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Heng Fan

Publications and source records attributed to Heng Fan.

At least 469 records · Page 26Linked to original sources
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↗
arXiv2004

The Dynamical Yang-Baxter Relation and the Minimal Representation of the Elliptic Quantum Group

In this paper, we give the general forms of the minimal $L$ matrix (the elements of the $L$-matrix are $c$ numbers) associated with the Boltzmann weights of the $A_{n-1}^1$ interaction-round-a-face (IRF) model and the minimal representation of the $A_{n-1}$ series elliptic quantum group given by Felder and Varchenko. The explicit dependence of elements of $L$-matrices on spectral parameter $z$ are given. They are of five different forms (A(1-4) and B). The algebra for the coefficients (which do not depend on $z$) are given. The algebra of form A is proved to be trivial, while that of form B obey Yang-Baxter equation (YBE). We also give the PBW base and the centers for the algebra of form B.

hep-th↗
arXiv2004

Entanglement in a Valence-Bond-Solid State

We study entanglement in Valence-Bond-Solid state. It describes the ground state of Affleck, Kennedy, Lieb and Tasaki quantum spin chain. The AKLT model has a gap and open boundary conditions. We calculate an entropy of a subsystem (continuous block of spins). It quantifies the entanglement of this block with the rest of the ground state. We prove that the entanglement approaches a constant value exponentially fast as the size of the subsystem increases. Actually we proved that the density matrix of the continuous block of spins depends only on the length of the block, but not on the total size of the chain [distance to the ends also not essential]. We also study reduced density matrices of two spins both in the bulk and on the boundary. We evaluated concurrencies.

quant-ph↗
arXiv2004

Entanglement of eta-pairing state with off-diagonal long-range order

Off-diagonal long-range order (ODLRO) is a quantum phenomenon not describable in classical mechanical terms. It is believed to be one characteristic of superconductivity. The quantum state constructed by eta-pairing which demonstrates ODLRO is an eigenstate of the three-dimensional Hubbard model. Entanglement is a key concept of the quantum information processing and has no classical counterpart. We study the entanglement property of eta-pairing quantum state. The concurrence is a well-known measure of quantum entanglement. We show that the concurrence of entanglement between one-site and the rest sites is exactly the correlation function of the ODLRO for the eta-pairing state in the thermodynamic limit. So, when the eta-pairing state is entangled, it demonstrates ODLRO and is thus in superconducting phase, if it is a separable state, there is no ODLRO. In the thermodynamic limit, the entanglement between M-site and other sites of the eta-pairing state does not vanish. Other types of ODLRO of eta-pairing state are presented. We show that the behavior of the ODLRO correlation functions is equivalent to that of the entanglement of the eta-pairing state. The scaling of the entropy of the entanglement for the eta-pairing state is studied.

quant-ph↗
arXiv2003

Distinguishability and indistinguishability by LOCC

We show that a set of linearly independent quantum states $\{(U_{m,n}\otimes I)ρ^{AB}(U_{m,n}^{\dagger}\otimes I)\}_{m,n=0}^{d-1}$, where $U_{m,n}$ are generalized Pauli matrices, cannot be discriminated deterministically or probabilistically by local operations and classical communications (LOCC). On the other hand, any $l$ maximally entangled states from this set are locally distinguishable if $l(l-1)\le 2d$. The explicit projecting measurements are obtained to locally discriminate these states. As an example, we show that four Werner states are locally indistinguishable.

quant-ph↗
arXiv2003

Quantum Cloning of Mixed States in Symmetric Subspace

Quantum cloning machine for arbitrary mixed states in symmetric subspace is proposed. This quantum cloning machine can be used to copy part of the output state of another quantum cloning machine and is useful in quantum computation and quantum information. The shrinking factor of this quantum cloning achieves the well-known upper bound. When the input is identical pure states, two different fidelities of this cloning machine are optimal.

quant-ph↗
arXiv2003

Remarks on entanglement assisted classical capacity

The property of the optimal signal ensembles of entanglement assisted channel capacity is studied. A relationship between entanglement assisted channel capacity and one-shot capacity of unassisted channel is obtained. The data processing inequalities, convexity and additivity of the entanglement assisted channel capacity are reformulated by simple methods.

quant-ph↗
arXiv2002

A note on quantum entropy inequalities and channel capacities

Quantum entropy inequalities are studied. Some quantum entropy inequalities are obtained by several methods. For entanglement breaking channel, we show that the entanglement-assisted classical capacity is upper bounded by $\log d$. A relationship between entanglement-assisted and one-shot unassisted capacities is obtained. This relationship shows the entanglement-assisted channel capacity is upper bounded by the sum of $\log d$ and the one-shot unassisted classical capacity.

quant-ph↗
arXiv2002

Phase-covariant quantum cloning of qudits

We study the phase-covariant quantum cloning machine for qudits, i.e. the input states in d-level quantum system have complex coefficients with arbitrary phase but constant module. A cloning unitary transformation is proposed. After optimizing the fidelity between input state and single qudit reduced density opertor of output state, we obtain the optimal fidelity for 1 to 2 phase-covariant quantum cloning of qudits and the corresponding cloning transformation.

quant-ph↗
arXiv2002

Quantify entanglement by concurrence hierarchy

We define the concurrence hierarchy as d-1 independent invariants under local unitary transformations in d-level quantum system. The first one is the original concurrence defined by Wootters et al in 2-level quantum system and generalized to d-level pure quantum states case. We propose to use this concurrence hierarchy as measurement of entanglement. This measurement does not increase under local quantum operations and classical communication.

quant-ph↗
arXiv2002

A note on separability criteria for multipartite state

The recent proposed realignment separability criterion for mixed is analyzed. We identify the essential part of this criterion is a swap operator followed by a partial transposition. Then we analyze the separability criterion of permutation indices of the density matrix for multipartite state which is a generalization of the realignment criterion. We give a method to solve the equivalence problem of the separability criterion of permutation indices of the density matrix. For tripartite state, we show the non-trivial separability criteria are either partial transposition criterion or realignment criterion.

quant-ph↗
arXiv2002

Additivity of entanglement of formation for some special cases

The proof of additivity of entanglement of formation for some special cases is given. The strong concavity of von Neumann entropy due to strong subadditivity of von Neumann entropy is presented. Some general relations concerning about the entanglement of formation are proposed.

quant-ph↗
arXiv2002

Cloning of symmetric d-level photonic states in physical systems

Optimal procedures play an important role in quantum information. It turns out that some naturally occurring processes like emission of light from an atom can realize optimal transformations. Here we study how arbitrary symmetric states of a number of d-level systems can be cloned using a multilevel atomic system. It is shown that optimality is always ensured even though the output number of systems is probabilistic.

quant-ph↗
arXiv2001

Quantum cloning machines for equatorial qubits

Quantum cloning machines for equatorial qubits are studied. For the case of 1 to 2 phase-covariant quantum cloning machine, we present the networks consisting of quantum gates to realize the quantum cloning transformations. The copied equatorial qubits are shown to be separable by using Peres-Horodecki criterion. The optimal 1 to M phase-covariant quantum cloning transformations are given.

quant-ph↗
arXiv2001

A universal cloner allowing the input to be arbitrary states in symmetric subspace

A generalized universal quantum cloning machine is proposed which allows the input to be arbitrary states in symmetric subspace. And it reduces to the universal quantum cloning machine (UQCM) if the input are identical pure states. The generalized cloner is optimal in the sense we compare the input and output reduced density operators at a single qubit. The result for qubits is extended to arbitrary-dimensional states.

quant-ph↗