Quantum Remote Control of Unitary Operations on a Qubit of Pure Entangled States

We consider the remote implementation of an arbitrary unitary operation on one qubit of a pure two-qubit entangled state with 100% efficiency via entanglement swapping in detail, then directly generalize this protocol from two-qubit to N-qubit entangled states. The overall classical information and distributed entanglement cost required for this quantum remote control protocol is less than the bi-directional quantum state teleportation method.     

Implementing a Nonlocal Toffoli Gate Using Partially Entangled Qubit Pairs

We investigate the local implementation of a nonlocal quantum Toffoli gate via partially entangled states. Firstly, we show how the nonlocal Toffoli gate can be implemented with unit fidelity and a certain probability by employing two partially entangled qubit pairs as quantum channels. The quantum circuit that does this proposed implementation is built entirely of local single-level and two-level gates if the target node harness a three-level qudit as a catalyser. This enables the construction of this key nonlocal quantum gate with existing technology. Then, we put forward a scheme to realize deterministic and exact implementation of this nonlocal gate via more partially entangled pairs. In this scheme, the control nodes’ local positive operator valued measurements (POVMs) lies at the heart. We construct the required POVMs. The fact that the deterministic and exact implementation of a nonlocal multi-qubit gate could be realized by using partially entangled qubit pairs and comparatively fewer resources cost is notable.     

Efficient Joint Remote Preparation of an Arbitrary m-qudit State with Partially Entangled States

We present an efficient scheme for multiparty joint remote preparation of an arbitrary m-qudit state by using partially entangled states as the quantum channel. One of the senders first performs a collective unitary transformation on his entangled particles and the auxiliary qubit, and then he performs a Z-basis measurement on the auxiliary qubit for transforming the partially entangled quantum channel into the two types of multi-particle entangled states. In the first case, the quantum channel shared by all the senders and the receiver is the target channel. In the second case, the quantum channel transforms into another partially entangled state which is the resource for the quantum channel transformation in the next round. Compared with other protocols, our scheme has advantage of having high success probability for joint remote preparation of an arbitrary m-qudit state via partially entangled states.     

Preparation of Macroscopic Entangled Coherent States in Nitrogen-Vacancy Centers Ensembles Coupled to a Superconducting Flux Qubit

We propose a potentially practical scheme for creating macroscopic entangled coherent state between two separate nitrogen-vacancy center spin ensembles placed near a superconducting flux qubit. Through the collective magnetic coupling and the in situ tunability of the flux qubit, the arbitrary entangled coherent states of spin ensembles can be achieved with high success possibilities under the influence from decoherence of the flux qubit and spin ensembles.The experimental feasibility and challenge are justified using currently available technology.     

Distance Between Qubit States with Initial System-Environment Correlation

The time-evolution of the trace distance between two qubit states in the presence of an initial correlation with an environment is investigated by means of the exactly solvable model of qubit and environmental system, where there is at most one excitation in the whole system, It is found that the trace distance can exceed its initial value during the time-evolution under certain conditions if the qubit is initially entangled with the environment. Furthermore the Bures distance between two qubit states is investigated. It is seen that the time-evolution of the Bures distance is quite different from that of the trace distance.     

Quantum cobwebs: Universal entangling of quantum states

Entangling an unknown qubit with one type of reference state is generally impossible. However, entangling an unknown qubit with two types of reference states is possible. To achieve this, we introduce a new class of states called zero sum amplitude (ZSA) multipartite, pure entangled states for qubits and study their salient features. Using shared-ZSA states, local operations and classical communication, we give a protocol for creating multipartite entangled states of an unknown quantum state with two types of reference states at remote places. This provides a way of encoding an unknown pure qubit state into a multiqubit entangled state.     

Joint Remote State Preparation of a Single-Atom Qubit State via a GHZ Entangled State

We proposed a physical protocol for the joint remote preparation of a single-atom qubit state via a three-atom entangled GHZ-type state previously shared by the two senders and one receiver. Only rotation operations of single-atom, which can be achieved though the resonant interaction between the two-level atom and the classical field, are required in the scheme. It shows that the splitting way of the classical information of the secret qubit not only determines the success of reconstruction of the secret qubit, but also influences the operations of the senders.     

Activating the Violation of Steering Inequality for Two‐Qubit X States

The phenomenon of superactivation of quantum steering, that is, the fact that by combining several copies of the unsteerable quantum state one can get a steerable quantum state, has recently attracted much attention. This property is currently only known for isotropic states, and whether there exists an example other than isotropic states is so far an open question. It is of great importance to learn the activation property of non‐isotropic states. In this paper, it is shown that the violation of the local uncertainty relations (LUR) steering inequality can be activated for two‐qubit X type entangled mixed states. Although the activation phenomenon proven in this paper cannot guarantee the superactivation of steering for two‐qubit X states, it does provide clues for this goal. In addition, previous results indicate that two copies are enough for the superactivation of steering, while the price to pay is a high local dimension, and it is unclear whether superactivation is possible with few copies in low‐dimensional systems such as two‐qubit systems. By providing examples of activation of LUR steering inequality with two copies in a two‐qubit system, the work may open a potential way to the solution of this question.     

