Geometrical self-testing of partially entangled two-qubit states

Abstract

Quantum nonlocality has recently been intensively studied in connection to device-independent quantum information processing, where the extremal points of the set of quantum correlations play a crucial role through self-testing. In most protocols, the proofs for self-testing rely on the maximal violation of the Bell inequalities, but there is another known proof based on the geometry of state vectors to self-test a maximally entangled state. We present a geometrical proof in the case of partially entangled states. We show that, when a set of correlators in the simplest Bell scenario satisfies a condition, the geometry of the state vectors is uniquely determined. The realization becomes selftestable when another unitary observable exists on the geometry. Applying this proven fact, we propose self-testing protocols by intentionally adding one more measurement. This geometrical scheme for self-testing is superior in that, by using this as a building block and repeatedly adding measurements, a realization with an arbitrary number of measurements can be self-tested. Besides the application, we also attempt to describe nonlocal correlations by guessing probabilities of distant measurement outcomes. In this description, the quantum set is also convex, and a large class of extremal points is identified by the uniqueness of the geometry.

Generation of entanglement between quantum dot molecule with the presence of phonon effects in a voltage-controlled junction

“…Fig. (4) illustrates that the entanglement can reappear after a period of temperature absence. We name the phenomenon of entanglement rebirth after the complete disappearance versus temperature as a thermal entanglement revival (TER).…”

“…Quantum entanglement has been considered as a crucial resource in quantum information processing which utilizes the non-local correlations without any classical analogs [1,2,3,4]. Generation and control of the entanglement have attracted a great deal of attention in different physics fields, such as atomic structures [5,6], photonic systems [7,8], and semiconductor quantum dots [9,10,11].…”

Self-testing quantum states via nonmaximal violation in Hardy's test of nonlocality

“…Then only from the input-output statistics termed as correlation or behavior of the box one can find the quantum state of the device. Such a certification is referred to as a self-test as it enables a user to verify the device without knowing details of its inner-workings [16][17][18][19][20][21][22][23][24][25][26][27][28].…”

“…Bell inequalities naturally fit into the deviceindependent paradigm for certification of quantum systems since their derivations, based on the assumptions of local-realism [29], are independent of a quantum description of the physical state of the system or measurements applied to it [30][31][32][33][34][35]. Therefore, various kind of Bell inequalities play a central role in the construction of self-testing protocols [16][17][18][19][20][21][22][23][24][25][26][27][28]. In a Bell test only some special type of input-output statistics can self-test a quantum state; the one which can be realized (up to local isometry) by a unique quantum state and measurements [28].…”

“…Further, within the (convex) set of all quantum behaviors in a given Bell experiment those leading to self-testing protocols must necessarily be ex-tremal points on the quantum boundary [26][27][28]. Then, the fact that any linear Bell inequality is maximized at some extremal point of the quantum set leads to a natural intuition that self-testing occurs on achieving maximal violation [18][19][20][21][22][23][24][25][26][27][28].…”