An optional remote state preparation protocol for a four-qubit entangled state

A scheme is proposed for quantum information splitting of a two-qubit Bell state by using a four-qubit entangled state as a quantum channel. In the scenario, it is supposed that there are three legitimate parties, say Alice, Bob and Charlie. Alice is the sender of quantum information. Bob and Charlie are two agents. Alice first performs GHZ state measurement and tells Bob and Charlie the measurement results via a classical channel. It is impossible for Bob to reconstruct the original state with local operations unless help is obtained from Charlie. If Charlie allows Bob to reconstruct the original state information, he needs to perform a single-qubit measurement and tell Bob the measurement result. Using the measurement results from Alice and Charlie, Bob can reconstruct the original state. We also consider the problem of security attacks. This protocol is considered to be secure.

Non-Bell-pair quantum channel for teleporting an arbitrary two-qubit state

Recently, an explicit protocol ${\cal E}_0$ for faithfully teleporting arbitrary two-qubit states using genuine four-qubit entangled states was presented by us [Phys. Rev. Lett. {\bf 96}, 060502 (2006)]. Here, we show that ${\cal E}_0$ with an arbitrary four-qubit mixed state resource $\Xi$ is equivalent to a generalized depolarizing bichannel with probabilities given by the maximally entangled components of the resource. These are defined in terms of our four-qubit entangled states. We define the generalized singlet fraction ${\cal G}[\Xi]$, and illustrate its physical significance with several examples. We argue that in order to teleport arbitrary two-qubit states with average fidelity better than is classically possible, we have to demand that ${\cal G}[\Xi] > 1/2$. In addition, we conjecture that when ${\cal G}[\Xi] < 1/4$ then no entanglement can be teleported. It is shown that to determine the usefulness of $\Xi$ for ${\cal E}_0$, it is necessary to analyze ${\cal G}[\Xi]$.

This study investigates the dynamics of two-qubit systems in open quantum environments, with a focus on the influence of exceptional points (EPs) and phase angle on entanglement dynamics. Two-qubit systems are pivotal in quantum information science, as they are the simplest system that reveals quantum entanglement, a crucial resource for quantum computing and communication. The research explores the effects of coupling, spontaneous emission, and environment on two-qubit states, specifically the $X$-states, within the framework of the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) or Lindblad master equation. EPs are unique to non-Hermitian systems. They affect the system’s dynamics significantly when the system approaches EP. Analytical and numerical analyses reveal that third-order EPs occur at specific parameters for two-qubit system, leading to critical changes in eigenvalues and eigenvectors of the Liouvillian superoperator. The study demonstrates that EPs can enhance or suppress entanglement. The concurrence, a quantitative measure of entanglement, peaks around the EPs under certain initial conditions. Furthermore, the impact of phase angle, $\theta$, that parameterizes the relative phase of maximally entangled states is analyzed. For initial states labeled as $\rho_\Psi(\theta,p)$ in this thesis, the phase angle significantly influences concurrence evolution, enabling tunability of entanglement dynamics. In contrast, for other class of initial states labeled as $\rho_\Phi(\theta,p)$, concurrence exhibits phase invariance, ensuring stability across the variations in $\theta$. Besides this, the analysis shows that the maximum concurrence occurs around EP for some states, the phase angle can also be tuned to increase the concurrence for some initial states. These findings highlight the importance of both EPs and phase angle in optimizing entanglement generation and control. This research offers valuable insights into the interplay between non-Hermitian physics and quantum entanglement, paving the way for advancements in quantum technologies. The outcomes provide possible practical implications in the field of quantum computation.

In this paper we design a deterministic controllable quantum communication protocol for remotely preparing three-qubit GHZ-type and four-qubit W-type entangled states at two different locations at the same time. Two parties (the preparers) along with a third party (the controller) are connected through a proper multipartite entangled resource. The states to be prepared are not physically available, only the classical information of each state is known by a party who intends to remotely prepare it at the end of the other party under the same control of a third party. Concretely, it is a multi-tasking protocol in which remote preparations of the two inequivalent states are accomplished not only simultaneously but also controllably through execution of a single protocol by utilizing an eleven-qubit entangled state as shared quantum resource. We also propose a generation process of the multipartite quantum resource used.

A necessary and sufficient condition is given for general exact remote state preparation (RSP) protocols to be oblivious, that is, no information about the target state can be retrieved from the classical message. A novel criterion in terms of commutation relations is also derived for the existence of deterministic exact protocols in which Alice's measurement eigenstates are related to each other by fixed linear operators similar to Bob's unitaries. For non-maximally entangled resources, it provides an easy way to search for RSP protocols. As an example, we show how to reduce the case of partially entangled resources to that of maximally entangled ones, and we construct RSP protocols exploiting the structure of the irreducible representations of Abelian groups.

