We investigate the amount of communication that must augment classical local hidden variable models in order to simulate the behaviour of entangled quantum systems. We consider the scenario where a bipartite measurement is given from a set of possibilities and the goal is to obtain exactly the same correlations that arise when the actual quantum system is measured. We show that, in the case of a single pair of qubits in a Bell state, a constant number of bits of communication is always sufficient--regardless of the number of measurements under consideration. We also show that, in the case of a system of n Bell states, a constant times 2^n bits of communication are necessary.
This note shows how quantum entanglement may be simulated in classical computing. The simulated entanglement protocol is implemented using oblivious transfer in the simplest case and other many-to-one mappings in more general cases. For the case where the mapping is of order k, we prove a theorem that gives us the function of the entangled state. A useful generalization beyond this research will be the implementation of quantum states with arbitrary probability amplitude functions.
Entanglement appears in two different ways in quantum mechanics, namely as a property of states and as a property of measurement outcomes in joint measurements. By combining these two aspects of entanglement, it is possible to generate nonlocality between particles that never interacted, using the protocol of entanglement swapping. We investigate the communication cost of classically simulating this process. While the communication cost of simulating nonlocal correlations of entangled states appears to be generally quite low, we show here that infinite communication is required to simulate ent…
We study the time evolution of the amount of entanglement generated by one dimensional spin-1/2 Ising-type Hamiltonians composed of many-body interactions. We investigate sets of states randomly selected during the time evolution generated by several types of time-independent Hamiltonians by analyzing the distributions of the amount of entanglement of the sets. We compare such entanglement distributions with that of typical entanglement, entanglement of a set of states randomly selected from a Hilbert space with respect to the unitarily invariant measure. We show that the entanglement distribu…
Simulating quantum systems constructively furthers our understanding of qualitative and quantitative features which may be analytically intractable. In this letter, we directly simulate and explore the entanglement structure present in a paradigmatic example of quantum information: Shor's wavefunction. The methodology employed is a dynamical tensor network which is initially constructed as a tree tensor network, inspired by the modular exponentiation quantum circuit, and later efficiently mapped to a matrix product state. Utilizing the Schmidt number as a local entanglement metric, our constru…
The fact that the computational cost of simulating a many-body quantum system on a computer increases with the amount of entanglement has been considered as the major bottleneck for simulating its out-of-equilibrium dynamics. Some aspects of the dynamics are, nevertheless, robust under appropriately devised approximations. Here we present a possible algorithm that allows to systematically approximate the equilibration value of local operators after a quantum quench. At the core of our proposal there is the idea to transform entanglement between distant parts of the system into mixture, and at …
We investigate the correlations between different bipartitions of an exactly solvable one-dimensional many-body Moshinsky model consisting of Nn "nuclei" and Ne "electrons". We study the dependence of entanglement on the inter-particle interaction strength, on the number of particles, and on the particle masses. Consistent with kinematic intuition, the entanglement between two subsystems vanishes when the subsystems have very different masses, while it attains its maximal value for subsystems of comparable mass. We show how this entanglement feature can be inferred by means of the Born-Oppenhe…
Exactly solvable many-body systems are few and far between, and the utility of approximate methods cannot be overestimated. Entanglement mean field theory is an approximate method to handle such systems. While mean field theories reduce the many-body system to an effective single-body one, entanglement mean field theory reduces it to a two-body system. And in contrast to mean field theories where the self-consistency equations are in terms of single-site physical parameters, those in entanglement mean field theory are in terms of both single- and two-site parameters. Hitherto, the theory has b…
