Spin Squeezing Criterion with Local Unitary Invariance

We propose a spin squeezing criterion for arbitrary multi-qubit states that is invariant under local unitary operations. We find that, for arbitrary pure two-qubit states, spin squeezing is equivalent to entanglement, and multi-qubit states are entangled if this new spin squeezing parameter is less than unity. PACS: 03.67.-a; 03.65.Ud     

Operator-Schmidt decomposition and the geometrical edges of two-qubit gates

Nonlocal two-qubit quantum gates are represented by canonical decomposition or equivalently by operator-Schmidt decomposition. The former decomposition results in geometrical representation such that all the two-qubit gates form tetrahedron within which perfect entanglers form a polyhedron. On the other hand, it is known from the later decomposition that Schmidt number of nonlocal gates can be either 2 or 4. In this work, some aspects of later decomposition are investigated. It is shown that two gates differing by local operations possess same set of Schmidt coefficients. Employing geometrical method, it is established that Schmidt number 2 corresponds to controlled unitary gates. Further, all the edges of tetrahedron and polyhedron are characterized using Schmidt strength, a measure of operator entanglement. It is found that one edge of the tetrahedron possesses the maximum Schmidt strength, implying that all the gates in the edge are maximally entangled.     

Testing Hardy’s ladder proof of nonlocality by joint measurements of qubits

We propose an experimentally feasible scheme to test Hardy’s ladder proof of nonlocality with two qubits (two-level atoms) dispersively coupled to a driven cavity. First, we find that the required nonmaximally entangled two-qubit pure state can be prepared by only one-step two-qubit operation from the ground state $|00\rangle $ | 00 〉 , assisted by two single-qubit gates. Next, we perform two single-qubit operations to encode the local information into the prepared nonmaximally entangled state. Finally, the nonlocal correlations between the two qubits can be directly detected by the joint measurement of the two-qubit register in one of selected computational basis, implemented by probing the steady-state transmitted spectra of the driven cavity. Consequently, the Hardy’s ladder proof of nonlocality can be effectively tested. The feasibility of our proposal with the current experimental technology is also analyzed.     

以最大slice态为信道的受控量子远程控制

利用三量子最大slice态作为量子信道,提出了单量子酉算子的受控远程执行的两个协议.首先,利用双向量子隐形传态(BQST),给出了一个任意单量子酉算子的受控隐形传输方案.结果 表明,通过非最大纠缠信道,发送者能够在遥远的接受者的量子系统上远程地执行一个任意单量子酉算子.如果发送者和控制者对各自量子执行恰当的投影测量,那...     

On the Generation of Sequential Unitary Gates from Continuous Time Schrödinger Equations Driven by External Fields

In most of the proposals for quantum computers, a common feature is that the quantum circuits are expected to be made of cascades of unitary transformations acting on the quantum states. Such unitary gates are normally assumed to belong to a given discrete set of transformations. However, arbitrary superposition of quantum states may be achieved by utilizing a fixed number of transformations, each depending on a parameter. A framework is proposed to dynamically express these parameters directly in terms of the control inputs entering into the continuous time forced Schrouml;dinger equation. PACS: 03.67.Lx; 03.65.Fd; 02.30.Mv; 02.30.Xy     

Towards Scalable Linear-Optical Quantum Computers

Scalable quantum computation with linear optics was considered to be impossible due to the lack of efficient two-qubit logic gates, despite the ease of implementation of one-qubit gates. Two-qubit gates necessarily need a non-linear interaction between the two photons, and the efficiency of this non-linear interaction is typically very small in bulk materials. However, it has recently been shown that this barrier can be circumvented with effective non-linearities produced by projective measurements, and with this work linear-optical quantum computing becomes a new avenue towards scalable quantum computation. We review several issues concerning the principles and requirements of this scheme. PACS: 03.67.Lx, 03.67.Pp, 42.50.Dv, 42.65.Lm     

