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An optical encryption (OE) scheme based on the spread spectrum ghost imaging (SSGI), named SSGI-OE, is proposed to obtain a high security with a smaller key. In the scheme, the randomly selected row number of a Hadamard matrix of order $N$ is used as the secure key, and shared with the authorized user, Bob, through a private channel. Each corresponding row vector of the order $N$ Hadamard matrix is then used as the direct sequence code to modulate a speckle pattern for the ghost imaging system, and an image is encrypted with the help of the SSGI. The measurement results from the bucket detector, named ciphertext, are then transmitted to Bob through a public channel. The illuminating speckle patterns are also shared with Bob by the public channel. With the correct secure key, Bob could reconstruct the image with the aid of the SSGI system, whereas, the unauthorized user, Eve, could not obtain any useful information of the encrypted image. The numerical simulations and experimental results show that the proposed scheme is feasible with a higher security and a smaller key. For the $32 \times 32$ pixels image, the number of bits sent from Alice to Bob by using SSGI-OE ($M=1024,N=2048$) scheme is only $0.0107$ times over the computational ghost imaging optical encryption(CGI-OE) scheme. When the eavesdropping ratio (ER) is less than 40%, the eavesdropper cannot acquire any information of the encrypted image. The extreme circumstance for the proposed SSGI-OE scheme is also discussed, where the eavesdropper begins to extract the information when ER is up to 15%.

In the paper, the single-qubit quantum classifier(SQC) based on a gradient-free optimization(GFO) algorithm, named GFO-based SQC, is proposed to overcome the effects of barren plateau caused by quantum devices. Here, a rotation gate R X (φ) is applied on the single-qubit binary quantum classifier, and the training data and parameters are loaded into φ with the form of vector multiplication. The cost function is decreased by finding the value of each parameter that yields the minimum expectation value of measuring the quantum circuit. The algorithm is performed iteratively for all parameters one by one until the cost function satisfies the stop condition. The proposed GFO-based SQC is demonstrated for classification tasks in Iris and MNIST datasets and compared with the Adam-based SQC and quantum support vector machine(QSVM). Furthermore, the performance of the GFO-based SQC is discussed when the rotation gate in the quantum device is under different noise. The simulation results show that the GFO-based SQC can reach a high accuracy with reduced time. Additionally, the proposed GFO algorithm can quickly complete the training process of the SQC. Importantly, the GFO-based SQC has a good performance in noisy environments.

In the paper, we first present a quantum multiplier based on quantum Fourier transform (QFT), which is composed by a series of double-controlled phase gates, the control qubits are from the two multipliers, and the controlled qubits are in the ancillary state. By the sequential usage of the double-controlled phase gates, the product could be obtained after the inverse quantum Fourier transform (IQFT) on the final ancillary output state. Then, we further optimize the proposed quantum multiplier. The circuit analysis shows that the proposed multiplier could reduce the number of qubits in ancillary, and the multiplication result of finite qubits can be directly obtained by using fewer quantum gates. The optimization has reduced the resource cost of quantum multiplier greatly.

Orbital angular momentum (OAM) has the characteristics of mutual orthogonality between modes, and has been applied to underwater wireless optical communication (UWOC) systems to increase the channel capacity. In this work, we propose a diffractive deep neural network (DDNN) based OAM mode recognition scheme, where the DDNN is trained to capture the features of the intensity distribution of the OAM modes and output the corresponding azimuthal indices and radial indices. The results show that the proposed scheme can recognize the azimuthal indices and radial indices of the OAM modes accurately and quickly. In addition, the proposed scheme can resist weak oceanic turbulence (OT), and exhibit excellent ability to recognize OAM modes in a strong OT environment. The DDNN-based OAM mode recognition scheme has potential applications in UWOC systems.

Ghost imaging (GI) offers great potential with respect to conventional imaging techniques. However, there are still some obstacles for reconstructing images with high quality, especially in the case that the orthogonal measurement matrix is impossible to construct. In this paper, we propose a new scheme based on the orthogonal-triangular (QR) decomposition, named QR decomposition ghost imaging (QRGI) to reconstruct a better image with good quality. In the scheme, we can change the randomly non-orthogonal measurement matrix into orthonormal matrix by performing QR decomposition in two cases. (1) When the random measurement matrix is square, it can be firstly decomposed into an orthogonal matrix Q and an upper triangular matrix R . Then let the off-diagonal values of R equal to 0.0, the diagonal elements of R equal to a constant k, where k is the average of all values of the main diagonal, so the resulting measurement matrix can be obtained. (2) When the random measurement matrix is with full rank, we firstly compute its transpose, and followed with above QR operation. Finally, the image of the object can be reconstructed by correlating the new measurement matrix and corresponding bucket values. Both experimental and simulation results verify the feasibility of the proposed QRGI scheme. Moreover, the results also show that the proposed QRGI scheme could improve the imaging quality comparing to traditional GI (TGI) and differential GI (DGI). Besides, in comparison with the singular value decomposition ghost imaging (SVDGI), the imaging quality and the reconstruction time by using QRGI are similar to those by using SVDGI, while the computing time (the time consuming on the light patterns computation) is substantially shortened.

