Simple family of nonadditive quantum codes

Most known quantum codes are additive, meaning the code can be described as the simultaneous eigenspace of an Abelian subgroup of the Pauli group. While in some scenarios such codes are strictly suboptimal, very little is understood about how to construct nonadditive codes with good performance. Here we present a family of distance 2 nonadditive quantum codes for all odd block lengths n, that has a particularly simple form. Our codes detect single qubit errors (or correct single qubit erasures) while encoding a higher dimensional space than is possible with an additive code or, for n> or =11, any previous codes. We exhibit the encoding circuits and automorphism group for our codes as well.     

Substituting a qubit for an arbitrarily large number of classical bits

We show that a qubit can be used to substitute for a classical analog system requiring an arbitrarily large number of classical bits to represent digitally. Let a physical system S interact locally with a classical field varphi(x) as S travels directly from point A to point B. Our task is to use S to answer a simple yes/no question about varphi(x). If S is a qubit, the task can be done perfectly. We show that any classical system S must encode an arbitrarily large number of classical bits to solve the same task. This result implies a large quantum advantage in the memory size necessary for some computations. We also show that no finite amount of one-way classical communication can perfectly simulate the effect of quantum entanglement.     

Stabilizing distinguishable qubits against spontaneous decay by detected-jump correcting quantum codes

A new class of error-correcting quantum codes is introduced capable of stabilizing qubits against spontaneous decay arising from couplings to statistically independent reservoirs. These quantum codes are based on the idea of using an embedded quantum code and exploiting the classical information available about which qubit has been affected by the environment. They are immediately relevant for quantum computation and information processing using arrays of trapped ions or nuclear spins. Interesting relations between these quantum codes and basic notions of design theory are established.     

Quantum secure direct communication and deterministic secure quantum communication

In this review article, we review the recent development of quantum secure direct communication (QSDC) and deterministic secure quantum communication (DSQC) which both are used to transmit secret message, including the criteria for QSDC, some interesting QSDC protocols, the DSQC protocols and QSDC network, etc. The difference between these two branches of quantum communication is that DSQC requires the two parties exchange at least one bit of classical information for reading out the message in each qubit, and QSDC does not. They are attractive because they are deterministic, in particular, the QSDC protocol is fully quantum mechanical. With sophisticated quantum technology in the future, the QSDC may become more and more popular. For ensuring the safety of QSDC with single photons and quantum information sharing of single qubit in a noisy channel, a quantum privacy amplification protocol has been proposed. It involves very simple CHC operations and reduces the information leakage to a negligible small level. Moreover, with the one-party quantum error correction, a relation has been established between classical linear codes and quantum one-party codes, hence it is convenient to transfer many good classical error correction codes to the quantum world. The one-party quantum error correction codes are especially designed for quantum dense coding and related QSDC protocols based on dense coding.      

一类基于级联结构的量子好码

借助经典级联码的思想，详细阐述了通过适当选择量子码作为外码和内码，构造一般意义量子级联码的过程.在此基础上，通过选择量子RS码作为外码，一组特殊结构的量子码作为内码，具体构造出了一类量子级联码，证明了其是量子好码.在量子纠错码领域中，这是首次利用经典坏码构造出量子好码.     

A small error-correction code for protecting three-qubit quantum information

We present a quantum error correction code which protects three quantum bits (qubits) of quantum information against one erasure, i.e., a single-qubit arbitrary error at a known position. The present code has a high encoding efficiency, since only one auxiliary qubit is needed for one message qubit on average. In addition, we note that the code can also work even in a worse case that the interaction with the environment causes a leakage out of the qubit space. The code may have some applications in the storage of quantum information for small-scale quantum computing, quantum information processing, and quantum communication.     

Delayed commutation in quantum computer networks

In the same way that classical computer networks connect and enhance the capabilities of classical computers, quantum networks can combine the advantages of quantum information and communication. We propose a nonclassical network element, a delayed commutation switch, that can solve the problem of switching time in packet switching networks. With the help of some local ancillary qubits and superdense codes, we can route a qubit packet after part of it has left the network node.     