Entangled Qubit States and Linear Entropy in the Probability Representation of Quantum Mechanics

The superposition states of two qubits including entangled Bell states are considered in the probability representation of quantum mechanics. The superposition principle formulated in terms of the nonlinear addition rule of the state density matrices is formulated as a nonlinear addition rule of the probability distributions describing the qubit states. The generalization of the entanglement properties to the case of superposition of two-mode oscillator states is discussed using the probability representation of quantum states.     

Perfect Single Qubit Mirroring Effects on Two and Three Maximally Entangled Qubits

Perfect quantum state mirroring in a chain of N spins is defined as the condition in which the state |iof the chain is swapped into the state |N-i within a time evolution interval τ.Such a phenomenon is an interesting way of transfering entanglement.An expressions for the perfect mirroring of a single qubit contained in a spin chain were proposed in the past.We exploit such an expressions for calculating the evolution times in chains of both two and three spins.In the case of a chain of two qubits,we derive conditions under which the associated four Bell states diagonalize the Hamiltonian.It is found that for the two Bell states |Φ+and|Φ-,perfect mirroring does not occur(i.e.entanglement is not preserved under swapping).On the other hand,perfect single qubit mirror effect(entanglement preservation) indeed occurs for the other two Bell states |Ψ+and|Ψ- which are mapped into |Φ+and|Φ-respectively.For the case of a chain of three qubits,the effects of a perfect single qubit mirroring on a set of four maximally entangled three qubit states ψ1,ψ2,χ1,and χ2 are studied.Due to the fact that quantum mirroring preserves maximal entanglement,the states ψ1 and ψ2 are not altered.However,quantum mirroring changes the states χ1 and χ2 only if we apply perfect quantum state mirroring in the site a=1 of the three qubits spin chain.The above constrains the preservation of maximal entanglement under qubit mirroring of such a state.Due to the fact that swapping has already been experimentally tested,a posible experimental implementations of single qubit mirroring is possible.     

Speeding up the Generation of Entangled State between a Superconducting Qubit and Cavity Photons via Counterdiabatic Driving

Optimal generation of entangled states is of critical significance for robust quantum information processing. An effective scheme is presented for speeding up the generation of an entangled state between a superconducting qubit and microwave photons via counterdiabatic driving. At a magic bias point, the first three levels of a charge-phase quantum circuit constitute an effective qutrit. An entangled state based on adiabatic population transfer is first achieved. By the technique of shortcuts to adiabaticity, a counterdiabatic driving is applied to the qutrit, which then accelerates the entanglement generation significantly. Moreover, with the accessible decoherence rates, the rapid operations in a shortcut way are highly robust when compared with adiabatic manipulations. The scheme could offer a promising approach toward optimal preparation of entangled states with superconducting artificial atoms in circuit quantum electrodynamics, experimentally.     

High efficient scheme for remote state preparation with cavity QED

In this paper, a scheme is proposed for remote state preparation （RSP） with cavity quantum electrodynamics （QED）. In our scheme, two observers share two-atom nonmaximally entangled state as quantum channels and can realize remote preparation of state of an atom. We also propose a generalization for remote preparation of N-atom entangled state by （N＋1）-atom GHZ-like state （N ≥ 2）. By this scheme, one single-atom projective measurement is enough for the RSP of a qubit or N-atom entangled state, and the probability of success for RSP is unity. Furthermore, we have considered the case where observers use W-like state as quantum channels to realize RSP of a qubit. We compare our scheme with existing ones.     

Unextendible Product Bases,Uncompletable Product Bases and Bound Entanglement

We report new results and generalizations of our work on unextendible product bases (UPB), uncompletable product bases and bound entanglement. We present a new construction for bound entangled states based on product bases which are only completable in a locally extended Hilbert space. We introduce a very useful representation of a product basis, an orthogonality graph. Using this representation we give a complete characterization of unextendible product bases for two qutrits. We present several generalizations of UPBs to arbitrary high dimensions and multipartite systems. We present a sufficient condition for sets of orthogonal product states to be distinguishable by separable superoperators. We prove that bound entangled states cannot help increase the distillable entanglement of a state beyond its regularized entanglement of formation assisted by bound entanglement.     

