arXiv subjects

Heng Fan

Publications and source records attributed to Heng Fan.

At least 451 records · Page 25Linked to original sources

arXiv2009

Quantum gravity and mass of gauge field: a four-dimensional unified quantum theory

We present in detail a four-dimensional unified quantum theory. In this theory, we identify three class of parameters, coordinate-momentum, spin and gauge, as all and as the only fundamental parameters to describe quantum fields. The coordinate-momentum is formulated by the general relativity in four-dimensional space-time. This theory satisfies the general covariance condition and the general covariance derivative operator is given. In an unified and combined description, the matter fields, gravity field and gauge fields satisfy Dirac equation, Einstein equation and Yang-Mills equation in operator form. In the framework of our theory, we mainly realize the following aims: (1) The gravity field is described by a quantum theory, the graviton is massless, it is spin-2; (2) The mass problem of gauge theory is solved. Mass arises naturally from the gauge space and thus Higgs mechanism is not necessary; (3) Color confinement of quarks is explained; (4) Parity violation for weak interactions is obtained; (5) Gravity will cause CPT violation; (6) A dark energy solution of quantum theory is presented. It corresponds to Einstein's cosmological constant. We propose that the candidate for dark energy should be gluon which is one of the elementary particles.

physics.gen-ph↗

arXiv2009

A quantum model of dark energy

We propose a quantum model of dark energy. The proposed candidate for dark energy is gluon field, as is well-known, gluons are the elementary particles. We assume that gluons may not be completely massless but have tiny masses, thus the gluon field can provide a non-zero energy-momentum tensor. This model corresponds to Einstein's cosmological constant which is one of the generally accepted models for dark energy. Besides the gluon field, we also discuss the properties of electroweak boson field and compare our results with previous known results.

physics.gen-ph↗

arXiv2009

A new quantum theory of gravity in the framework of general relativity

Observed physical phenomena can be described well by quantum mechanics or general relativity. People may try to find an unified fundamental theory which mainly aims to merge gravity with quantum theory. However, difficulty in merging those theories self-consistently still exists, and no such theory is generally accepted. Here we try to propose a quantum theory with space and time in symmetrical positions in the framework of general relativity. In this theory, Dirac matter fields, gauge fields and gravity field are formulated in an unified way which satisf Dirac equation, Yang-Mills equation and Einstein equation in operator form. This combines the quantum mechanics and general relativity .

physics.gen-ph↗

arXiv2009

Correlations in Grover search

Grover search is a well-known quantum algorithm that outperforms any classical search algorithm. It is known that quantum correlations such as entanglement are necessary for the power of quantum computation. But entanglement is not the only kind of quantum correlations. Other quantum correlations such as quantum discord are also useful to capture some aspects of the nonclassical correlation. We investigate several kinds of correlations including both quantum and classical in the whole process of Grover search algorithm. These correlations are the concurrence, entanglement of formation, quantum discord, classical correlation and mutual information. The behaviors of quantum discord, classical correlation and mutual information are almost the same while the concurrence is different. When the search is over, all kinds of correlations are zero, we argue that this is necessary for the final step in the search.

quant-ph↗

arXiv2009

The Decay of Multiqudit Entanglement

We investigate the decay of entanglement of a generalized N-qudit GHZ state, with each qudit passing through independently in a quantum noisy channel. By studying the time at which the entanglement completely vanishes and the time at which the entanglement becomes arbitrarily small, we try to find how the robustness of entanglement is influenced by dimension d and the number of particles N.

quant-ph↗

arXiv2009

Entanglement swapping of the valence-bond solid state with local filtering operations

A basic problem of quantum communication is to generate entangled states between distant sites. Using entanglement swapping, we are able to generate an entangled state of the desired distance from connecting many short distance entangled states. We investigate the entanglement swapping of the Valence-Bond Solid state with un-identical local filtering operations. It is found that not only a long distance entangled state can be generated from the VBS state, but also there is a trade-off between the probability and the degree of the entanglement in the resultant state. The results are also generalized to higher dimensional cases.

quant-ph↗

arXiv2009

The Dynamics of the Bounds of Squared Concurrence

We study the dynamics of upper and lower bounds of squared concurrence.Our results are similar to that of Konard et al. and can help the estimation of high-dimension bipartite entanglement in experiments.

quant-ph↗

arXiv2008

Concurrence and a proper monogamy inequality for arbitrary quantum states

We obtain an analytical lower bound of entanglement quantified by concurrence for arbitrary bipartite quantum states. It is shown that our bound is tight for some mixed states and is complementary to the previous known lower bounds. On the other hand, it is known that the entanglement monogamy inequality proposed by Coffman, Kundu, and Wootters is in general not true for higher dimensional quantum states. Inducing from the new lower bound of concurrence, we find a proper form of entanglement monogamy inequality for arbitrary quantum states.

quant-ph↗

arXiv2008

Remote controlled-NOT gate of d-dimension

Single qubit rotation gate and the controlled-NOT (CNOT) gate constitute a complete set of gates for universal quantum computation. In general the CNOT gate are only for two nearby qubits. For two qubits which are remote from each other, we need a series of swap gates to transfer these two qubits to the nearest neighboring sites, and then after the CNOT gate we should transfer them to their original sites again. However, a series of swap gates are resource for quantum information processing. One economy way which does not consume so much resource is to implement CNOT gate remotely. The remote CNOT gate is to implement the CNOT gate for two remotely separated qubits with the help of one additional maximally entangled state. The original remote CNOT gate is for two qubits, here we will present the d-dimensional remote CNOT gate. The role of quantum teleportation is identified in the process of the remote CNOT gate.

