Abstract Direct measurement of entanglement is an efficient method for obtaining the degree of entanglement without full reconstruction of the quantum state. But most of the current entanglement direct measurement schemes are designed for the states in specific physical systems, and are not universal for different physical systems. So, in this paper, we want to design a universal direct measurement algorithm for the entanglement of two-qubit states, where universal means that the algorithm does not depend on specific physical systems. Although the conventional quantum walk (QW) model does not have this universal property, we find that by introducing auxiliary qubits and CNOT gates in quantum circuits, a generalized QW model can be realized in any qubit system, i.e. it is universal for different physical systems. Inspired by the universal property of this generalized QW model, a universal quantum algorithm is designed for directly measuring the entanglement degree of two-qubit states, which we call the QW inspired algorithm. To demonstrate the feasibility of the algorithm, analytical calculations and numerical simulations for three representative quantum states are studied. The results show that the algorithm can be used to directly measure two-qubit entanglement, and the universality of the algorithm guarantees that it works not only in optical systems but also in any other physical system. Furthermore, this algorithm may find more applications in other quantum information tasks necessitating qubit–qubit coupling.Abstract Direct measurement of entanglement is an efficient method for obtaining the degree of entanglement without full reconstruction of the quantum state. But most of the current entanglement direct measurement schemes are designed for the states in specific physical systems, and are not universal for different physical systems. So, in this paper, we want to design a universal direct measurement algorithm for the entanglement of two-qubit states, where universal means that the algorithm does not depend on specific physical systems. Although the conventional quantum walk (QW) model does not have this universal property, we find that by introducing auxiliary qubits and CNOT gates in quantum circuits, a generalized QW model can be realized in any qubit system, i.e. it is universal for different physical systems. Inspired by the universal property of this generalized QW model, a universal quantum algorithm is designed for directly measuring the entanglement degree of two-qubit states, which we call the QW inspired algorithm. To demonstrate the feasibility of the algorithm, analytical calculations and numerical simulations for three representative quantum states are studied. The results show that the algorithm can be used to directly measure two-qubit entanglement, and the universality of the algorithm guarantees that it works not only in optical systems but also in any other physical system. Furthermore, this algorithm may find more applications in other quantum information tasks necessitating qubit–qubit coupling.

Laser Physics LettersApr 1, 20250 citations

Relationship Between Entanglement and Coherence in Some Two-Qubit States

Fa Zhao, Dong Wang, Ye Liu

International Journal of Theoretical PhysicsJan 1, 202211 citations

Optimal manipulations with qubits: Universal quantum entanglers

Vladimír Bužek, Mark S. Hillery

We analyze various scenarios for entangling two initially unentangled qubits. In particular, we propose an optimal universal entangler that entangles a qubit in unknown state $|\ensuremath{\Psi}〉$ with a qubit in a reference (known) state $|0〉.$ That is, our entangler generates the output state that is as close as possible to the pure (symmetrized) state $(|\ensuremath{\Psi}〉|0〉+|0〉|\ensuremath{\Psi}〉).$ The most attractive feature of this entangling machine, is that the fidelity of its performance (i.e., the distance between the output and the ideally entangled---symmetrized state) does not depend on the input and takes the constant value $\mathcal{F}=(9+3\sqrt{2})/14\ensuremath{\simeq}0.946.$ We also analyze how to optimally generate from a single qubit initially prepared in an unknown state $|\ensuremath{\Psi}〉$ a two qubit entangled system, which is as close as possible to a Bell state $(|\ensuremath{\Psi}〉|{\ensuremath{\Psi}}^{\ensuremath{\perp}}〉+|{\ensuremath{\Psi}}^{\ensuremath{\perp}}〉|\ensuremath{\Psi}〉),$ where $〈\ensuremath{\Psi}|{\ensuremath{\Psi}}^{\ensuremath{\perp}}〉=0.$We analyze various scenarios for entangling two initially unentangled qubits. In particular, we propose an optimal universal entangler that entangles a qubit in unknown state $|\ensuremath{\Psi}〉$ with a qubit in a reference (known) state $|0〉.$ That is, our entangler generates the output state that is as close as possible to the pure (symmetrized) state $(|\ensuremath{\Psi}〉|0〉+|0〉|\ensuremath{\Psi}〉).$ The most attractive feature of this entangling machine, is that the fidelity of its performance (i.e., the distance between the output and the ideally entangled---symmetrized state) does not depend on the input and takes the constant value $\mathcal{F}=(9+3\sqrt{2})/14\ensuremath{\simeq}0.946.$ We also analyze how to optimally generate from a single qubit initially prepared in an unknown state $|\ensuremath{\Psi}〉$ a two qubit entangled system, which is as close as possible to a Bell state $(|\ensuremath{\Psi}〉|{\ensuremath{\Psi}}^{\ensuremath{\perp}}〉+|{\ensuremath{\Psi}}^{\ensuremath{\perp}}〉|\ensuremath{\Psi}〉),$ where $〈\ensuremath{\Psi}|{\ensuremath{\Psi}}^{\ensuremath{\perp}}〉=0.$

