Logical proof of quantum correlations requiring entanglement measurements

Abstract

We present a logical type of proof of contextuality for a two-qubit state. We formulate a paradox that cannot be verified by a two-qubit system with local measurements while it is possible by using entanglement measurements. With our scheme we achieve p Hardy ≈ 0.167, which is the highest probability obtained for a system of similar dimension. Our approach uses graph theory and the global exclusivity principle to give an interpretation of logical type of proofs of quantum correlations. We review the Hardy paradox and find connection to the KCBS inequality. We apply the same method to build a paradox based the CHSH inequality.Contextuality refers to the property of measurements statistics to have their outcomes depending on the set of measurements that are simultaneously performed. Originally discovered by Bell, Kochen and Specker [1,2], it uses the notion of compatibility, which refers to the property of several measurements to be performed simultaneously. Recent efforts have been made on understanding contextuality using a graph theory approach [3-6]. Contextuality has shown an advantage in quantum computing [7][8][9][10], in quantum cryptography [11,12], quantum communication [13,14] and state discrimination [15].Contextuality generalizes non-locality [4] and the ability to experimentally observe these two fundamental properties of quantum physics is an important point when it comes to their uses in information technology tasks. It is then one of the most fundamental challenge to develop tools to characterize and classify measurements statistics belonging to different theories. A common technic to witness non-locality and contextuality is through inequalities of measurements statistics. Another possibility is by using logical arguments [16][17][18][19][20], where a set of conditions if satisfied assert the non-local or contextual nature of the system considered. While it is clear that a verification of non-locality or contextuality with a logical proof implies the violation of an inequality [21], the inverse is not straightforward to answer.When such properties are observed on spatially separated systems, entanglement is a needed resource. Entangled states and local measurements are a sufficient resource to observe non-locality. Moreover, a quantum measurement can also have entanglement properties when its eigenstates are entangled. This is a crucial key in the architectures of quantum network using quantum repeaters [22], where independent sources send entangled photons to distant parties. When entanglement measurements are performed on pair of photons from different sources it can create entanglement between initially uncorrelated parties. In particular Bell state measurements can create maximally entangled states and can also be self-tested device-independently [23,24].Recent advances on the classification of correlations * sohbi@kias.re.kr

Certifying dimension of quantum systems by sequential projective measurements

“…With the recent development of quantum technologies and the different promising applications, it is essential to guarantee the good functioning of the used apparatus through certification or benchmarking methods [1,2]. Such methods can rely on fundamental properties of quantum physics to assert properties of quantum systems such as self-testing [3][4][5][6][7], randomness certification [8][9][10] and dimension witnesses [11][12][13][14][15][16][17][18].…”

Certifying dimension of quantum systems by sequential projective measurements

“…With the recent development of quantum technologies and the different promising applications, it is essential to guarantee the good functioning of the used apparatus through certification or benchmarking methods [1,2]. Such methods can rely on fundamental properties of quantum physics to assert properties of quantum systems such as self-testing [3][4][5][6][7], randomness certification [8][9][10] and dimension witnesses [11][12][13][14][15][16][17][18].…”

Experimental Approach to Demonstrating Contextuality for Qudits

“…There is a deep interest in developping experimental schemes to manipulate qudits and test their quantumness. Indeed using qudits instead of qubits can be beneficial in a range of applications in quantum informnation such as quantum simulation [33], quantum algorithms [34][35][36], quantum error correction [37][38][39], universal optics-based quantum computation [40], quantum communication [41,42] and fault-tolerant quantum computation [43][44][45], entanglement measurements certification [46]. From a foundational interest more complex quantum features can be obrtained from higher dimensions such as contextuality [47] or coherence of measurements [48].…”