Bipartite Quantum Systems Research Articles

Quantum null-hypothesis device-independent Schmidt number witness

We investigate the dimensionality of bipartite quantum systems by construction of a device-independent null witness test. This test assesses whether a given bipartite state conforms with the expected quantum dimension, Schmidt number, and distinguishes between real and complex spaces. By employing local measurements on each party, the proposed method aims to determine the minimal rank. By performing an experimental demonstration on IBM Quantum devices, we prove the exceptional accuracy of the test and its usefulness in diagnostics beyond routine calibrations. One of the tests shows agreement with theoretical expectations within statistical errors. However, the second test failed by more than 6 standard deviations, indicating unspecified parasitic entanglements, with no known simple origin.

Magnetic bilayer qubits: A bipartite quantum system

An exfoliated monolayer CrI3 possessing the ferromagnetic (FM) nature of out-of-plane Ising spin-up (or spin-down) electrons can be considered as a qubit with a quantum state of |ѱ>=|↑>=|0> (or |ѱ>=|↓>=|1>) due to the theory of the Bloch sphere. Therefore, here a bipartite quantum system of the antiferromagnetic (AFM) and FM bilayer CrI3 is proposed for four fundamental two-qubit (2Q) quantum states (≡|ѱѱ>) of |↑↓>=|01>, |↓↑>=|10>, |↑↑>=|00> and |↓↓>=|11>, respectively. Energy-resolved magnetic circular dichroism (MCD) spectropolarimetry was used to detect d-d transitions of the FM and AFM bilayer CrI3 for the four fundamental quantum states. The obtained MCD spectra of the d-d transitions with spin-frustration and spin-parallelism possess quantum signals of the four fundamental 2Q quantum states at θB = 0, where θB is the angle between the magnetic field and the surface normal. Hence, the bilayer CrI3 is a potential candidate for use in quatum computer.

Geometry of entanglement and separability in Hilbert subspaces of dimension up to three

We present a complete classification of the geometry of the mutually complementary sets of entangled and separable states in three-dimensional Hilbert subspaces of bipartite and multipartite quantum systems. Our analysis begins by finding the geometric structure of the pure product states in a given three-dimensional Hilbert subspace, which determines all the possible separable and entangled mixed states over the same subspace. In bipartite systems, we characterise the 14 possible qualitatively different geometric shapes for the set of separable states in any three-dimensional Hilbert subspace (5 classes which also appear in two-dimensional subspaces and were found and analysed by Boyer et al. (Phys Rev A 95:032308, 2017. https://doi.org/10.1103/PhysRevA.95.032308), and 9 novel classes which appear only in three-dimensional subspaces), describe their geometries, and provide figures illustrating them. We also generalise these results to characterise the sets of fully separable states (and hence the complementary sets of somewhat entangled states) in three-dimensional subspaces of multipartite systems. Our results show which geometrical forms quantum entanglement can and cannot take in low-dimensional subspaces.

Work and heat of a quantum system far from its equilibrium state

In this paper, we give a computational approach of work and heat for any quantum systems. We use the strategy that the part of energy exchange with the von Neumann entropy unchanging is defined as work, and the part with the von Neumann entropy changing is defined as heat. We define the work and heat and they are formulated. This method is suitable for the study of any quantum systems (not only bipartite quantum systems, but also single-body, and multi-body quantum systems). As examples, firstly we investigate a bipartite model whose dynamics can be rigorously solved by using the Bloch equation, and secondly, we study two single-body models by using the numerical method of master equation of Redfield form.

Generation of entanglement using a short-wavelength seeded free-electron laser.

Quantum entanglement between the degrees of freedom encountered in the classical world is challenging to observe due to the surrounding environment. To elucidate this issue, we investigate the entanglement generated over ultrafast timescales in a bipartite quantum system comprising two massive particles: a free-moving photoelectron, which expands to a mesoscopic length scale, and a light-dressed atomic ion, which represents a hybrid state of light and matter. Although the photoelectron spectra are measured classically, the entanglement allows us to reveal information about the dressed-state dynamics of the ion and the femtosecond extreme ultraviolet pulses delivered by a seeded free-electron laser. The observed generation of entanglement is interpreted using the time-dependent von Neumann entropy. Our results unveil the potential for using short-wavelength coherent light pulses from free-electron lasers to generate entangled photoelectron and ion systems for studying spooky action at a distance.

Exact exponent for atypicality of random quantum states

We study the properties of the random quantum states induced from the uniformly random pure states on a bipartite quantum system by taking the partial trace over the larger subsystem. Most of the previous studies have adopted a viewpoint of ‘concentration of measure’ and have focused on the behavior of the states close to the average. In contrast, we investigate the large deviation regime, where the states may be far from the average. We prove the following results: first, the probability that the induced random state is within a given set decreases no slower or faster than exponential in the dimension of the subsystem traced out. Second, the exponent is equal to the quantum relative entropy of the maximally mixed state and the given set, multiplied by the dimension of the remaining subsystem. Third, the total probability of a given set strongly concentrates around the element closest to the maximally mixed state, a property that we call conditional concentration. Along the same line, we also investigate an asymptotic behavior of coherence of random pure states in a single system with large dimensions.

