Arbitrary Two-qubit State Research Articles

Mutual Restriction between Concurrence and Intrinsic Concurrence for Arbitrary Two-Qubit StatesSupported by the National Science Foundation of China (Grant Nos. 12075001, 61601002 and 11575001), the Anhui Provincial Natural Science Foundation (Grant No. 1508085QF139), and the Fund from CAS Key Laboratory of Quantum Information (Grant No. KQI201701).

Concurrence is viewed as the most commonly approach for quantifying entanglement of two-qubit states, while intrinsic concurrence contains concurrence of four pure states consisting of a special pure state ensemble concerning an arbitrary two-qubit state. Thus, a natural question arises: Whether there is a specified relation between them. We firstly examine the relation between concurrence and intrinsic concurrence for the maximally nonlocal mixed state under a special unitary operation, which is not yet rigorously proved. In order to obtain a general result, we investigate the relation between concurrence and intrinsic concurrence using randomly generated two-qubit states, and derive an inequality relation between them. Finally, we take into account the relation between concurrence and intrinsic concurrence in open systems, and reveal the ratio of the two quantum resources, which is only correlated with the experiencing channels.

Nonlocality, entanglement, and randomness in different conflicting interest Bayesian games

We analyse different Bayesian games where payoffs of players depend on the types of players involved in a two-player game. The dependence is assumed to commensurate with the CHSH game setting. For this, we consider two different types of each player (Alice and Bob) in the game, thus resulting in four different games clubbed together as one Bayesian game. Considering different combinations of common interest, and conflicting interest coordination and anti-coordination games, we find that quantum strategies are always preferred over classical strategies if the shared resource is a pure non-maximally entangled state. However, when the shared resource is a class of mixed state, then quantum strategies are useful only for a given range of the state parameter. Surprisingly, when all conflicting interest games (Battle of the Sexes game and Chicken game) are merged into the Bayesian game picture, then the best strategy for Alice and Bob is to share a set of non-maximally entangled pure states. We demonstrate that this set not only gives higher payoff than any classical strategy, but also outperforms a maximally entangled pure Bell state, mixed Werner states, and Horodecki states. We further propose the representation of a special class of Bell inequality- tilted Bell inequality, as a common as well as conflicting interest Bayesian game. We thereafter, study the effect of sharing an arbitrary two-qubit pure state and a class of mixed state as quantum resource in those games; thus verifying that non-maximally entangled states with high randomness help attain maximum quantum benefit. Additionally, we propose a general framework of a two-player Bayesian game for d-dimensions Bell-CHSH inequality, with and without the tilt factor.

Experimental realization of controlled quantum teleportation of arbitrary qubit states via cluster states

Controlled quantum teleportation involves a third party as a controller for the teleportation of state. Here, we present the novel protocols for controlling teleportation of the arbitrary two-qubit and three-qubit states through five-qubit and seven-qubit cluster states respectively. In these schemes, Alice sends the arbitrary qubit states to the remote receiver Bob through the cluster states as quantum channels under the control of Charlie. Bob can recover the mentioned states by making appropriate unitary operations, and we point out that the efficiency in our schemes is 100%. In the process of our analysis, we find the classical communication cost in our protocols is remarkably reduced when compared to the previous protocols. We perform the experimental realization of the above protocols on “IBM 16 Melbourne” quantum computer and “IBM quantum simulator” and we calculate the fidelity. We also examine the security analysis against Charlie, and these schemes which we considered here are secure against Charlie’s attacks.

Numerical and analytical results for geometric measure of coherence and geometric measure of entanglement

Quantifying coherence and entanglement is extremely important in quantum information processing. Here, we present numerical and analytical results for the geometric measure of coherence, and also present numerical results for the geometric measure of entanglement. On the one hand, we first provide a semidefinite algorithm to numerically calculate geometric measure of coherence for arbitrary finite-dimensional mixed states. Based on this semidefinite algorithm, we test randomly generated single-qubit states, single-qutrit states, and a special kind of d-dimensional mixed states. Moreover, we also obtain an analytical solution of geometric measure of coherence for a special kind of mixed states. On the other hand, another algorithm is proposed to calculate the geometric measure of entanglement for arbitrary two-qubit and qubit-qutrit states, and some special kinds of higher dimensional mixed states. For other states, the algorithm can get a lower bound of the geometric measure of entanglement. Randomly generated two-qubit states, the isotropic states and the Werner states are tested. Furthermore, we compare our numerical results with some analytical results, which coincide with each other.

