A generalized notion of higher order nonclassicality (in terms of higher order moments) is introduced. Under this generalized framework of higher order nonclassicality, conditions of higher order squeezing and higher order subpoissonian photon statistics are derived. A simpler form of the Hong-Mandel higher order squeezing criterion is derived under this framework by using an operator ordering theorem introduced by us in [J. Phys. A. 33 (2000) 5607]. It is also generalized for multi-photon Bose operators of Brandt and Greenberg. Similarly, condition for higher order subpoissonian photon statistics is derived by normal ordering of higher powers of number operator. Further, with the help of simple density matrices, it is shown that the higher order antibunching (HOA) and higher order subpoissonian photon statistics (HOSPS) are not the manifestation of the same phenomenon and consequently it is incorrect to use the condition of HOA as a test of HOSPS. It is also shown that the HOA and HOSPS may exist even in absence of the corresponding lower order phenomenon. Binomial state, nonlinear first order excited squeezed state (NLESS) and nonlinear vacuum squeezed state (NLVSS) are used as examples of quantum state and it is shown that these states may show higher order nonclssical characteristics. It is observed that the Binomial state which is always antibunched, is not always higher order squeezed and NLVSS which shows higher order squeezing does not show HOSPS and HOA. The opposite is observed in NLESS and consequently it is established that the HOSPS and HOS are two independent signatures of higher order nonclassicalityComment: 14 pages, 7 figure
Since the introduction of binomial state as an intermediate state, different intermediate states have been proposed. Different nonclassical effects have also been reported in these intermediate states. But till now higher order antibunching or higher order subpoissonian photon statistics is predicted only in one type of intermediate state, namely shadowed negative binomial state. Recently we have shown the existence of higher order antibunching in some simple nonlinear optical processes to establish that higher order antibunching is not a rare phenomenon (J. Phys. B 39 (2006) 1137). To establish our earlier claim further, here we have shown that the higher order antibunching can be seen in different intermediate states, such as binomial state, reciprocal binomial state, hypergeometric state, generalized binomial state, negative binomial state and photon added coherent state. We have studied the possibility of observing the higher order subpoissonian photon statistics in different limits of intermediate states. The effect of different control parameters have also been studied in this connection and it has been shown that the depth of nonclassicality can be tuned by controlling various physical parameters.Comment: 12 Pages LaTeX 2e, 11 figure
Recently, a large number of protocols for bidirectional controlled state teleportation (BCST) have been proposed using n-qubit entangled states (n ∈ {5, 6, 7}) as quantum channel. Here, we propose a general method of selecting multi-qubit (n > 4) quantum channels suitable for BCST and show that all the channels used in the existing protocols of BCST can be obtained using the proposed method. Further, it is shown that the quantum channels used in the existing protocols of BCST forms only a negligibly small subset of the set of all the quantum channels that can be constructed using the proposed method to implement BCST. It is also noted that all these quantum channels are also suitable for controlled bidirectional remote state preparation (CBRSP). Following the same logic, methods for selecting quantum channels for other controlled quantum communication tasks, such as controlled bidirectional joint remote state preparation (CJBRSP) and controlled quantum dialogue, are also provided.
Experimental realization of various quantum states of interest has become possible in the recent past due to the rapid developments in the field of quantum state engineering. Nonclassical properties of such states have led to various exciting applications, specifically in the area of quantum information processing. The present article aims to study lower-and higher-order nonclassical features of such an engineered quantum state (a generalized binomial state based on Abel's formula). Present study has revealed that the state studied here is highly nonclassical. Specifically, higher-order nonclassical properties of this state are reported using a set of witnesses, like higher-order antibunching, higher-order sub-Poissonian photon statistics, higher-order squeezing (both Hong Mandel type and Hillery type). A set of other witnesses for lower-and higher-order nonclassicality (e.g., Vogel's criterion and Agarwal's A parameter) have also been explored. Further, an analytic expression for the Wigner function of the generalized binomial state is reported and the same is used to witness nonclassicality and to quantify the amount of nonclassicality present in the system by computing the nonclassical volume (volume of the negative part of the Wigner function). Optical tomogram of the generalized binomial state is also computed for various conditions as Wigner function cannot be measured directly in an experiment in general, but the same can be obtained from the optical tomogram with the help of Radon transform. arXiv:1811.10557v1 [quant-ph] 26 Nov 2018 state (BS) [36] and can be defined aswhere B M n (p) is the probability amplitude of the binomial state which corresponds to the occurrence of n photons with equal probability p obtained in M independent ways [36]. Mathematically, the binomial state is equivalent to a molecular system having same photon emitting probability p from the different energy levels of the excited states of the molecule which undergoes the M level vibrational relaxation [37]. Binomial state being an intermediate state, reduces to various existing states at different limits. For example, it reduces to a (a) vacuum state |0 (if p→0,It is interesting to note that coherent states are closest to classical states and the number states are the most nonclassical states. Thus, fundamentally different states of electromagnetic field can be obtained as limiting cases of BS. Naturally, properties of BS has been studied since long [38].The interest on the BS is not restricted to the state of the form Eq.(1), it has been extended to various variants of BS, too. Specifically, in Refs. [39,40] negative binomial state was proposed, and subsequently its properties were studied in Refs. [10]. Similarly, reciprocal binomial state was introduced in Ref. [12] and studied in [9,10]. Further, a couple of generalized binomial states (GBS) 1 have been proposed [37] and their nonclassical properties have also been investigated [9,10]. More interestingly, possible applications of GBS have been explored in the field of quantum co...
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