Neural network representations of quantum many-body states

Machine learning is currently the most active interdisciplinary field having numerous applications;additionally,machine-learning techniques are used to research quantum many-body problems.In this study,we first propose neural network quantum states(NNQSs)with general input observables and explore a few related properties,such as the tensor product and local unitary operation.Second,we determine the necessary and sufficient conditions for the representability of a general graph state using normalized NNQS.Finally,to quantify the approximation degree of a given pure state,we define the best approximation degree using normalized NNQSs.Furthermore,we observe that some 7V-qubit states can be represented by a normalized NNQS,such as separable pure states,Bell states and GHZ states.     

Manipulating many-body quantum states via single-photon resonance

For an atomic Bose-Hubbard dimer quantum control via multiphoton processes have been investigated widely. We here explore how to manipulate the many-body quantum states via single-photon resonance by treating the periodic driving as a weak perturbation. The transition probabilities up to second-order approximation are given as functions of the driving parameters, which are considerable only for the single-photon resonance case. Due to some transition matrix elements vanishing, the first-order quantum transition obeys a selection rule. The non-forbidden transitions involve states of different entanglement entropies and all (part) of the forbidden transitions relate to the entropy balances between two states for odd (even) number of particles. The results provide a new route for manipulating many-body quantum states and entanglement entropies, and controlling the atomic tunnelings of the Bose-Hubbard dimer.     

Macroscopic quantum control of exact many-body coherent states

We demonstrate that the idea of quantum control can be generalized to construct the exact many-body coherent state (MBCS) in a trapped Bose-Einstein condensate (BEC) of N atoms. Such a MBCS possesses the form of the single-particle coherent state, which does not deform in propagation and is stable for a repulsive BEC. The results suggest an experimental scheme for resonantly generating and coherently controlling the MBCSs.     

Generic entanglement can be generated efficiently

We find that generic entanglement is physical, in the sense that it can be generated in polynomial time from two-qubit gates picked at random. We prove as the main result that such a process generates the average entanglement of the uniform (unitarily invariant) measure in at most O(N3) steps for N qubits. This is despite an exponentially growing number of such gates being necessary for generating that measure fully on the state space. Numerics furthermore show a variation cutoff allowing one to associate a specific time with the achievement of the uniform measure entanglement distribution. Various extensions of this work are discussed. The results are relevant to entanglement theory and to protocols that assume generic entanglement can be achieved efficiently.     

Auxiliary field Monte-Carlo for quantum many-body ground states

We develop an algorithm for determining the exact ground state properties of quantum many-body systems which is equally applicable to bosons and fermions. The Schroedinger eigenvalue equation for the ground state energy is recast as a many-dimensional integral using the Hubbard-Stratonovitch representation of the imaginary-time many-body evolution operator. The integral is then evaluated stochastically. We test the algorithm for an exactly soluble boson system with an attractive potential and then extend it to fermions and repulsive potentials. Importance sampling is crucial to the success of the method, particularly for more complex systems. Computational efficiency is improved by performing the calculations in Fourier space.     

Degeneracy of many-body quantum states in an optical lattice under a uniform magnetic field

We prove a theorem that shows the degeneracy of many-body states for particles in a periodic lattice and under a uniform magnetic field depends on the total particle number and the flux filling ratio. Noninteracting fermions and weakly interacting bosons are given as two examples. For the latter case, the phenomenon can also be physically understood in terms of destructive quantum interference of multiple symmetry-related tunneling paths between classical energy minima, which is reminiscent of the spin-parity effect discovered in magnetic molecular clusters. We also show that the quantum ground state of a mesoscopic number of bosons in this system is not a simple mean-field state but a fragmented state even for very weak interactions.     

Quantum nonlocality can be distributed via separable states

正Quantum nonlocality is one of the most astonishing features in quantum physics.It is of great importance in understanding the conceptual foundations of quantum theory and is closely related to certain quantum information processing such as quantum protocols for decreasing communication complexity[1]and secure quantum communication[2,3],see refs.[4-9]for more details.     

What can be tested in quantum electrodynamics?

In this paper we examine the theoretical foundations underlying the testing of quantum electrodynamics. We show that for the photon propagator (together with the contiguous vertices) it is not necessary to introduce ad hoc modifications in sufficiently accurate scattering experiments. Energy, momentum transfer, and accuracy determine the tested length in a model-independent way. The situation is quite different with the electron propagator. If gauge invariance is taken for granted, the electron propagator cannot be tested with processes where diagrams with open electron lines are important in the lowest order of perturbation theory. These processes can only give limits for anomalous moment and multiphoton parts of the vertices. On the other hand, processes with closed electron loops (vacuum polarization), such as photon-photon and Delbrück scattering, as well as photon splitting or corresponding low-energy, high-precision experiments can give limits also for the electron propagator. But in these cases only less accurate limits can be obtained, which depend on the modification model. Hence testing of the electron propagator, i.e., roughly speaking, the Dirac equation, is much more difficult than testing of the photon propagator, i.e, Maxwell's equations.Dedicated to the memory of Prof. Wolfgang Yourgrau (1908–1979).Presented at the 1975 International Symposium on Lepton and Photon Interactions at High Energies, Stanford University, Stanford, California.     