Two-qubit state recovery from amplitude damping based on weak measurement

In the quantum control process, arbitrary pure or mixed initial states need to be protected from amplitude damping through the noise channel using measurements and quantum control. However, how to achieve it on a two-qubit quantum system remains a challenge. In this paper, we propose a feed-forward control approach to protect arbitrary two-qubit pure or mixed initial states using the weak measurement. A feed-forward operation and measurements are used before the noise channel, and afterwards a reversed operation and measurements are applied to recover the state back to its initial state. In the case of two-qubit pure states, we use the unravelling trick to describe the state of the system in each step of the control procedure. For two-qubit mixed states, a completely-positive trace-preserving (CPTP) map is implemented. Finally, the fidelity and success probability are used to evaluate the effect of protection. The complete recovery conditions for the measurement strengths are derived, under which we achieve the optimal fidelity and the success probability of recovering the initial pure or mixed states.

Deterministic quantum cyclic controlled teleportation of arbitrary multi-qubit states using multi-qubit partially entangled channel

In this paper, we present a deterministic four-party quantum cyclic controlled teleportation (QCYCT) scheme, by using a multi-qubit partially entangled state as the quantum channel. In this scheme, Alice can teleport an arbitrary [Formula: see text]-qubit state to Bob, Bob can teleport an arbitrary [Formula: see text]-qubit state to Charlie and Charlie can teleport an arbitrary [Formula: see text]-qubit state to Alice under the control of the supervisor David. We utilize rotation gate, Hadamard gates and controlled-NOT (CNOT) gates to construct the multi-qubit partially entangled channel. Only Bell-state measurements, single-qubit von-Neumann measurement and proper unitary operations are required in this scheme, which can be realized in practice easily based on the present quantum experiment technologies. The direction of cyclic controlled teleportation of arbitrary multi-qubit states can also be changed by altering the quantum channel. Analysis demonstrates that the success probability of the proposed scheme can still reach 100% although the quantum channel is non-maximally entangled. Furthermore, the proposed four-party scheme can be generalized into the case involving [Formula: see text] correspondents, which is more suitable for quantum communication networks. We also calculate the intrinsic efficiency and discuss the security of the proposed scheme. Compared with the existing QCYCT schemes which realized cyclic controlled teleportation of arbitrary single-qubit states, specific two-qubit and three-qubit states, the proposed scheme is of general significance.

A reinforcement learning approach for quantum state engineering

Machine learning (ML) has become an attractive tool for solving various problems in different fields of physics, including the quantum domain. Here, we show how classical reinforcement learning (RL) could be used as a tool for quantum state engineering (QSE). We employ a measurement based control for QSE where the action sequences are determined by the choice of the measurement basis and the reward through the fidelity of obtaining the target state. Our analysis clearly displays a learning feature in QSE, for example in preparing arbitrary two-qubit entangled states and delivers successful action sequences that generalise previously found human solutions from exact quantum dynamics. We provide a systematic algorithmic approach for using RL for quantum protocols that deal with a non-trivial continuous state space, and discuss the scaling of these approaches for the preparation of larger entangled (cluster) states.

