arXiv subjects

Che-Ming Li

Publications and source records attributed to Che-Ming Li.

52 records · Page 3Linked to original sources

arXiv2010

Verifying Genuine High-Order Entanglement

High-order entanglement embedded in multipartite multilevel quantum systems (qudits) with many degrees of freedom (DOFs) plays an important role in quantum foundation and quantum engineering. Verifying high-order entanglement without the restriction of system complexity is a critical need in any experiments on general entanglement. Here, we introduce a scheme to efficiently detect genuine high-order entanglement, such as states close to genuine qudit Bell, Greenberger-Horne-Zeilinger, and cluster states as well as multilevel multi-DOF hyperentanglement. All of them can be identified with two local measurement settings per DOF regardless of the qudit or DOF number. The proposed verifications together with further utilities such as fidelity estimation could pave the way for experiments by reducing dramatically the measurement overhead.

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arXiv2010

Experimental demonstration of a heralded entanglement source

The heralded generation of entangled states is a long-standing goal in quantum information processing, because it is indispensable for a number of quantum protocols. Polarization entangled photon pairs are usually generated through spontaneous parametric down-conversion, but the emission is probabilistic. Their applications are generally accompanied by post-selection and destructive photon detection. Here, we report a source of entanglement generated in an event-ready manner by conditioned detection of auxiliary photons. This scheme benefits from the stable and robust properties of spontaneous parametric down-conversion and requires only modest experimental efforts. It is flexible and allows the preparation efficiency to be significantly improved by using beamsplitters with different transmission ratios. We have achieved a fidelity better than 87% and a state preparation efficiency of 45% for the source. This could offer promise in essential photonics-based quantum information tasks, and particularly in enabling optical quantum computing by reducing dramatically the computational overhead.

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arXiv2007

Quantum correlations for arbitrarily high-dimensional Bell inequality

We analyze the correlation structure of bipartite arbitrary-dimensional Bell inequalities via novel conditions of correlations in terms of differences of joint probabilities called correlators. The conditions of correlations are shown to be necessary for the multi-level Bell state. In particular, we find that the bipartite arbitrary-dimensional Bell-type inequalities introduced by Collins-Gisin-Linden-Massar-Popescu [Phys. Rev. Lett. 88, 040404 (2002)] and Son-Lee-Kim [Phys. Rev. Lett. 96, 060406 (2006)] are composed of correlators, and we reveal that the maximal violations by the Bell state just fit the conditions of quantum correlations. Correlators can be considered as essential elements of Bell inequalities.

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arXiv2007

Experimental realization of one-way quantum computing with two-photon four-qubit cluster states

We report an experimental realization of one-way quantum computing on a two-photon four-qubit cluster state. This is accomplished by developing a two-photon cluster state source entangled both in polarization and spatial modes. With this special source, we implemented a highly efficient Grover's search algorithm and high-fidelity two qubits quantum gates. Our experiment demonstrates that such cluster states could serve as an ideal source and a building block for rapid and precise optical quantum computation.

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arXiv2007

Entanglement detection via condition of quantum correlation

We develop a novel necessary condition of quantum correlation. It is utilized to construct $d$-level bipartite Bell-type inequality which is strongly resistant to noise and requires only analyses of $O(d)$ measurement outcomes compared to the previous result $O(d^{2})$. Remarkably, a connection between the arbitrary high-dimensional bipartite Bell-type inequality and entanglement witnesses is found. Through the necessary condition of quantum correlation, we propose that the witness operators to detect truly multipartite entanglement for a generalized Greenberger-Horne-Zeilinger (GHZ) state with two local measurement settings and a four-qubit singlet state with three settings. Moreover, we also propose the first robust entanglement witness to detect four-level tripartite GHZ state with only two local measurement settings.

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arXiv2006

Correlation criteria for Bell type inequalities and entanglement detection

We provide a novel criterion for identifying quantum correlation, which allows us to find connections between Bell type inequalities, entanglement detection, and correlation. We utilize the criterion to construct witness operators that can detect genuine multi-qubit entanglement with fewer local measurements. The connection between identifications of quantum correlation and Mermin's inequality is discussed. Detection of genuine four-level tripartite entanglement with two local measurement settings is shown in the same manner. Further, through the criterion of quantum correlation, we derive a new Bell inequality for arbitrary high-dimensional bipartite systems, which requires fewer analyses of the measured outcomes.

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arXiv2005

Analytical technique for simplification of the encoder-decoder circuit for a perfect five-qubit error correction

Simpler encoding and decoding networks are necessary for more reliable quantum error correcting codes (QECCs). The simplification of the encoder-decoder circuit for a perfect five-qubit QECC can be derived analytically if the QECC is converted from its equivalent one-way entanglement purification protocol (1-EPP). In this work, the analytical method to simplify the encoder-decoder circuit is introduced and a circuit that is as simple as the existent simplest circuits is presented as an example. The encoder-decoder circuit presented here involves nine single- and two-qubit unitary operations, only six of which are controlled-NOT (CNOT) gates.