We propose a method for imaging a periodic moving/state-changed object based on computational ghost imaging with Hadamard speckle patterns and a slow bucket detector, named as PO-HCGI. In the scheme, speckle patterns are produced from a part of each row of a Hadamard matrix. Then, in each cycle, multiple speckle patterns are projected onto the periodic moving/state-changed object, and a bucket detector with a slow sampling rate records the total intensities reflected from the object as one measurement. With a series of measurements, the frames of the moving/state-changed object can be obtained directly by the second-order correlation function based on the Hadamard matrix and the corresponding bucket detector measurement results. The experimental and simulation results demonstrate the validity of the PO-HCGI. To the best of our knowledge, PO-HCGI is the first scheme that can image a fast periodic moving/state-changed object by computational ghost imaging with a slow bucket detector.

Measurement can reveal the difference between quantum physics and classical one. Recently, a quantum witness $$W_q$$ was proposed to characterize quantumness (Li et al. in Sci Rep 2:885, 2012; Kofler and Brukner in Phys Rev A 87:052115, 2013). It is built upon the no-signaling-in-time condition, and there is only one-time intermediate measurement. As an extension, we consider here multiple intermediate measurements at different moments of time. And we discuss the quantumness of a damped and driven qubit. Uniform, quasiperiodic and random time-interval sequences (TISs) of measurements are considered, respectively. Numerical results show that $$W_q$$ depends on the kind of TISs when the number of measurements N is less than 10, while it is almost independent of the kind of TISs when N is larger. Further, $$W_q\le W_q^{max}(N)=(1-\frac{1}{2N}) e^{-\gamma \tau }$$ for all cases, where $$\tau $$ is the evolution time, $$\gamma $$ is the dephasing intensity, and $$W_q^{max}(N)$$ is the maximum violation of the quantum witness equality.

The transmission loss of photons during quantum key distribution (QKD) process leads to the linear key rate bound for practical QKD systems without quantum repeaters. Phase matching quantum key distribution (PM-QKD) protocol, an novel QKD protocol, can overcome the constraint with a measurement-device-independent structure, while it still requires the light source to be ideal. This assumption is not guaranteed in practice, leading to practical secure issues. In this paper, we propose a modified PM-QKD protocol with a light source monitoring, named PM-QKD-LSM protocol, which can guarantee the security of the system under the non-ideal source condition. The results show that our proposed protocol performs almost the same as the ideal PM-QKD protocol even considering the imperfect factors in practical systems. PM-QKD-LSM protocol has a better performance with source fluctuation, and it is robust in symmetric or asymmetric cases.

We propose a scheme to fast prepare the three-qubit W state via superadiabatic-based shortcuts in a circuit quantum electrodynamics (circuit QED) system. We derive the effective Hamiltonian to suppress the unwanted transitions between different eigenstates by counterdiabatic driving, and obtain the W state with high-fidelity based on the superadiabatic passage. The numerical simulation results demonstrate that the proposed scheme can accelerate the evolution, and is more efficient than that with the adiabatic passage. In addition, the proposed scheme is robust to the decoherence caused by the resonator decay and qubit relaxation, and does not need additional parameters, which could be feasible in experiment.

We propose a novel quantity to measure the degree of localization properties of various types of one-dimension single electron states. The quantity includes information about the spatial variation of probability density of quantum states. Numerical results show that it can distinguish localized states from delocalized ones, so it can be used as a fruitful index to monitor the localization–delocalization transition. Comparing with existing measures, such as geometric average density of states, inverse participation ratio, and quantum information entropies, our proposed quantity has some advantages over them.