The evolution of entanglement in a 3-spin chain with nearest-neighbor Heisenberg-XY interactions for different initial states is investigated here. In an NMR experimental implementation, we generate multipartite entangled states starting from initial separable pseudo-pure states by simulating nearest-neighbor XY interactions in a 3-spin linear chain of nuclear spin qubits. For simulating XY interactions, we follow algebraic method of Zhang et al. [Phys. Rev. A 72, 012331 (2005)]. Bell state between end qubits has been generated by using only the unitary evolution of the XY Hamiltonian. For gen…
We investigate the performance of superconducting flux qubits for the adiabatic quantum simulation of long distance entanglement (LDE), namely a finite ground-state entanglement between the end spins of a quantum spin chain with open boundary conditions. As such, LDE can be considered an elementary precursor of edge modes and topological order. We discuss two possible implementations which simulate open chains with uniform bulk and weak end bonds, either with Ising or with XX nearest-neighbor interactions. In both cases we discuss a suitable protocol for the adiabatic preparation of the ground…
We investigate the entanglement-related features of the eigenstates of two exactly soluble atomic models: a one-dimensional three-electron Moshinsky model, and a three-dimensional two-electron Moshinsky system in an external uniform magnetic field. We analytically compute the amount of entanglement exhibited by the wavefunctions corresponding to the ground, first and second excited states of the three-electron model. We found that the amount of entanglement of the system tends to increase with energy, and in the case of excited states we found a finite amount of entanglement in the limit of va…
We show how phase-space simulations of Gaussian quantum states in a photonic network permit verification of measurable correlations of Gaussian boson sampling (GBS) quantum computers. Our results agree with experiments for up to 100-th order correlations, provided decoherence is included. We extend this to more than 16,000 modes, and describe how to simulate genuine multipartite entanglement.
A genuine tripartite entanglement monotone is presented for $(2\otimes 2\otimes n)$-dimensional tripartite pure states by introducing a new entanglement measure for bipartite pure states. As an application, we consider the genuine tripartite entanglement of the ground state of the exactly solvable isotropic spin-1/2 chain with three-spin interaction. It is shown that the singular behavior of the genuine tripartite entanglement exactly signals a quantum phase transition.
We have studied dynamical properties of an exactly solvable quantum coupled double-well (DW) systems with Razavy's hyperbolic potential. With the use of four kinds of initial wavepackets, the correlation function $Γ(t)$ and the concurrence $C(t)$ which is a typical measure of the entanglement in two qubits, are calculated. We obtain the orthogonality time $τ$ which signifies a time interval for an initial state to evolve to its orthogonal state, and the temporal average of $C(t)$, $C_{av}$ $(=\sqrt{\langle C(t)^2 \rangle})$. The coupling dependence of $τ$ and the concurrence [$C_{av}$ or $C(0)…
The communication cost of simulating probability distributions obtained by measuring quantum states is a natural way to quantify quantum non-locality. While much is known in the case of bipartite entanglement, little has been done in the multipartite setting. In this paper, we focus on the GHZ state. Specifically, equatorial measurements lead to correlations similar to the ones obtained with Bell states. We give a protocol to simulate these measurements on the n-partite GHZ state using O(n^2) bits of communication on average.
In the quantum world correlations can take form of entanglement which is known to be monogamous. In this work we show that another type of correlations, indistinguishability, is also restricted by some form of monogamy. Namely, if particles A and B simulate bosons, then A and C cannot perfectly imitate fermions. Our main result consists in demonstrating to what extent it is possible.
We give a classical protocol to exactly simulate quantum correlations implied by a spin $s$ singlet state for the infinite sequence of \textit{integer} spin $s={1,4,13,...}$ satisfying $(2s+1)=3^{n}$,where $n$ is a positive integer.The required amount of communication is found to increase as $log_{3}d^{2}$ where $d=2s+1$ is the dimension of the spin $s$ Hilbert space.