Some New Quantum BCH Codes over Finite Fields

Quantum error correcting codes (QECCs) play an important role in preventing quantum information decoherence. Good quantum stabilizer codes were constructed by classical error correcting codes. In this paper, Bose–Chaudhuri–Hocquenghem (BCH) codes over finite fields are used to construct quantum codes. First, we try to find such classical BCH codes, which contain their dual codes, by studying the suitable cyclotomic cosets. Then, we construct nonbinary quantum BCH codes with given parameter sets. Finally, a new family of quantum BCH codes can be realized by Steane’s enlargement of nonbinary Calderbank-Shor-Steane (CSS) construction and Hermitian construction. We have proven that the cyclotomic cosets are good tools to study quantum BCH codes. The defining sets contain the highest numbers of consecutive integers. Compared with the results in the references, the new quantum BCH codes have better code parameters without restrictions and better lower bounds on minimum distances. What is more, the new quantum codes can be constructed over any finite fields, which enlarges the range of quantum BCH codes.     

Nonlocality,asymmetry, and distinguishing bipartite states

Entanglement is a useful resource because some global operations cannot be locally implemented using classical communication. We prove a number of results about what is and what is not locally possible. We focus on orthogonal states, which can always be globally distinguished. We establish the necessary and sufficient conditions for a general set of 2 x 2 quantum states to be locally distinguishable, and for a general set of 2 x n quantum states to be distinguished given an initial measurement of the qubit. These results reveal a fundamental asymmetry to nonlocality, which is the origin of "nonlocality without entanglement," and we present a very simple proof of this phenomenon.     

Equivalence of a Bit Pixel Image to a Quantum Pixel Image

We propose a new method to transform a pixel image to the corresponding quantum-pixel using a qubit per pixel to represent each pixels classical weight in a quantum image matrix weight.All qubits are linear superposition,changing the coefficients level by level to the entire longitude of the gray scale with respect to the base states of the qubit.Classically,these states are just bytes represented in a binary matrix,having code combinations of 1 or 0 at all pixel locations.This method introduces a qubit-pixel image representation of images captured by classical optoelectronic methods.     

Simultaneous cooling of an artificial atom and its neighboring quantum system

We propose an approach for cooling both an artificial atom (e.g., a flux qubit) and its neighboring quantum system, the latter modeled by either a quantum two-level system or a quantum resonator. The flux qubit is cooled by manipulating its states, following an inverse process of state population inversion, and then the qubit is switched on to resonantly interact with the neighboring quantum system. By repeating these steps, the two subsystems can be simultaneously cooled. Our results show that this cooling is robust and effective, irrespective of the chosen quantum systems connected to the qubit.     

Equivalence of a Bit Pixel Image to a Quantum Pixel Image

We propose a new method to transform a pixel image to the corresponding quantum-pixel using a qubit per pixel to represent each pixels classical weight in a quantum image matrix weight. All qubits are linear superposition, changing the coefficients level by level to the entire longitude of the gray scale with respect to the base states of the qubit. Classically, these states are just bytes represented in a binary matrix, having code combinations of 1 or 0 at all pixel locations. This method introduces a qubit-pixel image representation of images captured by classical optoelectronic methods.     

Probing tiny motions of nanomechanical resonators: classical or quantum mechanical?

We propose a spectroscopic approach to probe tiny vibrations of a nanomechanical resonator (NAMR), which may reveal classical or quantum behavior depending on the decoherence-inducing environment. Our proposal is based on the detection of the voltage-fluctuation spectrum in a superconducting transmission line resonator (TLR), which is indirectly coupled to the NAMR via a controllable Josephson qubit acting as a quantum transducer. The classical (quantum mechanical) vibrations of the NAMR induce symmetric (asymmetric) Stark shifts of the qubit levels, which can be measured by the voltage fluctuations in the TLR. Thus, the motion of the NAMR, including if it is quantum mechanical or not, could be probed by detecting the voltage-fluctuation spectrum of the TLR.     