We propose a complex quantity, A L , to characterize the degree of disorder of L -length binary symbolic sequences. As examples, we respectively apply it to typical random and deterministic sequences. One kind of random sequences is generated from a periodic binary sequence and the other is generated from the logistic map. The deterministic sequences are the Fibonacci and Thue–Morse sequences. In these analyzed sequences, we find that the modulus of A L , denoted by | A L | , is a (statistically) equivalent quantity to the Boltzmann entropy, the metric entropy, the conditional block entropy and/or other quantities, so it is a useful quantitative measure of disorder. It can be as a fruitful index to discern which sequence is more disordered. Moreover, there is one and only one value of | A L | for the overall disorder characteristics. It needs extremely low computational costs. It can be easily experimentally realized. From all these mentioned, we believe that the proposed measure of disorder is a valuable complement to existing ones in symbolic sequences.

Round-robin differential-phase-shift (RRDPS) quantum key distribution (QKD) scheme provides an effective way to overcome the signal disturbance from the transmission process. However, most RRDPS-QKD schemes use weak coherent pulses (WCPs) as the replacement of the perfect single-photon source. Considering the heralded pair-coherent source (HPCS) can efficiently remove the shortcomings of WCPs, we propose a RRDPS-QKD scheme with HPCS in this paper. Both infinite-intensity decoy-state method and practical three-intensity decoy-state method are adopted to discuss the tight bound of the key rate of the proposed scheme. The results show that HPCS is a better candidate for the replacement of the perfect single-photon source, and both the key rate and the transmission distance are greatly increased in comparison with those results with WCPs when the length of the pulse trains is small. Simultaneously, the performance of the proposed scheme using three-intensity decoy states is close to that result using infinite-intensity decoy states when the length of pulse trains is small.

A recent paper (Chuan Wang in Phys Rev A 86:012323, 2012) discussed an entanglement concentration protocol (ECP) for partially entangled electrons using a quantum dot and microcavity coupled system. In his paper, each two-electron spin system in a partially entangled state can be concentrated with the assistance of an ancillary quantum dot and a single photon. In this paper, we will present an efficient ECP for such entangled electrons with the help of only one single photon. Compared with the protocol of Wang, the most significant advantage is that during the whole ECP, the single photon only needs to pass through one microcavity which will increase the total success probability if the cavity is imperfect. The whole protocol can be repeated to get a higher success probability. With the feasible technology, this protocol may be useful in current long-distance quantum communications.

We investigate numerically the quantum discord and the classical correlation in a one-dimensional slowly varying potential model and a one-dimensional Soukoulis–Economou ones, respectively. There are well-defined mobility edges in the slowly varying potential model, while there are discrepancies on mobility edges in the Soukoulis–Economou ones. In the slowly varying potential model, we find that extended and localized states can be distinguished by both the quantum discord and the classical correlation. There are sharp transitions in the quantum discord and the classical correlation at mobility edges. Based on these, we study “mobility edges” in the Soukoulis–Economou model using the quantum discord and the classical correlation, which gives another perspectives for these “mobility edges”. All these provide us good quantities, i.e., the quantum discord and the classical correlation, to reflect mobility edges in these one-dimensional aperiodic single-electron systems. Moreover, our studies propose a consistent interpretation of the discrepancies between previous numerical results about the Soukoulis–Economou model.

We put forward an efficient entanglement concentration protocol (ECP) for arbitrary less-entangled NOON state. In the protocol, we resort to the weak cross-Kerr nonlinearity to complete this task. Different from other ECPs, this protocol can be reused to get a high success probability. We do not need to know the exact coefficients of the initial state. Moreover, we even do not need to know the exact photon number of the initial NOON state. This protocol may be useful and convenient in the current quantum information processing.

Combination of channel coding and modulation has been demonstrated to have high power and bandwidth efficiency. Compared with polar codes, the concatenated polar codes boost the error rate probability to almost exponential in the block-length with essentially no loss in computational complexity. In this paper, a concatenated polar-coded multilevel modulation scheme is proposed, where polar codes are the inner codes and Reed-Solomon or low density parity check codes are chosen as the outer codes. The bit error rate (BER) performances of the proposed scheme are analyzed for different inner polar code length and different inner polar code rate. The numerical simulation results show that the scheme has significantly improved in the BER performance in comparison with those results using multilevel polar-coded modulation and single level concatenated-polar coded modulation scheme. With the increase of code length and the decrease of code rate of the inner polar codes, the system has a better BER performance.