Indian Institute of Engineering Science And Technology（印度工程科学理工学院）；University of Waterloo（滑铁卢大学）；Institute for Quantum Computing, University of Waterloo（滑铁卢大学量子计算研究所）；Indian Institute of Science Education and Research, Thiruvananthapuram（特鲁万纳姆拉浦尔印度科学教育与研究学院）；Wilfrid Laurier University（威尔弗里德·劳雷尔大学）
本文提出一种经典-量子混合方法，利用NISQ量子计算机模拟量子 kicked top 的混沌行为，展示了其在不同混沌参数范围内的实验探索能力，并验证了纠缠与去局部化的理论预测。
Quantum many-body systems out of equilibrium pose some of the most intriguing questions in physics. Unfortunately, numerically keeping track of time evolution of states under Hamiltonian dynamics constitutes a severe challenge for all known methods. Prominently, tensor network methods are marred by an entanglement blowup, which allows to simulate systems following global quenches only to constant time. In this work, we present a scheme that allows to significantly extend the simulation time for interacting fermionic or equivalent spin systems. In the past when keeping track of evolution in one…
In this paper we investigate a open two-qubit model whose dynamics is not exactly solvable. When the initial state is the maximum entangled state, as the exactly solvable open two-qubit model [D. Tolkunov and V. Privman, Phys. Rev. A 71, 060308(R) (2005)], the decay of entanglement of formation of the model, expressed by concurrence is also governed by the product of suppression factors describing decoherence of the subsystems (qubits). However, if the initial state is not the maximum entangled state, its concurrence will decrease faster than the product of the suppression factors describing d…
We study multipartite entanglement measures for a one-dimensional Ising chain that is capable of showing both integrable and nonintegrable behaviour. This model includes the kicked transverse Ising model, which we solve exactly using the Jordan-Wigner transform, as well as nonintegrable and mixing regimes. The cluster states arise as a special case and we show that while one measure of entanglement is large, another measure can be exponentially small, while symmetrizing these states with respect to up and down spins, produces those with large entanglement content uniformly. We also calculate e…
We show exactly that the $α$th power of Bures measure of entanglement and geometric measure of entanglement, as special case of entanglement measures based on fidelity, obey a class of general monogamy inequalities in an arbitrary multiqubit mixed state for $α\geq1$.
We compute the entanglement entropy of a wide class of exactly solvable models which may be characterized as describing matter coupled to gauge fields. Our principle result is an entanglement sum rule which states that entropy of the full system is the sum of the entropies of the two components. In the context of the exactly solvable models we consider, this result applies to the full entropy, but more generally it is a statement about the additivity of universal terms in the entropy. We also prove that the Renyi entropy is exactly additive and hence that the entanglement spectrum factorizes. …
For certain joint measurements on a pair of spatially separated particles, we ask how much entanglement is needed to carry out the measurement exactly. For a class of orthogonal measurements on two qubits with partially entangled eigenstates, we present upper and lower bounds on the entanglement cost. The upper bound is based on a recent result by D. Berry [Phys. Rev. A 75, 032349 (2007)]. The lower bound, based on the entanglement production capacity of the measurement, implies that for almost all measurements in the class we consider, the entanglement required to perform the measurement is s…
We study the non-Markovian effects on the dynamics of entanglement in an exactly-solvable model that involves two independent oscillators each coupled to its own stochastic noise source. First, we develop Lie algebraic and functional integral methods to find an exact solution to the single-oscillator problem which includes an analytic expression for the density matrix and the complete statistics, i.e., the probability distribution functions for observables. For long bath time-correlations, we see non-monotonic evolution of the uncertainties in observables. Further, we extend this exact solutio…
We exactly evaluate the entanglement of a six vertex and a nine vertex graph states which correspond to non ''two-colorable'' graphs. The upper bound of entanglement for five vertices ring graph state is improved to 2.9275, less than upper bound determined by LOCC. An upper bound of entanglement is proposed based on the definition of graph state.
The divergence in the interaction term of the Calogero model can be prevented introducing a cutoff length parameter, this modification leads to a quasi-exactly solvable model whose eigenfunctions can be written in terms of Heun's polynomials. It is shown both, analytical and numerically. that the reduced density matrix obtained tracing out one particle from the two-particle density operator can be obtained exactly as well as its entanglement spectrum. The number of non-zero eigenvalues in these cases is finite. Besides, it is shown that taking the limit in which the cutoff distance goes to zer…
It is impossible to discriminate four Bell states through local operations and classical communication (LOCC), if only one copy is provided. To complete this task, two copies will suffice and be necessary. When $n$ copies are provided, we show that the distillable entanglement is exactly $n-2$.
