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Parallel Quantum Annealing is a technique to solve multiple optimization problems simultaneously. Parallel quantum annealing aims to optimize the utilization of available qubits on a quantum topology by addressing multiple independent problems in a single annealing cycle. This study provides insights into the potential and the limitations of this parallelization method. The experiments consisting of two different problems are integrated, and various problem dimensions are explored including normalization techniques using specific methods such as DWaveSampler with Default Embedding, DWaveSampler with Custom Embedding and LeapHybridSampler. This method minimizes idle qubits and holds promise for substantial speed-up, as indicated by the Time-to-Solution (TTS) metric, compared to traditional quantum annealing, which solves problems sequentially and may leave qubits unutilized.

Stimulated emission tomography (SET) is an excellent tool for characterizing the process of spontaneous parametric down-conversion (SPDC), which is commonly used to create pairs of entangled photons for use in quantum information protocols. The use of stimulated emission increases the average number of detected photons by several orders of magnitude compared to the spontaneous process. In a SET measurement, the parametric down-conversion is seeded by an intense signal field prepared with specified mode properties rather than by broadband multi-modal vacuum fluctuations, as is the case for the spontaneous process. The SET process generates an intense idler field in a mode that is the complex conjugate to the signal mode. In this work we use SET to estimate the joint spatial mode distribution (JSMD) in the Laguerre-Gaussian (LG) basis of the two photons of an entangled photon pair. The pair is produced by parametric down-conversion in a beta barium borate (BBO) crystal with type-II phase matching pumped at a wavelength of 405 nm along with a 780-nm seed signal beam prepared in a variety of LG modes to generate an 842-nm idler beam of which the spatial mode distribution is measured. We observe strong idler production and good agreement with the theoretical prediction of its spatial mode distribution. Our experimental procedure should enable the efficient determination of the photon-pair wavefunctions produced by low-brightness SPDC sources and the characterization of high-dimensional entangled-photon pairs.

Certain predictions of quantum theory are not compatible with the notion of local-realism. This was the content of Bell's famous theorem of the year 1964. Bell proved this with the help of an inequality, famously known as Bell's inequality. The alternative proofs of Bell's theorem without using Bell's inequality are known as `nonlocality without inequality (NLWI)' proofs. We, review one such proof, namely the Hardy's proof which due to its simplicity and generality has been considered the best version of Bell's theorem.

We study local-realistic inequalities, Bell-type inequalities, for bipartite pure states of finite dimensional quantum systems -- qudits. There are a number of proposed Bell-type inequalities for such systems. Our interest is in relating the value of Bell-type inequality function with a measure of entanglement. Interestingly, we find that one of these inequalities, the Son-Lee-Kim inequality, can be used to measure entanglement of a pure bipartite qudit state and a class of mixed two-qudit states. Unlike the majority of earlier schemes in this direction, where number of observables needed to characterize the entanglement increases with the dimension of the subsystems, this method needs only four observables. We also discuss the experimental feasibility of this scheme. It turns out that current experimental set ups can be used to measure the entanglement using our scheme.

Leggett-Garg inequalities (LGI) are constrains on certain combinations of temporal correlations obtained by measuring one and the same system at two different instants of time. The usual derivations of LGI assume \emph macroscopic realism per se and \emph noninvasive measurability. We derive these inequalities under a different set of assumptions, namely the assumptions of \emphpredictability and \emphno signaling in time. As a novel implication of this derivation, we show that LGI can be used to certify randomness in a device independent way.

The ontological model framework for an operational theory has generated much interest in recent years. The debate concerning reality of quantum states has been made more precise in this framework. With the introduction of generalized notion of contextuality in this framework, it has been shown that completely mixed state of a qubit is \emphpreparation contextual. Interestingly, this new idea of preparation contextuality has been used to demonstrate nonlocality of some $\psi$-epistemic models without any use of Bell's inequality. In particular, nonlocality of a non maximally $\psi$-epistemic model has been demonstrated from preparation contextuality of a maximally mixed qubit and Schrödinger's steerability of the maximally entangled state of two qubits [Phys. Rev. Lett \bf 110, 120401 (2013)]. In this paper, we, show that any mixed state is preparation contextual. We, then, show that nonlocality of any bipartite pure entangled state, with Schmidt rank two, follows from preparation contextuality and steerability provided we impose certain condition on the epistemicity of the underlying ontological model. More interestingly, if the pure entangled state is of Schmidt rank greater than two, its nonlocality follows without any further condition on the epistemicity. Thus our result establishes a stronger connection between nonlocality and preparation contextuality by revealing nonlocality of any bipartite pure entangled states without any use of Bell-type inequality.

