Higher order nonclassical properties of fields propagating through a codirectional asymmetric nonlinear optical coupler which is prepared by combining a linear wave guide and a nonlinear (quadratic) wave guide operated by second harmonic generation are studied. A completely quantum mechanical description is used here to describe the system. Closed form analytic solutions of Heisenberg's equations of motion for various modes are used to show the existence of higher order antibunching, higher order squeezing, higher order two-mode and multi-mode entanglement in the asymmetric nonlinear optical coupler. It is also shown that nonclassical properties of light can transfer from a nonlinear wave guide to a linear wave guide.

Private comparison is a primitive for many cryptographic tasks, and recently several schemes for the quantum private comparison (QPC) have been proposed, where two users can compare the equality of their secrets with the help of a semi-honest third party (TP) without knowing each other's secret and without disclosing the same to the TP. In the exisiting schemes, secrecy is obtained by using conjugate coding, and considering all participants as quantum users who can perform measurement(s) and/or create states in basis other than computational basis. In contrast, here we propose two new protocols for QPC, first of which does not use conjugate coding (uses orthogonal states only) and the second one allows the users other than TP to be classical whose activities are restricted to either reflecting a quantum state or measuring it in computational basis. Further, the performance of the protocols is evaluated under various noise models. made to achieve QPC without TP [22,23], but they have been found to be insecure and/or unfair [24]. Thus, in what follows, we will concentrate on three party protocols of QPC, where a TP helps Alice and Bob to compare the equality of their information. Such protocols for QPC have been proposed using different types of entangled states. For example, in Ref.[5], a scheme for QPC has been proposed using χ-type state, W state was used in Ref. [12], Bell state was used in [6,7,13], GHZ state was used in [11]. Further, in Ref.[25], a group theoretic structure of the protocols of quantum dialogue was proposed using a large number of different types of entangled states (e.g., W, GHZ, cluster, Q 4, Q 5, and Brown states), and it was shown that the quantum dialogue scheme proposed there can be converted to a protocol of the socialist millionaire problem, which is equivalent to QPC. Thus, in [25], several options for realization of protocols for QPC were provided. Further, in the similar line, in [26], a set of new options (e.g., 4-qubit Ω state, 4-qubit cat state, etc.) for realization of QD, and thus, QPC have been proposed.It's already established that the schemes for QPC have useful applications in private bidding and auctions, secret ballot elections, e-commerce, etc. ( [8] and references therein). Due to the fact that a scheme for QPC has applications in many fields, many variants of QPC have been studied in the recent past. For example, Huang et al., have recently proposed a GHZ-state-based QPC scheme for n users [11]. Huang et al.'s scheme considers an almost-dishonest TP and allows him to compare the equality of the secrets of a subset of users, too.In what follows, we plan to propose two protocols for QPC in the line of modified Tseng-Lin-Hwang (TLH) protocol, which was proposed in its original form in 2012 [6]. In the original TLH protocol a scheme for quantum private comparison was proposed using Bell states, but almost immediately after the publication of TLH scheme, Yang et al., [13] had shown that there exist a security flaw in the original TLH scheme and other similar schemes, whic...

Semi-quantum protocols that allow some of the users to remain classical are proposed for a large class of problems associated with secure communication and secure multiparty computation. Specifically, first time semi-quantum protocols are proposed for key agreement, controlled deterministic secure communication and dialogue, and it is shown that the semi-quantum protocols for controlled deterministic secure communication and dialogue can be reduced to semi-quantum protocols for ecommerce and private comparison (socialist millionaire problem), respectively. Complementing with the earlier proposed semi-quantum schemes for key distribution, secret sharing and deterministic secure communication, set of schemes proposed here and subsequent discussions have established that almost every secure communication and computation tasks that can be performed using fully quantum protocols can also be performed in semi-quantum manner. Further, it addresses a fundamental question in context of a large number problems-how much quantumness is (how many quantum parties are) required to perform a specific secure communication task? Some of the proposed schemes are completely orthogonal-state-based, and thus, fundamentally different from the existing semi-quantum schemes that are conjugate-coding-based. Security, efficiency and applicability of the proposed schemes have been discussed with appropriate importance.Keywords: Semi-quantum protocol, quantum communication, key agreement, quantum dialogue, deterministic secure quantum communication, secure direct quantum communication. * plored using quantum resources. On the one hand, a large number of conjugate-coding-based (BB84type) schemes [2-4] have been proposed for various tasks including QKD [2-4], quantum key agreement (QKA) [5], quantum secure direct communication (QSDC) [6, 7], deterministic secure quantum communication (DSQC) [8,9], quantum e-commerce [10], quantum dialogue [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30], etc., on the other hand, serious attempts have been made to answer two extremely important foundational questions-(1) Is conjugate coding necessary for secure quantum communication? (2) How much quantumness is needed for achieving unconditional security? Alternatively, whether all the users involved in a secure communication scheme are required to be quantum in the sense of their capacity to perform quantum measurement, prepare quantum states in more than one mutually unbiased basis (MUBs) and/or the ability to store quantum information? Efforts to answer the first question have led to a set of orthogonal-state-based schemes [5,[31][32][33][34], where security is obtained without using our inability to simultaneously measure a quantum state using two or more MUBs. These orthogonal-state-based schemes [5,[31][32][33][34] have strongly established that any cryptographic task that can be performed using a conjugate-coding-based scheme can also be performed using an orthogonal-state-based scheme. Similarly, efforts to answer the sec...

Recently, several aspects of controlled quantum communication (e.g., bidirectional controlled state teleportation, controlled quantum secure direct communication, controlled quantum dialogue, etc.) have been studied using n-qubit (n ≥ 3) entanglement. Specially, a large number of schemes for bidirectional controlled state teleportation are proposed using m-qubit entanglement (m ∈ {5, 6, 7}). Here, we propose a set of protocols to illustrate that it is possible to realize all these tasks related to controlled quantum communication using only Bell states and permutation of particles (PoP). As the generation and maintenance of a Bell state is much easier than a multi-partite entanglement, the proposed strategy has a clear advantage over the existing proposals. Further, it is shown that all the schemes proposed here may be viewed as applications of the concept of quantum cryptographic switch which was recently introduced by some of us. The performances of the proposed protocols as subjected to the amplitude damping and phase damping noise on the channels are also discussed.

An explicit scheme (quantum circuit) is designed for the teleportation of an n-qubit quantum state. It is established that the proposed scheme requires an optimal amount of quantum resources, whereas larger amount of quantum resources has been used in a large number of recently reported teleportation schemes for the quantum states which can be viewed as special cases of the general n-qubit state considered here. A trade off between our knowledge about the quantum state to be teleported and the amount of quantum resources required for the same is observed. A proof of principle experimental realization of the proposed scheme (for a 2-qubit state) is also performed using 5-qubit superconductivity-based IBM quantum computer. Experimental results show that the state has been teleported with high fidelity. Relevance of the proposed teleportation scheme has also been discussed in the context of controlled, bidirectional, and bidirectional-controlled state teleportation.