We implement the discrete-time quantum walk model using the continuous-time evolution of the Hamiltonian that includes both the shift and the coin generators. Based on the Trotter-Suzuki first-order approximation, we consider an optimization problem in which the Hellinger distance between the walker probability distributions resulted from the evolution of such Hamiltonian and the quantum walk dynamics is minimized. The phase space implementation of the quantum walk is considered where the walker state is encoded on the coherent state of a resonator and the coin on the two-level state of a qubi…
Recently, constant-depth quantum circuits are proved more powerful than their classical counterparts at solving certain problems, e.g., the two-dimensional (2D) hidden linear function (HLF) problem regarding a symmetric binary matrix. To further investigate the boundary between classical and quantum computing models, in this work we propose a high-performance two-stage classical scheme to solve a full-sampling variant of the 2D HLF problem, which combines traditional classical parallel algorithms and a gate-based classical circuit model together for exactly simulating the target shallow quantu…
By exactly solving the underlying Schödinger equation we show that one and the same resonant cavity can be used as a catalyst to maximally entangle atoms of two nonidentical groups. The generation scheme is realistic and advantageous in the sense that it is deterministic, efficient, scalable and immune from decoherence effects.
The state evolution of the initial optical \textit{noon} state is investigated. The residue entanglement of the state is calculated after it is damped by amplitude and phase damping. The relative entropy of entanglement of the damped state is exactly obtained. The performance of direct application of the damped \textit{noon} state is compared with that of firstly distilling the docoherence damped state then applying it in measurement.
In closed systems, dynamical symmetries lead to conservation laws. However, conservation laws are not applicable to open systems that undergo irreversible transformations. More general selection rules are needed to determine whether, given two states, the transition from one state to the other is possible. The usual approach to the problem of finding such rules relies heavily on group theory and involves a detailed study of the structure of the respective symmetry group. We approach the problem in a completely new way by using entanglement to investigate the asymmetry properties of quantum sta…
We prove, in a multipartite setting, that it's always feasible to exactly transform a genuinely $m$-partite entangled state with sufficient many copies to any other $m$-partite state via local quantum operation and classical communication. This result affirms the comparability of multipartite pure entangled states.
In this paper we study the quantum phase transition and entanglement in s1=1/2 and s2=1 spin pair system by the exact diagonalization method. We show that, for this exactly solvable quantum bi-spin system, entanglement appears before quantum phase transition and disappears after it. Moreover, we show that the von Neumann entropy, as a measure of entanglement, can reveal quantum phase transition in this system.
Quantum entanglement is crucial for simulating and understanding exotic physics of strongly correlated many-body systems, such as high--temperature superconductors, or fractional quantum Hall states. The entanglement of non-identical particles exhibits richer physics of strong many-body correlations and offers more opportunities for quantum computation, especially with neutral atoms where in contrast to ions the interparticle interaction is widely tunable by Feshbach resonances. Moreover, the inter-species entanglement forms a basis for the properties of various compound systems, ranging from …
A bipartite quantum state (for two systems in any dimensions) can be decomposed as a superposition of many components. For a superposition of more than two components we prove that there is a bound of the entanglement of the superposition state which can be expressed according to entanglements of its component states. Especially, if the component states are mutually bi-orthogonal, the entanglement of the superposition state can be exactly given in terms of the entanglements of the states being superposed.