Unsharp POVM measurements allow a variety of measurement applications which minimally disrupt the state of the quantum system. Experimental schemes are proposed for implementing unsharp measurements on the qubit levels of a trapped ion. The schemes rely on introducing weak entanglement between the state of a target ion, and that of an auxiliary ion, using standard ion trap quantum logic operations, and then realizing an unsharp measurement through projective measurement on the auxiliary atom. We analyze common sources of error and their effect on different applications of unsharp measurements.

Gisin's theorem assures that for any pure bipartite entangled state, there is violation of Bell-CHSH inequality revealing its contradiction with local realistic model. Whether, similar result holds for three-qubit pure entangled states, remained unresolved. We show analytically that all three-qubit pure entangled states violate a Bell-type inequality, derived on the basis of local realism, by exploiting the Hardy's non-locality argument.

Hardy's non-locality theorem for multiple two-level systems is explored in the context of generalized nonlocal theory. We find nonlocal but non-signaling probabilities, providing Hardy's nonlocal argument, which are higher than those in Quantum Mechanics. Maximum probability of success of Hardy's argument is obtained for three two-level systems in quantum as well as in a more generalized theory. Interestingly, the maximum in the nonlocal generalized theory for both the cases turns out to be same.

We discuss (im)possibility of the exact cloning of orthogonal but genuinely entangled three qubit states aided with entangled ancila under local operation and classical communication. Whereas any two orthogonal GHZ states taken from the canonical GHZ basis, can be cloned with the help of a known GHZ state, surprisingly we find that no two W states can be cloned by using any known three qubit (possibly entangled) state as blank copy.

We discuss the exact cloning of orthogonal but entangled qubits under local operations and classical communication. The amount of entanglement necessary in blank copy is obtained for various cases. Surprisingly this amount is more than 1 ebit for certain set of two nonmaximal but equally entangled states of two qubits system. To clone any three two qubits Bell states at least log2 3 ebit is necessary.

Tsirelson showed that $2\sqrt{2}$ is the maximum value that CHSH expression can take for quantum-correlations [B. S.Tsirelson, Lett. Math. Phys, 4 (1980) 93]. This bound simply follows from the algebra of observables. Recently by exploiting the physical structure of quantum mechanics like unitarity and linearity, Buhrman and Massar [H. Buhrman and S.Massar, Phys. Rev. A, 72 (2005) 052103] have established that violation of Tsirelson's bound in quantum mechanics will imply signalling. We prove the same with the help of realistic joint measurement in quantum mechanics and a Bell's inequality which has been derived under the assumption of existence of joint measurement and no signalling condition.

Here we deal with a nonlocality argument proposed by Cabello which is more general than Hardy's nonlocality argument but still maximally entangled states do not respond. However, for most of the other entangled states maximum probability of success of this argument is more than that of the Hardy's argument.

Non existence of Universal NOT gate for arbitrary quantum mechanical states is a fundamental constraint on the allowed operations performed on physical systems. The largest set of states that can be flipped by using a single NOT gate is the set of states lying on a great circle of the Bloch-sphere. In this paper, we show the impossibility of universal exact-flipping operation, first by using the fact that no faster than light communication is possible and then by using the principle of "non-increase of entanglement under LOCC". Interestingly, exact flipping of the states of any great circle does not violate these two principles, as expected.

We analyze Hardy's non-locality argument for two spin-s systems and show that earlier solution in this regard was restricted due to imposition of some conditions which have no role in the argument of non-locality. We provide a compact form of non-locality condition for two spin-s systems and extend it to n number of spin-s particles. We also apply more general kind of non-locality argument still without inequality, to higher spin system.