quant-ph↗

arXiv2007

Optimal Broadcasting of Mixed States

The N to M (M>N) universal quantum broadcasting of mixed states are proposed for qubits system. The broadcasting of mixed states is universal and optimal in the sense that the shrinking factor is independent of input state and achieves the upper bound. The quantum broadcasting of mixed qubits is a generalization of the universal quantum cloning machine for identical pure input states. A new pure state decompositions of the identical mixed qubits are obtained.

quant-ph↗

arXiv2007

Boundary effects to the entanglement entropy and two-site entanglement of the spin-1 valence-bond solid

We investigate the von Neumann entropy of a block of subsystem for the valence-bond solid (VBS) state with general open boundary conditions. We show that the effect of the boundary on the von Neumann entropy decays exponentially fast in the distance between the subsystem considered and the boundary sites. Further, we show that as the size of the subsystem increases, its von Neumann entropy exponentially approaches the summation of the von Neumann entropies of the two ends, the exponent being related to the size. In contrast to critical systems, where boundary effects to the von Neumann entropy decay slowly, the boundary effects in a VBS, a non-critical system, decay very quickly. We also study the entanglement between two spins. Curiously, while the boundary operators decrease the von Neumann entropy of L spins, they increase the entanglement between two spins.

quant-ph↗

arXiv2007

Entangled multi-qubit states without higher-tangle

We analyze mixed multi-qubit states composed of a W class state and a product state with all qubit in |0>. We find the optimal pure state decomposition and convex roofs for higher-tangle with bipartite partition between one qubit and the rest qubits for those mixed states. The optimality of the decomposition is ensured by the Coffman-Kundu-Wootters (CKW) inequality which describes the monogamy of quantum entanglement. The generalized monogamy inequality is found to be true for W class states with arbitrary partitions between one qubit and multi-qubit.

quant-ph↗

arXiv2007

General sequential quantum cloning

Some multipartite quantum states can be generated in a sequential manner which may be implemented by various physical setups like microwave and optical cavity QED, trapped ions, and quantum dots etc. We analyze the general N to M qubits Universal Quantum Cloning Machine (UQCM) within a sequential generation scheme. We show that the N to M sequential UQCM is available. The case of d-level quantum states sequential cloning is also presented.

quant-ph↗

arXiv2007

Bounds on Negativity of Superpositions

The entanglement quantified by negativity of pure bipartite superposed states is studied. We show that if the entanglement is quantified by the concurrence two pure states of high fidelity to one another still have nearly the same entanglement. Furthermore this conclusion can be guaranteed by our obtained inequality, and the concurrence is shown to be a continuous function even in infinite dimensions. The bounds on the negativity of superposed states in terms of those of the states being superposed are obtained. These bounds can find useful applications in estimating the amount of the entanglement of a given pure state.

quant-ph↗

arXiv2007

Monogamy Inequality in terms of Negativity for Three-Qubit States

We propose a new entanglement measure to quantify three qubits entanglement in terms of negativity. A monogamy inequality analogous to Coffman-Kundu-Wootters (CKW) inequality is established. This consequently leads to a definition of residual entanglement, which is referred to as three-$π$ in order to distinguish from three-tangle. The three-$π$ is proved to be a natural entanglement measure. By contrast to the three-tangle, it is shown that the three-$π$ always gives greater than zero values for $W$ and GHZ classes, implying there always exists three-way entanglement for them, and three-tangle generally underestimates three-way entanglement of a given system. This investigation will offer an alternative tool to understand genuine multipartite entanglement.

quant-ph↗

arXiv2006

Vanishing environment-induced decoherence

For a central system uniformly coupled to a XY spin-1/2 bath in a transverse field, we explicitly calculate the Loschmidt echo(LE) to characterize decoherence quantitatively. We find that the anisotropy parameter $γ$ affects decoherence of the central system sensitively when $γ\in [0,1]$% , in particular, the LE becomes unit without varying with time when $γ=0 $, implying that environment-induced decoherence vanishes . Some other cases in which the LE is unit are discussed also.

quant-ph↗

arXiv2005

Valence-Bond-Solid state entanglement in a 2-D Cayley tree

The Valence-Bond-Solid (VBS) states are in general ground states for certain gapped models. We consider the entanglement of VBS states on a two-dimensional Cayley tree. We show that the entropy of the reduced density operator does not depend on the whole size of the Cayley tree. We also show that asymptotically, the entropy is liearly proportional to the number of singlet states cut by the reduced density operator of the VBS state.

quant-ph↗

arXiv2005

Optimal two-qubit quantum circuits using exchange interactions

The Heisenberg exchange interaction is a natural method to implement non-local (i.e., multi-qubit) quantum gates in quantum information processing. We consider quantum circuits comprising of $(SWAP)^α$ gates, which are realized through the exchange interaction, and single-qubit gates. A universal two-qubit quantum circuit is constructed from only three $(SWAP)^α$ gates and six single-qubit gates. We further show that three $(SWAP)^α$ gates are not only sufficient, but necessary. Since six single-qubit gates are known to be necessary, our universal two-qubit circuit is optimal in terms of the number of {\em both} $(SWAP)^α$ and single-qubit gates.

quant-ph↗