arXiv:quant-ph/0006045Physical Review AJul 12, 200031 citations

X states of the same spectrum and entanglement as all two-qubit states

Samuel R. Hedemann

arXiv:1802.03038Quantum Information ProcessingSep 18, 201812 citations

Proposal of Universal Detection of Two-photon Polarization Entanglement

Karol Bartkiewicz, Paweł Horodecki, Karel Lemr +2 more

Detecting and quantifying quantum entanglement of a given unknown state poses problems that are fundamentally important for quantum information processing. Surprisingly, no direct (i.e., without quantum tomography) universal experimental implementation of a necessary and sufficient test of entanglement has been designed even for a general two-qubit state. Here we propose an experimental method for detecting a collective universal witness, which is a necessary and sufficient test of two-photon polarization entanglement. It allows us to detect entanglement for any two-qubit mixed state, and to establish tight upper and lower bounds on its amount. A novel element of this method is the sequential character of its main components, which allows us to obtain relatively complicated information about quantum correlations with the help of simple linear-optical elements. As such, this proposal is the first to realize a universal two-qubit entanglement test within the present state of the art of quantum optics. We show the optimality of our setup with respect to the minimal number of measured quantities.Detecting and quantifying quantum entanglement of a given unknown state poses problems that are fundamentally important for quantum information processing. Surprisingly, no direct (i.e., without quantum tomography) universal experimental implementation of a necessary and sufficient test of entanglement has been designed even for a general two-qubit state. Here we propose an experimental method for detecting a collective universal witness, which is a necessary and sufficient test of two-photon polarization entanglement. It allows us to detect entanglement for any two-qubit mixed state, and to establish tight upper and lower bounds on its amount. A novel element of this method is the sequential character of its main components, which allows us to obtain relatively complicated information about quantum correlations with the help of simple linear-optical elements. As such, this proposal is the first to realize a universal two-qubit entanglement test within the present state of the art of quantum optics. We show the optimality of our setup with respect to the minimal number of measured quantities.

May 21, 20140 citations

|0〉.

That is, our entangler generates the output state that is as close as possible to the pure (symmetrized) state $(|\ensuremath{\Psi}〉|0〉+|0〉|\ensuremath{\Psi}〉).$ The most attractive feature of this entangling machine, is that the fidelity of its performance (i.e., the distance between the output and the ideally entangled---symmetrized state) does not depend on the input and takes the constant value $\mathcal{F}=(9+3\sqrt{2})/14\ensuremath{\simeq}0.946.$ We also analyze how to optimally generate from a single qubit initially prepared in an unknown state $|\ensuremath{\Psi}〉$ a two qubit entangled system, which is as close as possible to a Bell state $(|\ensuremath{\Psi}〉|{\ensuremath{\Psi}}^{\ensuremath{\perp}}〉+|{\ensuremath{\Psi}}^{\ensuremath{\perp}}〉|\ensuremath{\Psi}〉),$ where $〈\ensuremath{\Psi}|{\ensuremath{\Psi}}^{\ensuremath{\perp}}〉=0.$