite system can allow different possible mathematical descriptions, even when descriptions for the individual systems are assumed to be quantum. While in one extreme, namely, the maximal tensor product composition, the state space becomes quite exotic and permits composite states that are not allowed in quantum theory, the other extreme-minimal tensor product composition-contains only separable states, and the resulting theory allows only Bell local correlation. As we show, none of these compositions is commensurate with information causality, and hence cannot be the bona-fide description of nature. Information causality therefore promises an information-theoretical derivation of self duality of the state and effect cones for composite quantum systems.

Contextuality in composite systems: the role of entanglement in the Kochen-Specker theorem

The Kochen–Specker (KS) theorem reveals the nonclassicality of single quantum systems. In contrast, Bell's theorem and entanglement concern the nonclassicality of composite quantum systems. Accordingly, unlike incompatibility, entanglement and Bell non-locality are not necessary to demonstrate KS-contextuality. However, here we find that for multiqubit systems, entanglement and non-locality are both essential to proofs of the Kochen–Specker theorem. Firstly, we show that unentangled measurements (a strict superset of local measurements) can never yield a logical (state-independent) proof of the KS theorem for multiqubit systems. In particular, unentangled but nonlocal measurements—whose eigenstates exhibit ''nonlocality without entanglement"—are insufficient for such proofs. This also implies that proving Gleason's theorem on a multiqubit system necessarily requires entangled projections, as shown by Wallach [Contemp Math, 305: 291-298 (2002)]. Secondly, we show that a multiqubit state admits a statistical (state-dependent) proof of the KS theorem if and only if it can violate a Bell inequality with projective measurements. We also establish the relationship between entanglement and the theorems of Kochen–Specker and Gleason more generally in multiqudit systems by constructing new examples of KS sets. Finally, we discuss how our results shed new light on the role of multiqubit contextuality as a resource within the paradigm of quantum computation with state injection.

Any four orthogonal ququad–ququad maximally entangled states are locally markable

In quantum state discrimination, the observers are given a quantum system and aim to verify its state from the two or more possible target states. In the local quantum state marking as an extension of quantum state discrimination, there are N composite quantum systems and N possible orthogonal target quantum states. Distant Alice and Bob are asked to correctly mark the states of the given quantum systems via local operations and classical communication. Here we investigate the local state marking with N systems, N = 4, 5, 6, and 7. Therein, Alice and Bob allow for three local operations: measuring the local observable either σ z or σ x simultaneously, and entanglement swapping. It shows that, given arbitrary four systems, Alice and Bob can perform the perfect local quantum state marking. In the N = 5, 6 cases, they can perform perfect local state marking with specific target states. We conjecture the impossibility of the local quantum state marking given any seven target states since Alice and Bob cannot fulfill the task in the simplest case.

Gaussian fluctuations in the equipartition principle for Wigner matrices

Abstract The total energy of an eigenstate in a composite quantum system tends to be distributed equally among its constituents. We identify the quantum fluctuation around this equipartition principle in the simplest disordered quantum system consisting of linear combinations of Wigner matrices. As our main ingredient, we prove the Eigenstate Thermalisation Hypothesis and Gaussian fluctuation for general quadratic forms of the bulk eigenvectors of Wigner matrices with an arbitrary deformation.

Timelike correlations and quantum tensor product structure

The state space structure for a composite quantum system is postulated among several mathematically consistent possibilities that are compatible with local quantum description. For instance, unentangled Gleason's theorem allows a state space that includes density operators as a proper subset among all possible composite states. However, bipartite correlations obtained in Bell type experiments from this broader state space are in-fact quantum simulable, and hence such spacelike correlations are no good to make distinction among different compositions. In this work we analyze communication utilities of these different composite models and show that they can lead to distinct utilities in a simple communication game involving two players. Our analysis, thus, establishes that beyond quantum composite structure can lead to beyond quantum correlations in timelike scenario and hence welcomes new principles to isolate the quantum correlations from the beyond quantum ones. We also prove a no-go that the classical information carrying capacity of different such compositions cannot be more than the corresponding quantum composite systems.

Gravitational entanglement and the mass contribution of internal energy in nonrelativistic quantum systems

Recently, interest has increased in the entanglement of remote quantum particles through the Newtonian gravitational interaction, both from a fundamental perspective and as a test case for the quantization of gravity. Likewise, post-Newtonian gravitational effects in composite nonrelativistic quantum systems have been discussed, where the internal energy contributes to the mass, promoting the mass to a Hilbert space operator. Employing a modified version of a previously considered thought experiment, it can be shown that both concepts, when combined, result in inconsistencies, reinforcing the arguments for the necessity of a rigorous derivation of the nonrelativistic limit of gravitating quantum matter from first principles.