Quantum Comparison Machines with One-Sided Error

It is always possible to decide, with one-sided error, whether two quantum states are the same under a specific unitary transformation. However we show here that it is impossible to do so if the transformation is anti-linear and non-singular. This result implies that unitary and anti-unitary operations exist on an unequal footing in quantum information theory. PACS: 03.67.-a     

Multi-qubit non-adiabatic holonomic controlled quantum gates in decoherence-free subspaces

Non-adiabatic holonomic quantum gate in decoherence-free subspaces is of greatly practical importance due to its built-in fault tolerance, coherence stabilization virtues, and short run-time. Here, we propose some compact schemes to implement two- and three-qubit controlled unitary quantum gates and Fredkin gate. For the controlled unitary quantum gates, the unitary operator acting on the target qubit is an arbitrary single-qubit gate operation. The controlled quantum gates can be directly implemented by utilizing non-adiabatic holonomy in decoherence-free subspaces and the required resource for the decoherence-free subspace encoding is minimal by using only two neighboring physical qubits undergoing collective dephasing to encode a logical qubit.     

Quantum Codes for Simplifying Design and Suppressing Decoherence in Superconducting Phase-Qubits

We introduce simple qubit-encodings and logic gates which eliminate the need for certain difficult single-qubit operations in superconducting phase-qubits, while preserving universality. The simplest encoding uses two physical qubits per logical qubit. Two architectures for its implementation are proposed: one employing N physical qubits out of which N/2 are ancillas fixed in the |1 state, the other employing N/2+1 physical qubits, one of which is a bus qubit connected to all others. Details of a minimal set of universal encoded logic operations are given, together with recoupling schemes, that require nanosecond pulses. A generalization to codes with higher ratio of number of logical qubits per physical qubits is presented. Compatible decoherence and noise suppression strategies are also discussed. PACS: 03.67.Lx; 85.25.Hv; 03.67.-a; 89.70.+c     

On the role of the four-qubit state in two-qubit gate teleportation

The full analysis of quantum protocols requires the knowledge of the role of quantum states, bases of measurement and quantum gates involved. In what concerns the famous two-qubit quantum gate teleportation protocol, the role of the basis of measurement was considered in a recent work by Mendes and Ramos. In this work, we analyze the role of the four-qubit state used as resource. We show that the quantum two-qubit gate teleportation divides the set of pure four-qubit states in two classes. For one class, deterministic and probabilistic teleportation can be achieved, while for the other class, probabilistic remote two-qubit gate preparation is achieved.     

量子搜索算法体系的仿真实现及研究

核磁共振（NMR）技术被认为是最为有效的实现量子计算的物理体系之一。多量子算符代数理论可以将幺正变换分解为一系列有限的单量子门和对角双量子门的组合。本文以核磁共振和多量子算符代数理论为基础，提出了实现任意相位旋转角度的一般化量子搜索算法的核磁共振脉冲序列设计方法，并在量子计算仿真程序上进行了双量子位的不同相位旋转角度的量子搜索算法的实验验证。     

Multi-party quantum state sharing via various probabilistic channels

We present a new scheme to share an arbitrary multi-qubit state between n agents via various probabilistic channels under cooperation of m?1 controllers with a certain probability. Compared with existing ones in this literature, our scheme involves various probabilistic channels, which weakens the requirement for quantum channels. The proposed scheme is symmetric which means even though the designed receiver has no capability of adopting appropriate strategies in introducing auxiliary qubits and performing two-qubit gates, it is still possible to faithfully share a multi-qubit state with assistance of other participants. This scheme involves only single-qubit measurements, CNOT gates, and local two-qubit gates with an auxiliary qubit, which makes it more convenient for physical realization.     

Sequential generation of polynomial invariants and N-body non-local correlations

We report an inductive process that allows for sequential construction of local unitary invariant polynomials of state coefficients for multipartite quantum states. The starting point can be a physically meaningful invariant of a smaller part of the system. The process is applied to construct a chain of invariants that quantify non-local N-way correlations in an N-qubit pure state. It also yields the invariants to quantify the sum of N-way and (N-1)-way correlations. Analytic expressions for four-way and three-way correlation quantifiers for four-qubit states, as well as, five-way and four-way correlation quantifiers for five-qubit pure states are given.     