Theory of quantum error correction for general noise

A measure of quality of an error-correcting code is the maximum number of errors that it is able to correct. We show that a suitable notion of "number of errors" e makes sense for any quantum or classical system in the presence of arbitrary interactions. Thus, e-error-correcting codes protect information without requiring the usual assumptions of independence. We prove the existence of large codes for both quantum and classical information. By viewing error-correcting codes as subsystems, we relate codes to irreducible representations of operator algebras and show that noiseless subsystems are infinite-distance error-correcting codes.     

Charge Qubit Storage and Its Engineered Decoherence via Microwave Cavity

We study the entanglement of the superconducting charge qubit with the quantized electromagnetic field in a microwave cavity. It can be controlled dynamically by a classical external field threading the SQUID within the charge qubit. Utilizing the controllable quantum entanglement, we can demonstrate the dynamic process of the quantum storage of information carried by charge qubit. On the other hand, based on this engineered quantum entanglement, we can also demonstrate a progressive decoherence of charge qubit with quantum jump due to the coupling with the cavity field in quasi-classical state.     

Classical and quantum communication without a shared reference frame

We show that communication without a shared reference frame is possible using entangled states. Both classical and quantum information can be communicated with perfect fidelity without a shared reference frame at a rate that asymptotically approaches one classical bit or one encoded qubit per transmitted qubit. We present an optical scheme to communicate classical bits without a shared reference frame using entangled photon pairs and linear optical Bell state measurements.     

Quantum Key Distribution Using High-Dimensional Quantum Error-Avoiding Code

Using high-dimensional quantum error-avoiding code, we present two new quantum key distribution protocols over a collective noisy channel, i.e. six-photon and five-photon quantum error-avoiding codes. Compared with the previous protocols using four-photon and three-photon quantum error-avoiding code, the qubit efficiencies of the new protocols have increases of 16.67% and 5% respectively. In addition, the security of these protocols is analysed with a conclusion that the new protocols are much more secure than the four-photon and three-photon ones.     

量子卷积码的编译码方法

对于量子卷积码理论的研究旨在保护长距离通信中的量子信息序列. 定义了量子态的多项式表示形式,根据Calderbank-Shor-Steane(CSS)型量子码的构造方法,给出了CSS型量子卷积码的一种新的编译码方法,描述了编译码网络. 该方法将码字基态变换为信息多项式与生成多项式的乘积,然后用量子态上的多项式乘法操作实现编译码网络. 最后借鉴经典卷积码的译码思想,给出了具有线性复杂度的量子Viterbi算法. 关键词： 量子信息 量子卷积码 编译码 纠错算法     

Behavior of quantum correlations under local noise

We characterize the behavior of quantum correlations under the influence of local noisy channels. Intuition suggests that such noise should be detrimental for quantumness. When considering qubit systems, we show for which channels this is indeed the case: The amount of quantum correlations can only decrease under the action of unital channels. However, nonunital channels (e.g., such as dissipation) can create quantum correlations for some initially classical states. Furthermore, for higher-dimensional systems even unital channels may increase the amount of quantum correlations. Thus, counterintuitively, local decoherence can generate quantum correlations.     

Triangle Geometry for Qutrit States in the Probability Representation

We express the matrix elements of the density matrix of the qutrit state in terms of probabilities associated with artificial qubit states. We show that the quantum statistics of qubit states and observables is formally equivalent to the statistics of classical systems with three random vector variables and three classical probability distributions obeying special constrains found in this study. The Bloch spheres geometry of qubit states is mapped onto triangle geometry of qubits. We investigate the triada of Malevich’s squares describing the qubit states in quantum suprematism picture and the inequalities for the areas of the squares for qutrit (spin-1 system). We expressed quantum channels for qutrit states in terms of a linear transform of the probabilities determining the qutrit-state density matrix.