Abstract
Applications of quantum mechanics in the computational and information processing tasks is a recent research interest among the researchers. Certain operations which are impossible to achieve in the description of quantum mechanics are known as no-go theorems. One such theorem is no-splitting theorem of quantum states. The no-splitting theorem states that the information in an unknown quantum bit is an inseparable entity and cannot be split into two complementary qubits. In this work, we try to find out the class of operators for which the splitting is possible in a probabilistic way. The work also aims to find the connection between the unitary operators and probabilistic splitting.
Similar content being viewed by others
Data Availability
No datasets were generated or analyzed during the current study.
References
Nielsen, M., Chuang, I.: Introductory to the Tenth, Anniversary Cambridge University, Cambridge (2011)
Pati, A.K.: General impossible operations in quantum information. Phys. Rev. A. 66(6), 062319 (2002)
Chakrabarty, I., Adhikari, S., Choudhury, B.S.: Inseparability of quantum parameters. Int. J. Theor. Phys. 46(11), 2829–2835 (2007)
Wootters, W.K., Zurek, W.H.: A single quantum cannot be cloned. Nature. 299(5886), 802–803 (1982)
Dieks, D.G.B.J.: Communication by EPR devices. Phys. Lett. A. 92(6), 271–272 (1982)
Pati, A.K., Braunstein, S.L.: Impossibility of deleting an unknown quantum state. Nature. 404(6774), 164–165 (2000)
Horodecki, M., Horodecki, R., De, A.S., Sen, U.: No-deleting and no-cloning principles as consequences of conservation of quantum information. arXiv preprint quant-ph/0306044. (2003)
Bužek, V., Hillery, M., Werner, R.F.: Optimal manipulations with qubits: Universal-NOT gate. Phys. Rev. A. 60(4), R2626 (1999)
Zhou, D.L., Zeng, B., You, L.: Quantum information cannot be split into complementary parts. Phys. Lett. A. 352(1–2), 41–44 (2006)
Pati, A.K., Sanders, B.C.: No-partial erasure of quantum information. Phys. Lett. A. 359(1), 31–36 (2006)
Gisin, N.: Quantum cloning without signaling. Phys. Lett. A. 242(1–2), 1–3 (1998)
Pati, A.K., Braunstein, S.L.: Quantum deleting and signalling. Phys. Lett. A. 315(3–4), 208–212 (2003)
Chattopadhyay, I., Choudhary, S.K., Kar, G., Kunkri, S., Sarkar, D.: No-flipping as a consequence of no-signalling and non-increase of entanglement under LOCC. Phys. Lett. A. 351(6), 384–387 (2006)
Chakrabarty, I., Adhikari, S., Choudhury, B.S.: Revisiting impossible quantum operations using principles of no-signaling and nonincrease of entanglement under LOCC. Int. J. Theor. Phys. 46(10), 2513–2515 (2007)
Zhang, J., Vala, J., Sastry, S., Whaley, K.B.: Geometric theory of nonlocal two-qubit operations. Phys. Rev. A. 67(4), 042313 (2003)
Balakrishnan, S., Sankaranarayanan, R.: Characterizing the geometrical edges of nonlocal two-qubit gates. Phys. Rev. A. 79(5), 052339 (2009)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Kumar, B.S., Balakrishnan, S. Two-Qubit Operators in No-Splitting Theorems. Found Phys 52, 60 (2022). https://doi.org/10.1007/s10701-022-00577-7
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10701-022-00577-7