Bidirectional teleportation of a pure EPR state by using GHZ states

In the present paper, a novel bidirectional quantum teleportation protocol is proposed. By using entanglement swapping technique, two GHZ states are shared as a quantum channel between Alice and Bob as legitimate users. In this scheme, based on controlled-not operation, single-qubit measurement, and appropriate unitary operations, two users can simultaneously transmit a pure EPR state to each other, While, in the previous protocols, the users can just teleport a single-qubit state to each other via more than four-qubit state. Therefore, the proposed scheme is economical compared with previous protocols.     

Dynamics of quantum entanglement in quantum channels

Based on the von Neumann entropy, we give a computational formalism of the quantum entanglement dynamics in quantum channels, which can be applied to a general finite systems coupled with their environments in quantum channels. The quantum entanglement is invariant in the decoupled local unitary quantum channel, but it is variant in the non-local coupled unitary quantum channel. The numerical investigation for two examples, two-qubit and two-qutrit models, indicates that the quantum entanglement evolution in the quantum non-local coupling channel oscillates with the coupling strength and time, and depends on the quantum entanglement of the initial state. It implies that quantum information loses or gains when the state of systems evolves in the quantum non-local coupling channel.     

Direct implementation of an N-qubit controlled-unitary gate in a single step

We present a new scheme to implement an N-qubit controlled-unitary operation directly in a single step. The main advantage of our scheme is that we do not use conventional gate decomposition protocols to break an N-qubit controlled-unitary gate into one- and two-qubit gates. This greatly reduces the number of computational steps in implementing quantum algorithms and error-correcting codes, which use multi-control unitary operations. We show how to find analytic solutions to the time evolution of the system, so that system parameters can be found to realize the desired N-qubit controlled-unitary operations.     

Multi-party quantum key agreement with five-qubit brown states

In this paper, we propose a multi-party quantum key agreement protocol with five-qubit brown states and single-qubit measurements. Our multi-party protocol ensures each participant to contribute equally to the agreement key. Each party performs three single-qubit unitary operations on three qubits of each brown state. Finally, by measuring brown states and decoding the measurement results, all participants can negotiate a shared secret key without classical bits exchange between them. With the analysis of security, our protocol demonstrates that it can resist against both outsider and participant attacks. Compared with other schemes, it also possesses a higher information efficiency. In terms of physical operation, it requires single-qubit measurements only which weakens the hardware requirements of participant and has a better operating flexibility.     

多量子位Grover量子搜索算法的NMR仿真实现

核磁共振（NMR）技术目前是能有效实现量子计算的物理体系之一。多量子算符代数理论可以将幺正变换分解为一系列有限的单量子门和对角双量子门的组合。本文以核磁共振和多量子算符代数理论为基础,提出了实现多量子位Grover量子搜索算法的核磁共振脉冲序列设计方法,并在量子计算仿真程序上进行了3量子位的Grover量子搜索算法的实验验证。     

Geometric Approach to Digital Quantum Information

We present geometric methods for uniformly discretizing the continuous N-qubit Hilbert space H_N. When considered as the vertices of a geometrical figure, the resulting states form the equivalent of a Platonic solid. The discretization technique inherently describes a class of /2 rotations that connect neighboring states in the set, i.e., that leave the geometrical figures invariant. These rotations are shown to generate the Clifford group, a general group of discrete transformations on N qubits. Discretizing H_N allows us to define its digital quantum information content, and we show that this information content grows as N². While we believe the discrete sets are interesting because they allow extra-classical behavior—such as quantum entanglement and quantum parallelism—to be explored while circumventing the continuity of Hilbert space, we also show how they may be a useful tool for problems in traditional quantum computation. We describe in detail the discrete sets for one and two qubits.PACS: 03.67.Lx; 03.67.pp; 03.67.-a; 03.67.Mn.PACS: 03.67.Lx; 03.67.pp; 03.67.-a; 03.67.Mn.