Quantum Information Splitting of an Arbitrary Five-Qubit State Using Four-Qubit Entangled States

We discuss the exact remote state preparation (RSP) protocol of special ensembles of qubits at multiple locations. Generalization of this protocol for higher dimensional Hilbert space systems for multiparties is also presented. Using the "dark states", for multiparties in higher dimensions as quantum channels, we show several instances of remote state preparation protocol using multiparticle measurement and classical communication. We find that not all dark states can be used for exact remote state preparation, nevertheless any superposition of dark states can be used for exact RSP in a probabilistic manner.

Entanglement and polarization of pure, two-qubit systems are known to be constrained by the relationship C2+P2=1 . Here, C stands for concurrence, a standard measure of entanglement, and P refers to the degree of polarization of either of the two, single-qubit subsystems. The above constraint may be understood as reflecting that a system cannot be in a pure state, if it is entangled with another one. In order to explore the connection between entanglement and polarization beyond two-qubit systems, we addressed states in which at least one of the parties has dimensionality greater than two. The case of pure, tripartite states offered itself as a timely candidate. We focussed on three qubits and studied the connection between one qubit’s polarization and its entanglement with the other two taken together. We derived new constraints, akin to the above one, and submitted them to experimental tests using single photons entangled in polarization. The latter provided two qubits, each one attached to one photon. The third qubit was chosen to be the path (momentum) of one of the photons. Our experimental results confirmed the validity of the new constraints. Our theoretical results hold also for classical light. Possible experimental tests could be done with so-called structured light beams.

In this paper, the technique of weak measurement is employed in order to enhance the fidelity of joint remote state preparation (JRSP) protocol under decoherence. We design a quantum circuit of joint remote preparation of a single-qubit state through a GHZ state. Then, we analytically derive the average fidelity of the JRSP protocol under four types of noise usually encountered in real-world implementations of quantum communication protocols, i.e. the phase-flip, depolarizing, amplitude-damping and bit-flip noise. Our study shows that the application of weak measurement and measurement reversal could enhance the average fidelity of the JRSP process under the influence of phase-flip, depolarizing, amplitude-damping noise for most values of the decoherence parameters. If the JRSP process suffers from the bit-flip noise, the weak measurement technique is not useful for increasing the average fidelity.

We investigate the time evolution of entanglement of various entangled states of a two-qubit system exposed to either thermal or squeezed reservoirs. We show that, except for the vacuum reservoir, the sudden-death of entanglement always exists in the thermal and squeezed reservoirs. We present explicit expression for the sudden-death time of entanglement for various entangled states. We find that the sudden-death of entanglement results from the portion of the double excitation component in the initial entangled state. In this sense, the maximally entangled states of a two-qubit system that do not have the double excitation component is more robust against the quantum fluctuations of the vacuum reservoir.

We study the closest disentangled state to a given entangled state in any system (multi-party with any dimension). We obtain the set of equations the closest disentangled state must satisfy, and show that its reduction is strongly related to the extremal condition of the local filtering on each party. Although the equations we obtain are not still tractable, we find some sufficient conditions for which the closest disentangled state has the same reduction as the given entangled state. Further, we suggest a prescription to obtain a tight upper bound of the relative entropy of entanglement in two-qubit systems.

Disentanglement in a two-qubit system subjected to dissipative environment: Exact analysis

This paper provides a quantum information authentication protocol using entangled states. The two parties share EPR (Einstein-Podolsky-Rosen) pairs as authentication key. Information is coded in two-qubits systems. The two parties confirm the validity of the information by making the coding systems to interact with the authentication key. We prove that information from anyone who has no authentication key can't pass the authentication. So our protocol is secure. If there are no errors and eavesdroppers existing in transmission, the authentication key can be reused

In this paper, we demonstrate the efficacy of the universally robust dynamical decoupling (URDD) sequence to preserve multipartite maximally entangled quantum states on a cloud-based quantum computer via the IBM platform. URDD is a technique that can compensate for experimental errors and simultaneously protect the state against environmental noise. To further improve the performance of the URDD sequence, phase randomization (PR) as well as correlated PR (CPR) techniques are added to the basic URDD sequence. The performance of the URDD sequence is quantified by measuring the entanglement in several noisy entangled states (two-qubit triplet state, three-qubit Greenberger–Horne–Zeilinger (GHZ) state, four-qubit GHZ state and four-qubit cluster state) at several time points. Our experimental results demonstrate that the URDD sequence is successfully able to protect noisy multipartite entangled states and its performance is modestly improved by adding the PR and CPR sequences.