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arXiv2005

Effect of cavity photons on the generation of multi-particle entanglement

A study on the cause of the multi-particle entanglement is presented in this work. We investigate how dot-like single quantum well excitons, which are independently coupled through a single microcavity mode, evolve into maximally entangled state as a series of conditional measurements are taken on the cavity field state. We first show how cavity photon affects the entanglement purity of the double-exciton Bell state and the triple-exciton W state. Generalization to multi-excitons W states is then derived analytically. Our results pave the way for studying the crucial cause of multi-particle collective effect.

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arXiv2004

An improved phase error tolerance in Quantum search algorithm

As the matching condition in Grover search algorithm is transgressed due to inevitable errors in phase inversions, it gives a reduction in maximum probability of success. With a given degree of maximum success, we have derive the generalized and imroved criterion for tolerated error and corresponding size of quantum database under the inevitable gate imperfections. The vanished inaccurancy to this condition has also been shown. Besides, a concise formula for evaluating minimum number of iterations is also presented in this work.

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arXiv2004

Creating Boolean Functions for the Five-EPR-Pair, Single-Error-Correcting Code

A quantum single-error-correcting scheme can be derived from a one-way entanglement purification protocol in purifying one Bell state from a finite block of five Bell states. The main issue to be concerned with in the theory of such an error-correction is to create specific linear Boolean functions that can transform the sixteen error syndromes occurring in the error-correcting code onto their mappings so that one Bell state is corrected whenever the other four in the finite block are measured. The Boolean function is performed under the effect of its associated sequence of basic quantum unilateral and bilateral operations. Previously, the Boolean function is created in use of the Monte Carlo computer search method. We introduce here a systematic scenario for creating the Boolean function and its associated sequence of operations so that we can do the job in an analytical way without any trial and error effort. Consequently, all possible Boolean functions can in principle be created by using our method. Furthermore, for a deduced Boolean function, we can also in the spirit of our method derive its best associated sequence of operations which may contain the least number of total operations or the least number of the bilateral XOR operations alone. Some results obtained in this work show the capability of our method in creating the Boolean function and its sequence of operations.

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arXiv2004

A simplification of entanglement purification

An idea of hybrid maps is proposed to establish standard entanglement purification protocols which guarantee to purify any distillable state to a desired maximally entangled pure state all by the standard purification local operations and classical communications. The protocols proposed in this work, in which two state transformations are used, perform better than the IBM and Oxford protocols in the sense that they require fewer operation times in yielding a same amount of the desired pure state. One of the proposed protocol in this work can even lead to a higher improved output yield when it is combined with the hashing protocol, as compared with the combined algorithm consisting of the Oxford and the hashing protocol.

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arXiv2002

Formulation of a Family of Sure-Success Quantum Search Algorithms

In this work, we consider a family of sure-success quantum algorithms, which is grouped into even and odd members for solving a generalized Grover search problem. We prove the matching conditions for both groups and give the corresponding formulae for evaluating the iterations or oracle calls required in the search computation. We also present how to adjust the phase angles in the generalized Grover operator to ensure the sure-success if minimal oracle calls are demanded in the search.

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arXiv2002

Hamiltonian and measuring time for analog quantum search

We derive in this study a Hamiltonian to solve with certainty the analog quantum search problem analogue to the Grover algorithm. The general form of the initial state is considered. Since the evaluation of the measuring time for finding the marked state by probability of unity is crucially important in the problem, especially when the Bohr frequency is high, we then give the exact formula as a function of all given parameters for the measuring time.

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arXiv2002

Multi-object searching algorithm using subgrouped oracles

We present in this work, if a set of well organized suboracles is available, an algorithm for multiobject search with certainty in an unsorted database of $N$ items. Depending on the number of the objects, the technique of phase tunning is included in the algorithm. If one single object is to be searched, this algorithm performs a factor of two improvement over the best algorithm for a classical sorted database. While if the number of the objects is larger than one, the algorithm requires slightly less than $\log_{4}N$ queries, but no classical counterpart exists since the resulting state is a superposition of the marked states.

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arXiv2001

A General Phase Matching Condition for Quantum Searching Algorithm

A general consideration on the phase rotations in quantum searching algorithm is taken in this work. As four phase rotations on the initial state, the marked states, and the states orthogonal to them are taken account, we deduce a phase matching condition for a successful search. The optimal options for these phase are obtained consequently.

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arXiv2001

A General SU(2) Formulation for Quantum Searching with Certainty

A general quantum search algorithm with arbitrary unitary transformations and an arbitrary initial state is considered in this work. To serach a marked state with certainty, we have derived, using an SU(2) representation: (1) the matching condition relating the phase rotations in the algorithm, (2) a concise formula for evaluating the required number of iterations for the search, and (3) the final state after the search, with a phase angle in its amplitude of unity modulus. Moreover, the optimal choices and modifications of the phase angles in the Grover kernel is also studied.

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