With the goal of gaining a deeper understanding of quantum non-locality, we decompose quantum correlations into more elementary non-local correlations. We show that the correlations of all pure entangled states of two qubits can be simulated without communication, hence using only non-signaling resources. Our simulation model works in two steps. First, we decompose the quantum correlations into a local and a non-local part. Second, we present a model for simulating the nonlocal part using only non-signaling resources. In our model partially entangled states require more nonlocal resources than…
In this paper, we consider some frustrated spin models for which the ground states are known exactly. The concurrence, a measure of the amount of entanglement can be calculated exactly for entangled spin pairs. Quantum phase transitions involving macroscopic magnetization changes at critical values of the magnetic field are accompanied by macroscopic jumps in the (T=0) entanglement. A specific example is given in which magnetization plateaus give rise to a plateau structure in the amount of entanglement associated with nearest-neighbour bonds. We further show that macroscopic entanglement chan…
We show that for tripartite quantum pure states of qubits, all the kinds of entanglement in terms of SLOCC classification are experimentally measurable by simple projective measurements, provided that four copies of the composite quantum system are available. In particular, the entanglement of reduced density matrices, even though they are mixed states, can be exactly determined in experiment. Concurrence of assistance is also shown to be measurable by introducing an interesting equations with explicit physical meanings.
The phenomenon of quantum entanglement is explained in a way which is fully consistent with Einstein's Special Theory of Relativity. A subtle flaw is identified in the logic supporting the view that Bell's Inequality precludes all local hidden-variable theories, and it is shown how EPR-type experiments can be constructed to produce statistical correlation results in a purely classical manner which match exactly the predictions made by quantum theory.
Two qubit density matrices, which are of X-shape, are a natural generalization of Bell Diagonal States (BDSs) recently simulated on the IBM quantum device. We generalize the previous results and propose a quantum circuit for simulation of a general two qubit X-state, implement it on the same quantum device, and study its entanglement for several values of the extended parameter space. We also show that their X-shape is approximately robust against noisy quantum gates. To further physically motivate this study, we invoke the two-spin Heisenberg XYZ system and show that for a wide class of initi…
It is possible to construct a classical, macroscopic system which has a mathematical structure that is exactly the same as that of a quantum mechanical system and which can be put into a state which is identical to quantum mechanical entanglement. This paper presents a simple example, including a way in which the system can be measured to violate Bell's inequalities. This classical simulation of a quantum system allows us to visualize entanglement and also helps us to see what aspects of quantum mechanical systems are truly nonclassical.
Two dual questions in quantum information theory are to determine the communication cost of simulating a bipartite unitary gate, and to determine their communication capacities. We present a bipartite unitary gate with two surprising properties: 1) simulating it with the assistance of unlimited EPR pairs requires far more communication than with a better choice of entangled state, and 2) its communication capacity is far lower than its capacity to create entanglement. This suggests that 1) unlimited EPR pairs are not the most general model of entanglement assistance for two-party communication…
We note that massless fields within the future and past light cone may be quantized as independent systems. We show that the vacuum is an entangled state of these systems, exactly mirroring the known entanglement between the spacelike separated Rindler wedges. We describe a detector which exhibits a thermal response to the vacuum when switched on at t=0. The feasibility of experimentally detecting this effect is discussed.
We calculate the entanglement-assisted and unassisted channel capacities of an exactly solvable spin star system, which models the quantum dephasing channel. The capacities for this non-Markovian model exhibit a strong dependence on the coupling strengths of the bath spins with the system, the bath temperature, and the number of bath spins. For equal couplings and bath frequencies, the channel becomes periodically noiseless.
Entanglement is believed to be crucial in macroscopic physical systems for understanding the collective quantum phenomena such as quantum phase transitions. We start from and solve exactly a novel Yang-Baxter spin-1/2 chain model with inhomogeneous and anisotropic short-range interactions. For the ground state, we show the behavior of neighboring entanglement in the parameter space and find that the inhomogeneous coupling strengths affect entanglement in a distinctive way from the homogeneous case, but this would not affect the coincidence between entanglement and quantum criticality.
BosonSampling is a well-defined scheme for demonstrating quantum supremacy with photons in near term. Although relying only on multi-photon interference in nonadaptive linear-optical networks, it is hard to simulate classically. Here we study BosonSampling using matrix product states, a powerful method from quantum many-body physics. This method stores the instantaneous quantum state during the evolution of photons in the optical quantum circuit, which allows us to reveal the dynamical features of single photons in BosonSampling devices, such as entanglement entropy growth. We show the flexibl…
