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Heng Fan

Publications and source records attributed to Heng Fan.

At least 415 records · Page 23Linked to original sources
arXiv2012

1/2+1/2>1 for quantum error correction

Quantum error correction assisted by entanglement helps to transmit the encoded qudits through quantum channels with some of them being noiseless. Here we consider a more realistic scheme for experiments what we called as partial-noisy quantum channels in which, instead of completely free of noise, only part of the qudit suffers no noise. In this scenario we show by an explicit example that two half-noisy channels work better than one noiseless channel, a queer phenomenon showing 1/2+1/2>1. Our example also saturates a unified quantum Singleton bound, valid for the standard and entanglement-assisted codes as well. Furthermore, as illustrated by a mixed-alphabet code with half-noisy channels, a higher dimensional physical qudit can so improve the performance of a partial-noisy channel that it even outperforms a noiseless channel.

quant-ph↗
arXiv2012

Minimal sets determining universal and phase-covariant quantum cloning

We study the minimal input sets which can determine completely the universal and the phase-covariant quantum cloning machines. We find that the universal quantum cloning machine, which can copy arbitrary input qubit equally well, however can be determined completely by only four input states located at the four vertices of a tetrahedron. The phase-covariant quantum cloning machine, which can copy all qubits located on the equator of the Bloch sphere, can be determined by three equatorial qubits with equal angular distance. These results sharpen further the well-known results that BB84 states and six-states used in quantum cryptography can determine completely the phase-covariant and universal quantum cloning machines. This concludes the study of the power of universal and phase-covariant quantum cloning, i.e., from minimal input sets necessarily to full input sets by definition. This can simplify dramatically the testing of whether the quantum clone machines are successful or not, we only need to check that the minimal input sets can be cloned optimally.

quant-ph↗
arXiv2012

Genuine Correlations of Tripartite System

We define genuine total, classical and quantum correlations in tripartite systems. The measure we propose is based on the idea that genuine tripartite correlation exists if and only if the correlation between any bipartition does not vanish. We find in a symmetrical tripartite state, for total correlation and classical correlation, the genuine tripartite correlations are no less than pair-wise correlations. However, the genuine quantum tripartite correlation can be surpassed by the pair-wise quantum correlations. Analytical expressions for genuine tripartite correlations are obtained for pure states and rank-2 symmetrical states. The genuine correlations in both entangled and separable states are calculated.

quant-ph↗
arXiv2012

Quantum correlations with vacuum ambiguity in de Sitter space

We study the quantum correlations of free scalar field with vacuum ambiguity of de Sitter space. We show the occurrence of degradation of quantum entanglement and quantum discord between field modes for inertial observer in curved space due to the radiation associated with cosmological horizon. In particular, we find that quantum correlations can be used to encode infinite de Sitter invariant vacua, which correspond to infinite set of possible physical worlds. This may provide a superselection rule of physical vacuum via quantum information tasks. We also discuss the simulation of such quantum effects of vacuum ambiguity in ion trap experiments.

quant-ph↗
arXiv2012

Quantum Error-Correcting Codes over Mixed Alphabets

Errors are inevitable during all kinds quantum informational tasks and quantum error-correcting codes (QECCs) are powerful tools to fight various quantum noises. For standard QECCs physical systems have the same number of energy levels. Here we shall propose QECCs over mixed alphabets, i.e., physical systems of different dimensions, and investigate their constructions as well as their quantum Singleton bound. We propose two kinds of constructions: a graphical construction based a graph-theoretical object composite coding clique and a projection-based construction. We illustrate our ideas using two alphabets by finding out some 1-error correcting or detecting codes over mixed alphabets, e.g., optimal $((6,8,3))_{4^52^1}$, $((6,4,3))_{4^42^2}$ and $((5,16,2))_{4^32^2}$ code and suboptimal $((5,9,2))_{3^42^1}$ code. Our methods also shed light to the constructions of standard QECCs, e.g., the construction of the optimal $((6,16,3))_4$ code as well as the optimal $((2n+3,p^{2n+1},2))_{p}$ codes with $p=4k$.

quant-ph↗
arXiv2012

Entanglement-assisted local operations and classical communications conversion in the quantum critical systems