Arbitrated quantum signature scheme with quantum teleportation by using two three-qubit GHZ states

Arbitrated quantum signature (AQS) scheme based on quantum teleportation has better flexibility and practicability. In this paper, we propose an arbitrated quantum signature scheme with quantum teleportation by using two three-qubit GHZ states. It has been proved that a cluster state has a maximal persistence when compared with an entangled state, and it is also more robust against decoherence. To resist against Alice’s disavowals or Bob’s (outside attacker’s) repudiation, two secret quantum key strings are pre-shared and two random numbers are introduced. The security analysis results show that our AQS scheme can make sure about the impossibility of disavowals by the signer Alice and repudiations by the verifier Bob, and the impossibility of forgeries by any illegal attacker. In addition, the proposed scheme does not require the complex quantum measurement operation, only Bell state measurements, projective measurements and unitary operation are needed to recover the arbitrary two-qubit state, which is the message copy from the signer Alice to the verifier Bob, and that is an appealing advantage in the implementation of a practical quantum communication network.

Error correction schemes for fully correlated quantum channels protecting both quantum and classical information

We study efficient quantum error correction schemes for the fully correlated channel on an n-qubit system with error operators that assume the form \(\sigma _x^{\otimes n}\), \(\sigma _y^{\otimes n}\), \(\sigma _z^{\otimes n}\). Previous schemes are improved to facilitate implementation. In particular, when n is odd and equals \(2k+1\), we describe a quantum error correction scheme using one arbitrary qubit \(\sigma \) to protect the data state \(\rho \) in a 2k-qubit system. The encoding operation \(\sigma \otimes \rho \mapsto \Phi (\sigma \otimes \rho )\) only requires 3k CNOT gates (each with one control bit and one target bit). After the encoded state \(\Phi (\sigma \otimes \rho )\) goes through the channel, we can apply the inverse operation \(\Phi ^{-1}\) to produce \({\tilde{\sigma }} \otimes \rho \) so that a partial trace operation can recover \(\rho \). When n is even and equals \(2k+2\), we describe a hybrid quantum error correction scheme using any one of the two classical bits \(\sigma \in \{|ij{\rangle }{\langle }ij|: i, j \in \{0,1\}\}\) to protect a 2k-qubit state \(\rho \) and two classical bits. The encoding operation \(\sigma \otimes \rho \mapsto \Phi (\sigma \otimes \rho )\) can be done by \(3k+2\) CNOT gates and a single-qubit Hadamard gate. After the encoded state \(\Phi (\sigma \otimes \rho )\) goes through the channel, we can apply the inverse operation \(\Phi ^{-1}\) to produce \(\sigma \otimes \rho \) so that a perfect protection of the two classical bits \(\sigma \) and the 2k-qubit state is achieved. If one uses an arbitrary two-qubit state \(\sigma \), the same scheme will protect 2k-qubit states. The scheme was implemented using MATLAB, Mathematica, Python and the IBM’s quantum computing framework qiskit.

Fidelity deviation in quantum teleportation with a two-qubit state

Quantum teleportation with an arbitrary two-qubit state can be appropriately characterized in terms of maximal fidelity and fidelity deviation. The former quantifies optimality of the process and is defined as the maximal average fidelity achievable within the standard protocol and local unitary strategies, whereas the latter, defined as the standard deviation of fidelity over all input states, is a measure of fidelity fluctuations. The maximal fidelity for a two-qubit state is known and is given by a simple formula that can be exactly computed, but no such formula is known for the fidelity deviation. In this paper, we derive an exact computable formula for the fidelity deviation in optimal quantum teleportation with an arbitrary state of two qubits. From this formula, we obtain the dispersion-free condition, also known as the universality condition: the condition that all input states are teleported equally well and provide a necessary and sufficient condition for a state to be both useful (maximal fidelity larger than the classical bound) and universal (zero fidelity deviation). We also show that for any given maximal fidelity, larger than the classical bound, there always exist dispersion-free or universal states and argue that such states are the most desirable ones within the set of useful states. We illustrate these results with well-known families of two-qubit states: pure entangled states, Bell-diagonal states, and subsets of X states.