Thermodynamics of quantum dissipative many-body systems

We consider quantum nonlinear many-body systems with dissipation described within the Caldeira-Leggett model, i.e., by a nonlocal action in the path integral for the density matrix. Approximate classical-like formulas for thermodynamic quantities are derived for the case of many degrees of freedom, with general kinetic and dissipative quadratic forms. The underlying scheme is the pure-quantum self-consistent harmonic approximation (PQSCHA), equivalent to the variational approach by the Feynman-Jensen inequality with a suitable quadratic nonlocal trial action. A low-coupling approximation permits us to get manageable PQSCHA expressions for quantum thermal averages with a classical Boltzmann factor involving an effective potential and an inner Gaussian average that describes the fluctuations originating from the interplay of quanticity and dissipation. The application of the PQSCHA to a quantum phi(4) chain with Drude-like dissipation shows nontrivial effects of dissipation, depending upon its strength and bandwidth.     

Efficient simulation of one-dimensional quantum many-body systems

We present a numerical method to simulate the time evolution, according to a generic Hamiltonian made of local interactions, of quantum spin chains and systems alike. The efficiency of the scheme depends on the amount of entanglement involved in the simulated evolution. Numerical analysis indicates that this method can be used, for instance, to efficiently compute time-dependent properties of low-energy dynamics in sufficiently regular but otherwise arbitrary one-dimensional quantum many-body systems. As by-products, we describe two alternatives to the density matrix renormalization group method.     

Nonmaximally entangled states can be better for multiple linear optical teleportation

We investigate multiple linear optical teleportation in the Knill-Laflamme-Milburn scheme with both maximally and nonmaximally entangled states. We show that if the qubit is teleported several times via a nonmaximally entangled state, then the errors introduced in the previous teleportations can be corrected by the errors introduced in the following teleportations. This effect is so strong that it leads to another interesting phenomenon: i.e., the total probability of successful multiple linear optical teleportation is higher for nonmaximally entangled states than maximally entangled states.     

Experimental quantum simulation of entanglement in many-body systems

We employ a nuclear magnetic resonance (NMR) quantum information processor to simulate the ground state of an XXZ spin chain and measure its NMR analog of entanglement, or pseudoentanglement. The observed pseudoentanglement for a small-size system already displays a singularity, a signature which is qualitatively similar to that in the thermodynamical limit across quantum phase transitions, including an infinite-order critical point. The experimental results illustrate a successful approach to investigate quantum correlations in many-body systems using quantum simulators.     

Dilemma that cannot be resolved by biased quantum coin flipping

We show that a biased quantum coin flip (QCF) cannot provide the performance of a black-boxed biased coin flip, if it satisfies some fidelity conditions. Although such a QCF satisfies the security conditions of a biased coin flip, it does not realize the ideal functionality and, therefore, does not satisfy the demands for universally composable security. Moreover, through a comparison within a small restricted bias range, we show that an arbitrary QCF is distinguishable from a black-boxed coin flip unless it is unbiased on both sides of parties against insensitive cheating. We also point out the difficulty in developing cheat-sensitive quantum bit commitment in terms of the uncomposability of a QCF.     

Monotonically increasing functions of any quantum correlation can make all multiparty states monogamous

Monogamy of quantum correlation measures puts restrictions on the sharability of quantum correlations in multiparty quantum states. Multiparty quantum states can satisfy or violate monogamy relations with respect to given quantum correlations. We show that all multiparty quantum states can be made monogamous with respect to all measures. More precisely, given any quantum correlation measure that is non-monogamic for a multiparty quantum state, it is always possible to find a monotonically increasing function of the measure that is monogamous for the same state. The statement holds for all quantum states, whether pure or mixed, in all finite dimensions and for an arbitrary number of parties. The monotonically increasing function of the quantum correlation measure satisfies all the properties that are expected for quantum correlations to follow. We illustrate the concepts by considering a thermodynamic measure of quantum correlation, called the quantum work deficit.     

Exactness of two-body cluster expansions in many-body quantum theory

The Horn-Weinstein formula and the variational principle, combined with numerical results for a few many-electron systems, are used to provide support for a conjecture that the exact ground-state wave function for a Hamiltonian system containing up to two-body terms may be represented by an exponential cluster expansion employing a finite two-body operator.