Conversions between the ground states in quantum critical systems via entanglement-assisted local operations and classical communications (eLOCC) are studied. We propose a new method to reveal the different convertibility by local operations when a quantum phase transition occurs. We have studied the ground state local convertibility in the one dimensional transverse field Ising model, XY model and XXZ model. It is found that the eLOCC convertibility sudden changes at the phase transition points. In transverse field Ising model the eLOCC convertibility between the first excited state and the ground state are also distinct for different phases. The relation between the order of quantum phase transitions and the local convertibility is discussed.

quant-ph↗
arXiv2012

Quantum phases with differing computational power

The observation that concepts from quantum information has generated many alternative indicators of quantum phase transitions hints that quantum phase transitions possess operational significance with respect to the processing of quantum information. Yet, studies on whether such transitions lead to quantum phases that differ in their capacity to process information remain limited. Here We show that there exist quantum phase transitions that cause a distinct qualitative change in our ability to simulate certain quantum systems under perturbation of an external field by local operations and classical communication. In particular, we show that in certain quantum phases of the XY model, adiabatic perturbations of the external magnetic field can be simulated by local spin operations, whereas the resulting effect within other phases results in coherent non-local interactions. We discuss the potential implications to adiabatic quantum computation, where a computational advantage exists only when adiabatic perturbation results in coherent multi-body interactions.

quant-ph↗
arXiv2012

Quantum-correlating power of local quantum channels

Quantum correlation can be created by local operations from a classically correlated state. We define quantum-correlating power (QCP) of a local quantum channel as the maximum amount of quantum correlation that can be created by the channel. The quantum correlation that we discuss in this article is defined on the left part of the bipartite state. We prove that for any local channel, the optimal input state, which corresponds to the maximum quantum correlation in the output state, must be a classical-classical state. Further, the single-qubit channels with maximum QCP can be found in the class of rank-1 channels which take their optimal input states to rank-2 quantum-classical states. The analytic expression for QCP of single-qubit amplitude damping channel is obtained. Super-activation property of QCP, i.e., two zero-QCP channels can consist a positive-QCP channel, is discussed for single-qubit phase damping channels.

quant-ph↗
arXiv2012

Necessary and sufficient conditions for local creation of quantum correlation

Quantum correlation can be created by a local operation from some initially classical states. We prove that the necessary and sufficient condition for a local trace-preserving channel to create quantum correlation is that it is not a commutativity-preserving channel. This condition is valid for arbitrary finite dimension systems. We also derive the explicit form of commutativity-preserving channels. For a qubit, a commutativity-preserving channel is either a completely decohering channel or a mixing channel. For a three-dimensional system (qutrit), a commutativity-preserving channel is either a completely decohering channel or an isotropic channel.

quant-ph↗
arXiv2012

The one-way unlocalizable quantum discord

In this paper, we present the concept of the one-way unlocalizable quantum discord and investigate its properties. We provide a polygamy inequality for it in tripartite pure quantum system of arbitrary dimension. Several tradeoff relations between the one-way unlocalizable quantum discord and other correlations are given. If the von Neumann measurement is on a part of the system, we give two expressions of the one-way unlocalizable quantum discord in terms of partial distillable entanglement and quantum disturbance. Finally, we also provide a lower bound for bipartite shareability of quantum correlation beyond entanglement in a tripartite system.

quant-ph↗
arXiv2012

Maximally entangled state can be a mixed state

We find that the mixed maximally entangled states exist and prove that the form of the mixed maximally entangled states is unique in terms of the entanglement of formation. Moreover, even if the entanglement is quantified by other entanglement measures, this conclusion is still proven right. This result is a supplementary to the generally accepted fact that all maximally entangled states are pure. These states possess important properties of the pure maximally entangled states, for example, these states can be used as a resource for faithful teleportation and they can be distinguished perfectly by local operations and classical communication.

quant-ph↗
arXiv2012

Quantum Information Approach to Bose-Einstein Condensate in a Tilted Double-Well System