Deterministic joint remote state preparation of arbitrary two-qubit state through noisy cluster-GHZ channel

We have investigated the effect of different quantum noises on deterministic joint remote state preparation of arbitrary two-qubit systems, carried out through the collective action on a coupled cluster-GHZ state without introducing auxiliary qubit. The present scheme is deterministic, in comparison to the existing probabilistic schemes. The selection of measurement bases plays a crucial role in the success of our scheme. We have demonstrated the effect of six distinct noises on information loss, quantified through the fidelity measure. The loss of information is found to be minimum for amplitude damping channel and is maximum for the bit-flip channel.

Experimental realization of quantum teleportation of an arbitrary two-qubit state using a four-qubit cluster state

Quantum teleportation is extensively used in quantum communication where a sender sends a information to a receiver at a large distance through a quantum entangled channel. Li and Cao (Commun Theor Phys 47(3):464, 2007) proposed a theoretical scheme for teleportation of a two-particle entangled state via cluster state. Here, we present the above scheme of teleportation for an arbitrary state by using a four-qubit cluster state. We demonstrate the scheme on the IBM quantum computer by designing appropriate quantum circuits using single-qubit and two-qubit quantum gates. We collect the experimental results with good fidelity revealing the teleportation of an arbitrary two-qubit state using a four-qubit cluster state.

Quantum Risk Assessment Model Based on Two Three-Qubit GHZ States

With the acceleration of the construction of quantum communication networks, scholars have proposed different quantum communication protocols for different application scenarios. However, few scholars pay attention to the risk assessment process before communication. In this paper, we propose a novel quantum risk assessment model based on quantum teleportation technology with two three-qubit GHZ states. Only by using Bell states measurements (BSMs) and two-qubit projective measurements (PJMs), the communicators can recovery any arbitrary two-qubit state. This protocol can transmit two-dimension risk assessment factors with better security performance. On the one hand, more sufficient evaluation factors allow the two communicating parties to more objectively evaluate the risk level of communication with the other party, and on the other hand, it also improves the qubit efficiency of the protocol. Moreover, we introduce the third party in this scheme can be semi-trusted, which must be full-trusted in our previous work. This change can reduce the dependence of the communication parties on the third-party organization and improve the privacy of communication. The security analysis shows that this scheme can resist internal and external attacks, and the quantum circuit diagrams also prove that our protocol is physically easier to implement.

Quantum Information Splitting of Arbitrary Two-Qubit State Via a Five-Qubit Cluster State and a Bell-State

We propose a scheme for Quantum Information Splitting of Arbitrary Two-qubit State via a Five-qubit Cluster State and a Bell-state as the quantum channels. There exist a sender (Alice) and two receivers (Bob and Charlie), who share a seven-qubit cluster state as the quantum channel. Alice performs a Bell-state measurements (BSMs) on her qubit pairs, Alice reveals the results to Bob and Charlie via a classical channel. If it is impossible without the help from Charlie for Bob to reconstruct the original information. Charlie performs GHZ-state measurements on his particles and informs Bob about the result. Bob will perform unitary operations to reconstruct the original state information. This scheme is tested for different eavesdropping attacks, of which eavesdropping is easy to detect. In addition, we compared the agreement, such as the number of particles in the program itself, the method of measurement and the efficiency of measurement, etc. All of those prove the innovation of the comprehensive measurement method in this experiment. Overall, we can get the conclusion from the comparison that the scheme is more stable and robust in terms of transmission efficiency and security.

Effect of noise on joint remote preparation of an arbitrary two-qubit state via a Brown state

We present a scheme to realize joint remote state preparation (JRSP) of an arbitrary two-qubit state via a seven-qubit Brown state which is subjected to the noisy environment. Two basic noise models, the amplitude-damping noise and the phase-damping noise, are considered. The noise only affects the transmitted qubits of the quantum channel in our protocol. We put forward the detailed processes of JRSP protocol with these two kinds of noise. It is found out that the fidelities for both kinds of noise depend on the decoherence noisy rate and the amplitude factor of the prepared state. Interesting, the effect of phase-damping noise is much stronger than that of the amplitude-damping noise. Our study will contribute to the research on the effect of quantum noise for JRSP.

