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Study of quantum polarization and entanglement of coherent states of photons added

Keuliane da Silva Nogueira

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

Polarization has been used extensively in quantum information processing, and quantum entanglement is essential to many areas of research, including quantum computing. Here we investigate the degree of polarization and the entanglement of a family of quantum states known as photon-added entangled coherent states. Such states could serve as means of entanglement distribution and quantum key distribution. Using the quantum Stokes parameters and the Q function, we demonstrated that, in general, the polarization of a superposition of two two-mode photon-added coherent states increases significantly with the number of added photons. And using the concurrence, we showed that the amount of entanglement in this kind of superposition presents a behavior that is dependent on whether or not the number of added photons on each mode is the same.

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Polarization has been used extensively in quantum information processing, and quantum entanglement is essential to many areas of research, including quantum computing. Here we investigate the degree of polarization and the entanglement of a family of quantum states known as photon-added entangled coherent states. Such states could serve as means of entanglement distribution and quantum key distribution. Using the quantum Stokes parameters and the Q function, we demonstrated that, in general, the polarization of a superposition of two two-mode photon-added coherent states increases significantly with the number of added photons. And using the concurrence, we showed that the amount of entanglement in this kind of superposition presents a behavior that is dependent on whether or not the number of added photons on each mode is the same.
Polarization of light has been used extensively in quantum information processing, and quantum entanglement is essential to many areas of research, including quantum computing. Here we investigate the degree of polarization and the entanglement of a family of quantum states known as photon-added entangled coherent states. Such states could serve as means of entanglement distribution and quantum key distribution. Using the quantum Stokes parameters and the QQQ function, we demonstrate that, in general, the degree of polarization of two two-mode photon-added coherent states increases significantly with the number of added photons. And using the concurrence, we show that the amount of entanglement in this kind of superposition presents a behavior that is dependent on whether or not the number of added photons in each mode is the same.
Entanglment properties of photon-added two-mode entangled coherent states are analyzed and analytical expression of the concurrence entanglement is obtained.The results show that the concurrence of the photon-added entangled coherent states is very sensitive to the superposition phase.Schemes for preparation of photon-added coherent states and photon-added two-mode entangled coherent states are also proposed.The preparation procession of the photon-added coherent states is that the photon-added coherent states are firstly tansformed into a superposition state of coherent state and vacuum state(the superposition coefficient is associated with amplitude of the coherent state),then by applying the interaction of atom inside high-Q cavity with a classical light,finally added coherent states of cavity field is prepared.Preparation of photon-added two-mode entangled coherent states of cavity fields is based on interaction of the flying atom with two cavity fields.
As in two previous papers where nonclassical properties and entanglement dynamics were studied for entangled nonlinear coherent states (ENCS) [D. Afshar and A. Anbaraki, J. Opt. Soc. Am. B 33, 558 (2016).] and for photon-added entangled nonlinear coherent states (PAENCS) [A. Anbaraki, D. Afshar and M. Jafarpour, Eur. Phys. J. Plus 133, 2 (2018).], we study quantum mechanical treatments of photon-subtracted entangled nonlinear coherent states (PSENCS) introduced through applying annihilation operators on the ENCS, where the related nonlinearity functions are assumed to be harmonious. To gain insight into the effectiveness of photon subtracting from ENCS and comparing with the case already discussed as the PAENCS, we present a general analysis of nonclassical properties such as photon statistics and degree of polarization. We also derive the concurrence measure to quantify the entanglement of these states and look for conditions that provide information on whether they become maximally entangled. As a result, we can see that the photon depletion number m plays an important role in nonclassical effects. Especially, depending on whether the photon depletion number m is even or odd, one can observe different nonclassical effects.
In a general form, three-photon polarization states are superpositions of contributions from four three-photon polarization modes with four arbitrary complex coefficients. Entanglement of such states is defined as entanglement between their one-photon and two-photon parts. The degree of entanglement is found explicitly in terms of such entanglement quantifiers as the generalized concurrence, entropy of reduced states and the Schmidt parameter. Polarization Stokes vectors, as well as the Schmidt decompositions of three-photon states are found and discussed. Similarity and differences with respect to biphoton polarization states are discussed too.
We introduce a new entangled state, which is composed of two photon-added coherent states. We discuss the entanglement of this state by using several sufficient entanglement criteria, such as higher-order entanglement criterion, EPR criterion, SU(1,1) algebra and Cauchy–Schwarz inequality. These criteria reflect some entanglement effects of this new state, but fail to find the degree of entanglement directly. Thus, we use the covariance to measure the entanglement in this state. Our findings show that the degree of entanglement decreases with the increasing of photon-number and the amplitude of the coherent states. One interesting result is that the new entangled state becomes a maximally entangled state when the photon-added number is 1 and the amplitude of the coherent states is zero, which is just one of the four Bell states.