Characterizing the geometrical edges of nonlocal two-qubit gates

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We show a simple relation connecting entangling power and local invariants of two-qubit gates. From the relation, a general condition under which gates have same entangling power is derived. The relation also helps in finding the lower bound of entangling power for perfect entanglers, from which the classification of gates as perfect and non perfect entanglers is obtained in terms of local invariants.Entanglement, a nonlocal property of a quantum state, is regarded as a resource for realizing various fascinating features such as teleportation, quantum cryptography and quantum computation [1,2]. On one side, much work has been carried out to understand and exploit the entanglement for various information processing. On the other side, attention has been given to quantum operations (gates) as they are responsible for creating entanglement when acting on a state.Since two-qubit gates are capable of producing entanglement, it is of vital importance to understand their entangling characterization. One such useful tool is the entangling power of an operator which quantifies the average entanglement produced [3]. Another tool to characterize the nonlocal attributes of a two-qubit gate is local invariants, namely and (first introduced in Ref.[4]) such that gates differing only by local operations possess same invariants. Furthermore, nonlocal two-qubit gates form an irreducible geometry of tetrahedron known as Weyl chamber. Of all the gates, exactly half of them are perfect entanglers (operators capable of producing maximally entangled state from some input product state) and they form a polyhedron within the Weyl chamber [5].It is known that gates differing only by local operations possess the same entangling power.Similarly, gates which are inverse to each other possess the same entangling power. For instance, SWAP α and SWAP -α assume the same entangling power as they are inverse to each other. From our earlier study on the geometrical edges of two-qubit gates [6], it was found that gates which do not belong to the preceding category also possess same entangling power. For

“…In our earlier study on the geometrical edges of polyhedron, it was shown that for the edges QP, MN and PN [6]. In terms of Eq.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

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Entangling power and local invariants of two-qubit gates

Balakrishnan

Sankaranarayanan

2010

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“…From this relation, it is clear that the gates having the same and must necessarily possess the same 8 linear entropy, implying that the gates are equally entangled. For example, the edges QP and MN of polyhedron are such that their and are the same [13], resulting in the same linear entropy. Further, the above expression also facilitates to understand the operator entanglement of perfect entanglers.…”

Section: Linear Entropy and Local Invariantsmentioning

confidence: 99%

Measures of operator entanglement of two-qubit gates

Balakrishnan

Sankaranarayanan

2011

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Two different measures of operator entanglement of two-qubit gates, namely, Schmidt strength and linear entropy, are studied. While these measures are shown to have one-to-one relation between them for Schmidt number 2 class of gates, no such relation exists for Schmidt number 4 class, implying that the measures are inequivalent in general.Further, we establish a simple relation between linear entropy and local invariants of two-qubit gates. The implication of the relation is discussed.

“…Moreover, the entangling capability of U (C 0 ) can be quantified by the entangling power [31], which is evaluated as [32,33] …”

Section: Fig 3 (Color Online)mentioning

confidence: 99%

Electric nonadiabatic geometric entangling gates on spin qubits

Mousolou¹

2017

Producing and maintaining entanglement reside at the heart of the optimal construction of quantum operations and are fundamental issues in the realization of universal quantum computation. We here introduce a setup of spin qubits that allows for geometric implementation of entangling gates between the register qubits with any arbitrary entangling power. We show this by demonstrating a circuit through a spin chain, which performs universal nonadiabatic holonomic two-qubit entanglers. The proposed gates are all electric and geometric, which would help to realize fast and robust entangling gates on spin qubits. This family of entangling gates contains gates that are as efficient as the CNOT gate in quantum algorithms. We examine the robustness of the circuit to some extent.