Controlled Asymmetric Bidirectional Hybrid of Remote State Preparation and Quantum Teleportation

We propose a protocol of Asymmetric implementing controlled joint remote state preparation and meanwhile realizing controlled quantum teleportation. That is to say, Alice wants to teleport an arbitrary two-qubit state to Bob, and Bob wants to remotely prepare a known state for Alice via the control of supervisors Charlie. Compared with previous studies for the schemes of solely bidirectional quantum teleportation, the new protocol is a kind of hybrid approach of information communication which makes the quantum channel multipurpose.

Coherent transfer of quantum information in a silicon double quantum dot using resonant SWAP gates

Spin-based quantum processors in silicon quantum dots offer high-fidelity single and two-qubit operation. Recently multi-qubit devices have been realized; however, many-qubit demonstrations remain elusive, partly due to the limited qubit-to-qubit connectivity. These problems can be overcome by using SWAP gates, which are challenging to implement in devices having large magnetic field gradients. Here we use a primitive SWAP gate to transfer spin eigenstates in 100 ns with a fidelity of {bar{F}}_{{rm{SWAP}}}^{{rm{(p)}}}=98 %. By swapping eigenstates we are able to demonstrate a technique for reading out and initializing the state of a double quantum dot without shuttling charges through the quantum dot. We then show that the SWAP gate can transfer arbitrary two-qubit product states in 300 ns with a fidelity of {bar{F}}_{{rm{SWAP}}}^{{rm{(c)}}}=84 %. This work sets the stage for many-qubit experiments in silicon quantum dots.

On the Controlled Cyclic Quantum Teleportation of an Arbitrary Two-Qubit Entangled State by Using a Ten-Qubit Entangled State

Recently, Li et al. (Int J Theor Phys: 58:1541–1545, 2019) proposed a controlled cyclic quantum teleportation method of the arbitrary two-qubit entangled states. They claimed that their method can help each of three involved participants to teleport an arbitrary two-qubit entangled state to the next participant, and at the same time, none of the involved participants can obtain the teleported state without the controller’s permission. However, this study shows that two involved participants can reconstruct the teleported states without the controller’s permission. To solve this problem, a modification is proposed here.

Passive and active nonlocality sharing for a two-qubit system via weak measurements

A well-known property of quantum nonlocality is monogamy. However, recent research by Silva et al. shows that multiple observers can share the nonlocality by using weak measurements [Phys. Rev. Lett. 114, 250401 (2015)]. In this paper, we deeply discuss nonlocality sharing for an arbitrary two-qubit state via weak measurements. Two types of nonlocality sharing, passive nonlocality sharing and active nonlocality sharing, which is another type of double violation of Clauser-Horne-Shimony-Holt (CHSH) inequality with many counterintuitive results existing, are fully analyzed. The two types are quite distinct. Active nonlocality sharing can be observed when Bob1 performs strong measurements only except for the ideal strong measurements. Also, a double violation still can be observed in the active nonlocality sharing even using a square pointer type for weak measurements of Bob1, which is impossible in the passive one. As a special example, for a Bell state, a double violation of Clauser-Horne-Shimony-Holt inequality can be always observed in a broad range whether the weak measurement of Bob1 is with an optimal pointer or a square pointer.

Kraus operator formalism for quantum multiplexer operations for arbitrary two-qubit mixed states

The dynamics of open quantum systems are described using a set of operators called Kraus operators. In this paper, we show how to find system parameters for a closed system of two qubits undergoing quantum multiplexer operations such that Kraus operators can be written for a single open qubit system (the target qubit) when the initial density matrix of the joint system is in any arbitrary mixed state. The strategy used is to extend the single-qubit open system to a larger two-qubit closed system, which can evolve using unitary dynamics. The constructed two-qubit system is evolved using quantum multiplexer operations, and system parameters are derived to implement the operation. To derive the parameters, we use a reduced Hamiltonian technique wherein the qubit of interest (the target) evolves only in subspaces of the second qubit (the control). The main advantage of our scheme is that it is not restricted to separable product states and/or local unitary evolution of the joint system.