We study the ground state properties of bosons in a tilted double-well system. We use fidelity susceptibility to identify the possible ground state transitions under different tilt values. For a very small tilt (for example $10^{-10}$), two transitions are found. For a moderate tilt (for example $10^{-3}$), only one transition is found. For a large tilt (for example $10^{-1}$), no transition is found. We explain this by analyzing the spectrum of the ground state. The quantum discord and total correlation of the ground state under different tilts are also calculated to indicate those transitions. In the transition region, both quantities have peaks decaying exponentially with particle number $N$. This means for a finite-size system the transition region cannot be explained by the mean-field theory, but in the large-$N$ limit it can be.

quant-ph↗
arXiv2012

Dynamics of entropic measurement-induced nonlocality in structured reservoirs

We propose the entropic measurement-induced nonlocality (MIN) as the maximal increment of von Neumann entropy induced by the locally non-disturbing measurement, and study behaviors of it both in the independent and common structured reservoirs. We present schemes for preserving the MIN, and show that for certain initial states the MIN, including the quantum correlations, can even be enhanced by the common reservoir. Additionally, we also show that the different measures of MIN may give different qualitative characterizations of nonlocal properties, i.e., it is rather measure dependent than state dependent.

quant-ph↗
arXiv2012

Assisted state discrimination without entanglement

It is shown that the dissonance, a quantum correlation which is equal to quantum discord for separable state, is required for assisted optimal state discrimination. We find that only one side discord is required in the optimal process of assisted state discrimination, while another side discord and entanglement is not necessary. We confirm that the quantum discord, which is asymmetric depending on local measurements, is a resource for assisted state discrimination. With the absence of entanglement, we give the necessary and sufficient condition for vanishing one side discord in assisted state discrimination for a class of $d$ nonorthogonal states. As a byproduct, we find that the positive-partial-transposition (PPT) condition is the necessary and sufficient condition for the separability of a class of $2\times d$ states.

quant-ph↗
arXiv2012

Edge Mode Combinations in the Entanglement Spectra of Non-Abelian Fractional Quantum Hall States on the Torus

We present a detailed analysis of bi-partite entanglement in the non-Abelian Moore-Read fractional quantum Hall state of bosons and fermions on the torus. In particular, we show that the entanglement spectra can be decomposed into intricate combinations of different sectors of the conformal field theory describing the edge physics, and that the edge level counting and tower structure can be microscopically understood by considering the vicinity of the thin-torus limit. We also find that the boundary entropy density of the Moore-Read state is markedly higher than in the Laughlin states investigated so far. Despite the torus geometry being somewhat more involved than in the sphere geometry, our analysis and insights may prove useful when adopting entanglement probes to other systems that are more easily studied with periodic boundary conditions, such as fractional Chern insulators and lattice problems in general.

cond-mat.str-el↗
arXiv2012

Thermalization from a general canonical principle

We investigate the time evolution of a generic and finite isolated quantum many-body system starting from a pure quantum state. We find the kinematical general canonical principle proposed by Popescu-Short-Winter for statistical mechanics can be built in a more solid ground by studying the thermalization, i.e. comparing the density matrices themselves rather than the measures of distances. In particular, this allows us to explicitly identify that, from any instantaneous pure state after thermalization, the state of subsystem is like from a microcanonical ensemble or a generalized Gibbs ensemble, but neither a canonical nor a thermal ones due to finite-size effect. Our results are expected to bring the task of characterizing the state after thermalization to completion. In addition, thermalization of coupled systems with different temperatures corresponding to mixed initial states is studied.

quant-ph↗
arXiv2012

General Quantum Key Distribution in Higher Dimension

We study a general quantum key distribution protocol in higher dimension. In this protocol, quantum states in arbitrary $g+1$ ($1\le g\le d$) out of all $d+1$ mutually unbiased bases in a d-dimensional system can be used for the key encoding. This provides a natural generalization of the quantum key distribution in higher dimension and recovers the previously known results for $g=1$ and $d$. In our investigation, we study Eve's attack by two slightly different approaches. One is considering the optimal cloner for Eve, and the other, defined as the optimal attack, is maximizing Eve's information. We derive results for both approaches and show the deviation of the optimal cloner from the optimal attack. With our systematic investigation of the quantum key distribution protocols in higher dimension, one may balance the security gain and the implementation cost by changing the number of bases in the key encoding. As a side product, we also prove the equivalency between the optimal phase covariant quantum cloning machine and the optimal cloner for the $g=d-1$ quantum key distribution.

quant-ph↗