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Lower limits of spin detection efficiency for two-parameter two-qubit (TPTQ) states with non-ideal ferromagnetic detectors

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Abstract

We have investigated a TPTQ state as an input state of a non-ideal ferromagnetic detectors. Minimal spin polarization required to demonstrate spin entanglement according to entanglement witness and CHSH inequality with respect to (w.r.t.) their two free parameters have been found, and we have numerically shown that the entanglement witness is less stringent than the direct tests of Bell’s inequality in the form of CHSH in the entangled limits of its free parameters. In addition, the lower limits of spin detection efficiency fulfilling secure cryptographic key against eavesdropping have been derived. Finally, we have considered TPTQ state as an output of spin decoherence channel and the region of ballistic transmission time w.r.t. spin relaxation time and spin dephasing time has been found.

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Notes

  1. The bell basis is defined by: \(|{\Psi ^\pm } \rangle =\frac{1}{\sqrt{2}}(|{\uparrow \downarrow } \rangle \pm |{\downarrow \uparrow } \rangle )\), \(|{\Phi ^\pm } \rangle = \frac{1}{\sqrt{2}}(|{\uparrow \uparrow } \rangle \pm |{\downarrow \downarrow } \rangle )\).

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Authors and Affiliations

  1. Department of Engineering Science, College of Engineering, University of Tehran, Tehran, 11365-4563, Iran

    Nayereh Majd

  2. Department of Physics, Shahed University, Tehran, Iran

    Zahra Ghasemi

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  1. Nayereh Majd
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  2. Zahra Ghasemi
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Correspondence to Nayereh Majd.

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Majd, N., Ghasemi, Z. Lower limits of spin detection efficiency for two-parameter two-qubit (TPTQ) states with non-ideal ferromagnetic detectors. Quantum Inf Process 15, 4137–4157 (2016). https://doi.org/10.1007/s11128-016-1374-0

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