Experimental mutual coherence from separable coherent qubits

Quantum coherence is a fundamental resource in modern quantum physics with important applications in quantum technologies. In composite quantum systems, various forms of coherence emerge and play an important role, such as the global coherence, coherence of local subsystems, and the recently introduced mutual coherence. We investigate states that maximize the mutual coherence in various subspaces of the overall two-qubit Hilbert space and discover a nontrivial asymmetric optimal state in the three-dimensional subspace. We experimentally generate this optimal state from two factorized photonic qubits by a strictly incoherent probabilistic quantum operation that projects the input state onto the desired three-dimensional subspace. For comparison, we also experimentally test the preparation of states with maximal mutual coherence by unitary transformations of input product states. These proof-of-principle tests demonstrate the initial steps of control of mutual quantum coherence in qubit systems.

A roadmap for universal high-mass matter-wave interferometry

Creating quantum superposition states of bodies with increasing mass and complexity is an exciting and important challenge. Demonstrating such superpositions is vital for understanding how classical observations arise from the underlying quantum physics. Here, we discuss how recent progress in macromolecule interferometry can be combined with the state of the art in cluster physics to push the mass record for matter-wave interference with wide state separation by 3 to 4 orders of magnitude. We show how near-field interferometers in different configurations can achieve this goal for a wide range of particle materials with strongly varying properties. This universality will become important in advanced tests of wave function collapse and of other modifications of quantum mechanics, as well as in the search for light dark matter and in tests of gravity with composite quantum systems.

New phase space formulations and quantum dynamics approaches

AbstractWe report recent progress on the phase space formulation of quantum mechanics with coordinate‐momentum variables, focusing more on new theory of (weighted) constraint coordinate‐momentum phase space for discrete‐variable quantum systems. This leads to a general coordinate‐momentum phase space formulation of composite quantum systems, where conventional representations on infinite phase space are employed for continuous variables. It is convenient to utilize (weighted) constraint coordinate‐momentum phase space for representing the quantum state and describing nonclassical features. Various numerical tests demonstrate that new trajectory‐based quantum dynamics approaches derived from the (weighted) constraint phase space representation are useful and practical for describing dynamical processes of composite quantum systems in the gas phase as well as in the condensed phase.This article is categorized under: Molecular and Statistical Mechanics > Molecular Dynamics and Monte‐Carlo Methods Theoretical and Physical Chemistry > Reaction Dynamics and Kinetics Theoretical and Physical Chemistry > Statistical Mechanics

Dynamical approximations for composite quantum systems: assessment of error estimates for a separable ansatz

Numerical studies are presented to assess error estimates for a separable (Hartree) approximation for dynamically evolving composite quantum systems which exhibit distinct scales defined by their mass and frequency ratios. The relevant error estimates were formally described in our previous work Burghardt et al (2021 J. Phys. A: Math. Theor. 54 414002). Specifically, we consider a representative two-dimensional tunneling system where a double well and a harmonic coordinate are cubically coupled. The time-dependent Hartree approximation is compared with a fully correlated solution, for different parameter regimes. The impact of the coupling and the resulting correlations are quantitatively assessed in terms of a time-dependent reaction probability along the tunneling coordinate. We show that the numerical error is correctly predicted on moderate time scales by a theoretically derived error estimate.

Coupled Cluster Downfolding Theory: towards universal many-body algorithms for dimensionality reduction of composite quantum systems in chemistry and materials science

The recently introduced coupled cluster (CC) downfolding techniques for reducing the dimensionality of quantum many-body problems recast the CC formalism in the form of the renormalization procedure allowing, for the construction of effective (or downfolded) Hamiltonians in small-dimensionality sub-space, usually identified with the so-called active space, of the entire Hilbert space. The resulting downfolded Hamiltonians integrate out the external (out-of-active-space) Fermionic degrees of freedom from the internal (in-the-active-space) parameters of the wave function, which can be determined as components of the eigenvectors of the downfolded Hamiltonians in the active space. This paper will discuss the extension of non-Hermitian (associated with standard CC formulations) and Hermitian (associated with the unitary CC approaches) downfolding formulations to composite quantum systems commonly encountered in materials science and chemistry. The non-Hermitian formulation can provide a platform for developing local CC approaches, while the Hermitian one can serve as an ideal foundation for developing various quantum computing applications based on the limited quantum resources. We also discuss the algorithm for extracting the semi-analytical form of the inter-electron interactions in the active spaces.