Optimal quantum control of charging quantum batteries

Quantum control allows us to address the problem of engineering quantum dynamics for special purposes. While recently the field of quantum batteries has attracted much attention, optimization of their charging has not benefited from the quantum control methods. Here we fill this gap by using an optimization method. We apply for the first time the convergent iterative method for the control of the population of a bipartite quantum system in two cases, starting with a qubit-qubit case. The quantum charger-battery system is considered here, where the energy is pumped into the charger by an external classical electromagnetic field. Secondly, we systematically extend our investigation to a second case involving two harmonic oscillators in the Gaussian regime, presenting an original formulation of the method. In both cases, the charger is considered to be an open dissipative system, as its interaction with the drive may require a more pronounced exposure to general interaction with environment. A key consideration in our optimization strategy is the practical concern of turning the charging external field on and off. We find that optimizing the pulse shape yields a substantial enhancement in both the power and efficiency of the charging process compared to a sinusoidal drive. The harmonic oscillator configuration of quantum batteries is particularly intriguing, as the optimal driving pulse remains effective regardless of the environmental temperature. This study introduces a novel approach to quantum battery charging optimization, opening avenues for enhanced performance in real-world applications.

Entanglement detection in arbitrary-dimensional bipartite quantum systems through partial realigned moments

Entanglement detection in arbitrary-dimensional bipartite quantum systems through partial realigned moments

Sunburst quantum Ising model under interaction quench: Entanglement and role of initial state coherence.

We study the nonequilibrium dynamics of an isolated bipartite quantum system, the sunburst quantum Ising model, under interaction quench. The prequench limit of this model is two noninteracting integrable systems, namely a transverse Ising chain and finite number of isolated qubits. As a function of interaction strength, the spectral fluctuation property goes from Poisson to Wigner-Dyson statistics. We chose entanglement entropy as a probe to study the approach to thermalization or lack of it in postquench dynamics. In the near-integrable limit, as expected, the linear entropy displays oscillatory behavior, while in the chaotic limit it saturates. Along with the chaotic nature of the time evolution generator, we show the importance of the role played by the coherence of the initial state in deciding the nature of thermalization. We further show that these findings are general by replacing the Ising ring with a disordered XXZ model with disorder strength putting it in the many-body localized phase.

Bell nonlocality in maximal-length quantum mechanics

In this paper, we investigate the consequences of maximal length as well as minimal momentum scales on nonlocal correlations shared by two parties of a bipartite quantum system. To this aim, we rely on a general phenomenological scheme which is usually associated with the non-negligible spacetime curvature at cosmological scales, namely the extended uncertainty principle. In so doing, we find that quantum correlations are degraded if the deformed quantum mechanical model mimics a positive cosmological constant. This opens up the possibility to recover classicality at sufficiently large distances.

The Necessary and Sufficient Conditions When Global and Local Fidelities Are Equal.

In the field of quantum information theory, the concept of quantum fidelity is employed to quantify the similarity between two quantum states. It has been observed that the fidelity between two states describing a bipartite quantum system A⊗B is always less than or equal to the quantum fidelity between the states in subsystem A alone. While this fidelity inequality is well understood, determining the conditions under which the inequality becomes an equality remains an open question. In this paper, we present the necessary and sufficient conditions for the equality of fidelities between a bipartite system A⊗B and subsystem A, considering pure quantum states. Moreover, we provide explicit representations of quantum states that satisfy the fidelity equality, based on our derived results.

Improved bounds on some entanglement criteria in bipartite quantum systems

Entanglement detection is one of the core tasks in quantum information processing. Based on a broad class of informationally complete symmetric measurements, a series of separability criteria are proposed for different bipartite quantum systems using Cauchy–Schwarz inequality and ρ−ρA⊗ρB, respectively. In addition, by comparing and analyzing the existing entanglement criteria and detailed examples, it is not difficult to prove that our proposed criteria are more powerful and comprehensive in entanglement detection.

Completable sets of orthogonal product states with minimal nonlocality

Since the theory of quantum nonlocality without entanglement was proposed, great achievements have been made in the local distinguishability of bipartite orthogonal quantum states, but there are still many unresolved problems. In this paper, we first propose the concept of minimal nonlocality to characterize the lower bound of the amount of the elements contained in a nonlocal set of orthogonal product states. A nonlocal set of orthogonal product states has minimal nonlocality if and only if the set can be distinguished by local operations and classical communication (LOCC) after only a certain state of the set is removed. Then we give a novel method to construct completable sets with minimal nonlocality in bipartite quantum system. Compared with the existing results, the completable sets we construct have the least number of elements in the same quantum systems. Finally, we extend our construction method of completable nonlocal set with fewer elements in bipartite system to tripartite or even more multipartite quantum systems.