Controlled Remote Implementation of an Arbitrary Single-Qubit Operation with Partially Entangled Quantum Channel

We present a scheme for controlled remote implementation of an arbitrary single-qubit operation by using partially entangled states as the quantum channel. The sender can remote implement an arbitrary single-qubit operation on the remote receiver’s quantum system via partially entangled states under the controller’s control. The success probability for controlled remote implementation of quantum operation can achieve 1 if the sender and the controller perform proper projective measurements on their entangled particles. Moreover, we also discuss the scheme for remote sharing the partially unknown operations via partially entangled quantum channel. It is shown that the quantum entanglement cost and classical communication can be reduced if the implemented operation belongs to the restrict sets.     

利用非局域控制非门操作纯化三粒子纠缠态

提出了两套三粒子纠缠态的纯化方案.第一个方案选择部分纠缠GHZ态作为量子通道,利用具有一个控制位和一个靶位的非局域控制非门操作和采用集体么正操作及适当地制备三粒子A,B和C的初始态,可以以最佳几率2|β|2获得最大三粒子纠缠态.第二个方案选择EPR对作为量子通道,通过利用具有一个控制位和两个靶位的非局域控制非门操作和采用集体么正操作及适当地制备三粒子A,B和C的初始态,可以以与第一个方案相同的几率获得最大三粒子纠缠态.两个方案都可以推广到N粒子纠缠态的纯化.     

Generation of a displaced qubit and entangled displaced photon state via conditional measurement and their properties

We study optical schemes for generating both a displaced photon and a displaced qubit via conditional measurement. Combining one mode prepared in different microscopic states (one-mode qubit, single photon, vacuum state) and another mode in macroscopic states (coherent state, single photon added coherent state), a conditional state in the other output mode exhibits properties of a superposition of the displaced vacuum and a single photon. We propose to use the displaced qubit and entangled states composed of the displaced photon as components for quantum information processing. Basic states of such a qubit are distinguishable from each other with high fidelity. We show that the qubit reveals both microscopic and macroscopic properties. Entangled displaced states with a coherent phase as an additional degree of freedom are introduced. We show that additional degree of freedom enables to implement complete Bell state measurement of the entangled displaced photon states.     

Quantum teleportation using entangled 3-qubit states and the ‘magic bases’

We study quantum teleportation of single qubit information state using 3-qubit general entangled states. We propose a set of 8 GHZ-like states which gives (i) standard quantum teleportation (SQT) involving two parties and 3-qubit Bell state measurement (BSM) and (ii) controlled quantum teleportation (CQT) involving three parties, 2-qubit BSM and an independent measurement on one qubit. Both are obtained with perfect success and fidelity and with no restriction on destinations (receiver) of any of the three entangled qubits. For SQT, for each designated one qubit which is one of a pair going to Alice, we obtain a magic basis containing eight basis states. The eight basis states can be put in two groups of four, such that states of one group are identical with the corresponding GHZ-like states and states of the other differ from the corresponding GHZ-like states by the same phase factor. These basis states can be put in two different groups of four-states each, such that if any entangled state is a superposition of these with coefficients of each group having the same phase, perfect SQT results. Also, for perfect CQT, with each set of given destinations of entangled qubits, we find a different magic basis. If no restriction on destinations of any entangled qubit exists, three magic semi-bases, each with four basis states, are obtained, which lead to perfect SQT. For perfect CQT, with no restriction on entangled qubits, we find four magic quarter-bases, each having two basis states. This gives perfect SQT also. We also obtain expressions for co-concurrences and conditional concurrences.     

Generation of macroscopic entangled coherent states with large Josephson junctions

We propose a simple and experimental architecture to generate macroscopic entanglement in a solid system which consists of two large Josephson junctions and a flux qubit. Through quantum measuring of flux qubit, entangled coherent states of two large Josephson junctions are obtained. The concurrence of entangled coherent states can be accommodated by adjusted systematic parameters. We also give a brief discussion on the experimental feasibility of this proposal.     

Improved Superconducting Qubit State Readout by Path Interference

High fidelity single shot qubit state readout is essential for many quantum information processing protocols. In superconducting quantum circuit, the qubit state is usually determined by detecting the dispersive frequency shift of a microwave cavity from either transmission or reflection. We demonstrate the use of constructive interference between the transmitted and reflected signal to optimize the qubit state readout, with which we find a better resolved state discrimination and an improved qubit readout fidelity. As a simple and convenient approach, our scheme can be combined with other qubit readout methods based on the discrimination of cavity photon states to further improve the qubit state readout.     

Simultaneous minimum-uncertainty measurement of discrete-valued complementary observables

We have made the first experimental demonstration of the simultaneous minimum uncertainty product between two complementary observables for a two-state system (a qubit). A partially entangled two-photon state, where each of the photons carries (partial) information of the initial state, was used to perform such a measurement.