Shannon information entropy (SE), concurrence (CC), quantum discord (QD) and localization properties for various one-dimensional one-electron wave functions are intensively studied, respectively. They include Gaussian functions, power-law functions, and functions in the Anderson model and the Harper ones. For all these wave functions, we find that SE, CC and QD increase as the localization length of a wave function increases, respectively. There are linear or quadratic relationships between two of them. Therefore, we can confirm for the analyzed models that SE, CC and QD are statistically equivalent quantities to reflect the localization properties of wave functions though they are different measures of quantum information.

In this paper, a class of state-dependent relay channel with orthogonal channels from the source to the relay and from the source and the relay to the destination is studied. The two orthogonal channels are corrupted by common channel state which is known to both the source and the relay non-causally. The lower bound on the capacity for the channel is derived firstly. Then, we show that if the receiver output Y is a deterministic function of the relay input Xr, the channel state S and one of the source inputs XD, i.e. Y = f(Xr, XD, S), the explicit capacity can be characterized.

A homologous sequence was amplified from resurrection plant Selaginella pulvinta by RACE technique, proved to be the full-length cDNA of trehalose-6-phosphate synthase gene by homologous alignment and yeast complementation assay, and nominated as SpTPS1 gene. The open reading frame of this gene was truncated 225 bp at the 5′-end, resulting the N-terminal truncation modification of 75 amino acids for its encoding protein. The TPS1 deletion mutant strain YSH290 of the brewer's yeast transformed by the truncated gene SpTPS1Δ and its original full-length version restored growth on the medium with glucose as a sole carbon source and displayed growth curves with no significant difference, indicating their encoding proteins functioning as TPS enzyme. The TPS activity of the mutant strain transformed by the truncated gene SpTPS1Δ was about six fold higher than that transformed by its original version, reasoning that the extra N-terminal extension of the full-length amino acid sequence acts as an inhibitory domain to trehalose synthesis. However, the trehalose accumulation of the mutant strain transformed by the truncated gene SpTPS1Δ was only 8% higher than that transformed by its original version. This result is explained by the feedback balance of trehalose content coordinated by the comparative activities between trehalose synthase and trehalase. The truncated gene SpTPS1Δ is suggested to be used in transgenic operation, together with the inhibition of trehalase activity by the application of validamycin A or genetic deficiency of the endogenous trehalase gene, for the enhancement of trehalose accumulation and improvement of abiotic tolerance in transgenic plants.

We present two two-step practical entanglement concentration protocols (ECPs) for concentrating an arbitrary three-particle less-entangled W state into a maximally entangled W state assisted with single photons. The first protocol uses the linear optics and the second protocol adopts the cross-Kerr nonlinearity to perform the protocol. In the first protocol, based on the post-selection principle, three parties say Alice, Bob and Charlie in different distant locations can obtain the maximally entangled W state from the arbitrary less-entangled W state with a certain success probability. In the second protocol, it dose not require the parties to posses the sophisticated single-photon detectors and the concentrated photon pair can be retained after performing this protocol successfully. Moreover, the second protocol can be repeated to get a higher success probability. Both protocols may be useful in practical quantum information applications., 10 pages, 4 figures

We present two realistic entanglement concentration protocols (ECPs) for pure partially entangled photons. A partially entangled photon pair can be concentrated to a maximally entangled pair with only an ancillary single photon with a certain probability, while the conventional ECPs require two copies of partially entangled pairs at least. Our first protocol is implemented with linear optics and the second protocol is implemented with cross-Kerr-nonlinearities. Compared with other ECPs, they do not need to know the accurate coefficients of the initial state. With linear optics, it is feasible with current experiments. With cross-Kerr-nonlinearities, it does not require sophisticated single-photon detectors and can be repeated to get a higher success probability. Moreover, the second protocol can get the higher entanglement transformation efficiency and it may be the most economical protocol by far. Meanwhile, both protocols are more suitable for multiphoton system concentration because they need less operations and classical communications. All these advantages make the two protocols useful in current long-distance quantum communications.

We present an efficient entanglement concentration protocol (ECP) for mobile electrons with charge detection. This protocol is quite different from other ECPs for one can obtain a maximally entangled pair from a pair of less-entangled state and a single mobile electron with a certain probability. With the help of charge detection, it can be repeated to reach a higher success probability. It also does not need to know the coefficient of the original less-entangled states. All these advantages may make this protocol useful in current distributed quantum information processing., Comment: 6pages, 3figures

Polar codes, introduced by Arikan recently, can achieve capacity of symmetric channel with low complexity successive cancellation decoding strategy. In this paper, we design efficient Bhattacharyya Parameters in Polar codes construction for common communications channels. We present the satisfactory recursive formula for the four conventional channels and discuss the initial value of each recursive equations. Numerical simulations show that Polar codes are channel-specific designing codes; they can approach their capacities by selecting the frozen bits in our proposed Bhattacharyya Parameter calculating method.