Optimal High-Dimensional Entanglement Concentration for Pure Bipartite Systems.

Considering pure quantum states, entanglement concentration is the procedure where, from N copies of a partially entangled state, a single state with higher entanglement can be obtained. Obtaining a maximally entangled state is possible for N=1. However, the associated success probability can be extremely low when increasing the system's dimensionality. In this work, we study two methods to achieve a probabilistic entanglement concentration for bipartite quantum systems with a large dimensionality for N=1, regarding a reasonably good probability of success at the expense of having a non-maximal entanglement. Firstly, we define an efficiency function Q considering a tradeoff between the amount of entanglement (quantified by the I-Concurrence) of the final state after the concentration procedure and its success probability, which leads to solving a quadratic optimization problem. We found an analytical solution, ensuring that an optimal scheme for entanglement concentration can always be found in terms of Q. Finally, a second method was explored, which is based on fixing the success probability and searching for the maximum amount of entanglement attainable. Both ways resemble the Procrustean method applied to a subset of the most significant Schmidt coefficients but obtaining non-maximally entangled states.

Isomorphism of nonlocal sets of orthogonal product states in bipartite quantum systems

Isomorphism of nonlocal sets of orthogonal product states in bipartite quantum systems

Speed limits on correlations in bipartite quantum systems

Quantum speed limit is bound on the minimum time a quantum system requires to evolve from an initial state to final state under a given dynamical process. It sheds light on how fast a desired state transformation can take place, which is pertinent for design and control of quantum technologies. In this paper, we derive speed limits on correlations such as entanglement, Bell-CHSH correlation, and quantum mutual information of quantum systems evolving under dynamical processes. Our main result is a speed limit on an entanglement monotone called negativity, which holds for arbitrary-dimensional bipartite quantum systems and processes. Another entanglement monotone which we consider is the concurrence. To illustrate the efficacy of our speed limits, we analytically and numerically compute the speed limits on the negativity, concurrence, and Bell-CHSH correlation for various quantum processes of practical interest. We are able to show that, for practical examples we have considered, some of the speed limits we derived are actually attainable and hence these bounds can be considered to be tight.

Partial transpose moments, principal minors and entanglement detection

Recently, it has been shown that locally randomized measurements can be employed to get partial transpose moments of a density matrix [Elben A., {\it et al.} Phys. Rev. Lett. {\bf 125}, 200501 (2020)]. Consequently, two general entanglement detection methods were proposed based on partial transpose moments of a density matrix [Yu X-D., {\it et al.} Phys. Rev. Lett. {\bf 127}, 060504 (2021)]. In this context, a natural question arises that how partial transpose moments are related with entanglement and with well known idea of principal minors. In this work, we analytically demonstrate that for qubit-qubit quantum systems, partial transpose moments can be expressed as simple functions of principal minors. We expect this relation to exist for every bipartite quantum systems. In addition, we have extended the idea of PT-moments for tripartite qubit systems and have shown that PT-moments can only detect the whole range of being NPT for $GHZ$ and $W$ states mixed with white noise.

Quantum-Classical Hybrid Systems and Ehrenfest's Theorem.

The conceptual analysis of quantum mechanics brings to light that a theory inherently consistent with observations should be able to describe both quantum and classical systems, i.e., quantum-classical hybrids. For example, the orthodox interpretation of measurements requires the transient creation of quantum-classical hybrids. Despite its limitations in defining the classical limit, Ehrenfest's theorem makes the simplest contact between quantum and classical mechanics. Here, we generalized the Ehrenfest theorem to bipartite quantum systems. To study quantum-classical hybrids, we employed a formalism based on operator-valued Wigner functions and quantum-classical brackets. We used this approach to derive the form of the Ehrenfest theorem for quantum-classical hybrids. We found that the time variation of the average energy of each component of the bipartite system is equal to the average of the symmetrized quantum dissipated power in both the quantum and the quantum-classical case. We expect that these theoretical results will be useful both to analyze quantum-classical hybrids and to develop self-consistent numerical algorithms for Ehrenfest-type simulations.

Local Channels under Decomposition of Quantum Gates in Bipartite Systems

For a bipartite quantum system with Hilbert space H m ⊗ H n , this paper considers a quantum channel ϕ from the system to itself which preserves the set of separable states. Within this class of quantum channels, the paper characterizes those channels which preserve the Tsallis entropy of combinations of separable states through decomposing quantum gates, where the characterization is given in terms of the action of the channel on separable states.

Experimental Activation of Strong Local Passive States with Quantum Information.

Strong local passivity is a property of multipartite quantum systems from which it is impossible to extract energy locally. Surprisingly, if the strong local passive state displays entanglement, it could be possible to locally activate energy density by adding classical communication between different partitions of the system, through so-called "quantum energy teleportation" protocols. Here, we report both the first experimental observation of local activation of energy density on an entangled state and the first realization of a quantum energy teleportation protocol using nuclear magnetic resonance on a bipartite quantum system.