Taking advantages of the property of classical codes from balance incomplete block designs (BIBDs), an improved construction of quantum Low Density Parity Check (quantum LDPC) codes is proposed in this paper. In the construction, we modified the original "Construction B" procedures to assure the quantum parity check matrix commutativity. It is shown that this construction method is a systematic structured method, and it is easier to obtain quantum codes. By simulation, we find the quantum parity check matrix obtained by our method are sparser than those from the method proposed by Ivan, and the codes have more good performance with the belief propagation iterative decoding algorithms.

With the development of quantum error correction techniques, many counterparts of classical error correction coding techniques have been found in quantum area. As the quantum counterpart of a good error correction code in classical communications, quantum low density parity check code becomes a promising coding technique in quantum error correction area. In this paper, a construction method of quantum low density parity check code (quantum LDPC) based on Projective Geometry is proposed, and the quantum code QLDPC [21,6] is selected as an example to illustrate the whole construction procedures. By numerical simulation, the error correction performance of QLDPC [21,6] is discussed over the bit-flipping channel. It is shown that this method is available and has some advantages.

Quantum error correction is the basic technique for realization of quantum communication and quantum computation. So far, the theories of quantum error correction have become more and more perfect, and many counterpart of classical error correction coding technique have been found in quantum area. In this article, we proposed a new method of construction of parity check matrix of quantum low density parity check (LDPC) codes which based on classical quasi-cyclic LDPC codes, and selected the quantum code (3,8)(16,6) as the example to illustrate the construction of quantum code. We also gave its completing circuit by controlled-not gate and Hadamard gate.

To investigate the relationship between the expression of host human leukocyte antigen-B mRNA (HLA-B mRNA) and HLA-B antigen in peripheral blood leukocytes (PBLs) and the differentiation and metastasis of gastric carcinoma (GC).To design and screen specific primers of HLA-B gene independently, detect the expression of HLA-B mRNA from 30 GC patients by reverse transcription-PCR and compare with the HLA-B antigen expression measured by flow cytometry.The expression rate of PBL HLA-B mRNA from GC patients (23. 3% ) was very significantly lower than that of normals (87. 5% ) (P0. 01) , especially concerning the poorly differentiated GC patients with lymph node metastasis (16. 0% ). Measured by flow cytometry, the expression percentage of HLA-B antigen of well-differentiated GC patients without lymph node metastasis was 88. 2% , an obviously decreasing tendency was showed in comparison with that in the normal group (98. 8% ) , although the difference was not significant (P = 0. 056) , and the expression percentage in poorly differentiated GC patients with lymph node metastasis(73. 3% )was declined significantly (P0. 05).The expression of PBL HLA-B mRNA and HLA-B antigen in GC patients is decreased or lost, and correlated with differentiation and metastasis of the cancer. The expression of PBL HLA-B mRNA may more directly reflect its relationship with the tumor differentiation and metastasis than that of HLA-B antigen.

Covariance shaping least squares estimator is a new kind of linear estimator based on covariance shaping in quantum signal processing (QSP) framework, it is a biased estimator directed at improving the performance of traditional least- squares (LS) estimator. In this paper, we discuss the covariance shaping least squares (CSLS) estimator, and apply it in multi-user detection that leads to a new detection algorithm, and then we employ it in the detection of MIMO systems. The numerical results in synchronous DS-CDMA communications system show that the performance of covariance shaping multi-user detection which depends only on the users' signatures is better than that of traditional MF and decorrelation detection, and is an approach to the MMSE detection method. The results in MIMO systems also show that the performance of system is better than that of detection algorithm with Zero-forcing and MMSE solutions.

In this paper, we propose a measurement-device-independent quantum-key-distribution (MDI-QKD) protocol using orbital angular momentum (OAM) in free space links, named the OAM-MDI-QKD protocol. In the proposed protocol, the OAM states of photons, instead of polarization states, are used as the information carriers to avoid the reference frame alignment, the decoy-state is adopted to overcome the security loophole caused by the weak coherent pulse source, and the high efficient OAM-sorter is adopted as the measurement tool for Charlie to obtain the output OAM state. Here, Charlie may be an untrusted third party. The results show that the authorized users, Alice and Bob, could distill a secret key with Charlie's successful measurements, and the key generation performance is slightly better than that of the polarization-based MDI-QKD protocol in the two-dimensional OAM cases. Simultaneously, Alice and Bob can reduce the number of flipping the bits in the secure key distillation. It is indicated that a higher key generation rate performance could be obtained by a high dimensional OAM-MDI-QKD protocol because of the unlimited degree of freedom on OAM states. Moreover, the results show that the key generation rate and the transmission distance will decrease as the growth of the strength of atmospheric turbulence (AT) and the link attenuation. In addition, the decoy states used in the proposed protocol can get a considerable good performance without the need for an ideal source.

The classical optimal solution of CDMA multi-user detection is consistent with the optimization of a quadratic function, and to find the optimum is a NP hard problem. Reducing the complexity of optimum based on quantum parallel computation is a new trend of multi-user detection techniques. In this paper, we propose a scheme based on Grover's searching algorithm to find the optimum. We give the relationship of bit error rate against signal-to-noise and correlation coefficient by numerical simulation, and simply evaluate the computational complexity of our proposed scheme. The results show that our solution has almost the same performance to the classical optimal one, however, with low complexity.

We experimentally demonstrate a quantum key distribution (QKD) protocol using photon pairs entangled in orbit angular momentum (OAM). In our protocol, Alice and Bob modulate their OAM states on each entangled pair with spatial light modulators (SLMs), respectively. Alice uses a fixed phase hologram in her SLM, while Bob designs $N$ different suitable phase holograms and uses them to represent his $N$-based information in his SLM. With coincidences, Alice can fully retrieve the key stream sent by Bob without information reconciliation or privacy amplification. We report the experiment results with N=3 and the sector states with OAM eigenmodes l=1 and l=-1. Our experiment shows that the coincidence rates are in relatively distinct value regions for the three different key elements. Alice could recover fully Bob's keys by the protocol. Finally, we discuss the security of the protocol both form the light way and against the general attacks.

We propose a scheme capable of performing complete Bell-state analysis for a single-photon hybrid entangled state. Our single-photon state is encoded in both polarization and frequency degrees of freedom. The setup of the scheme is composed of polarizing beam splitters, half wave plates, frequency shifters, and independent wavelength division multiplexers, which are feasible using current technology. We also show that with this setup we can perform complete two-photon Bell-state analysis schemes for polarization degrees of freedom. Moreover, it can also be used to perform the teleportation scheme between different degrees of freedom. This setup may allow extensive applications in current quantum communications.

We present an efficient entanglement concentration protocol (ECP) for the less-entangled W state with some identical conventional polarized single photons. In the protocol, two of the parties say Alice and Charlie should perform the parity check measurements and they can ultimately obtain the maximally entangled W state with a certain success probability Otherwise, they can obtain another less-entangled W state, which can be reconcentrated into the maximally entangled W state. By iterating this ECP, a high success probability can be achieved. This ECP may be an optimal one and it is useful in current quantum information processing.

We put forward an efficient entanglement concentration protocol (ECP) for recovering the single-photon less-entangled W state into the maximally entangled W state with only two conventional auxiliary photons. The ECP includes two local steps, both of which are based on the weak cross-Kerr nonlinearities and the variable beam splitter (VBS). Benefiting from the cross-Kerr nonlinearities and the VBS, the ECP can be used repeatedly to further concentrate the less-entangled W state. All the advantages indicate that our protocol may be feasible and convenient in current quantum communications areas.

We present an efficient entanglement purification protocol (EPP) with controlled-not (CNOT) gates and linear optics. With the CNOT gates, our EPP can reach a higher fidelity than the conventional one. Moreover, it does not require the fidelity of the initial mixed state to satisfy F > 1/2. If the initial state is not entangled, it still can be purified. With the linear optics, this protocol can get pure maximally entangled pairs with some probabilities. Meanwhile, it can be used to purify the entanglement between the atomic ensembles in distant locations. This protocol may be useful in long-distance quantum communication.

We introduce joint difference sets as a generalization of cyclic difference sets, and we construct a new class of quantum error-correcting codes (QECCs) from these joint difference sets. The main benefits of our method are as follows. First, we can construct quantum codes that are both high rate and with large block length, while maintaining good performance. Second, the density of constructed quantum parity check matrix can approach zero when the code length is very large. This allows us to use a simple iterative decoding algorithm. Interestingly, our method yields the well-known [5,1,3] QECC.