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MINIMUM UNCERTAINTY AND ENTANGLEMENT

N. D. HARI DASS

Chennai Mathematical Institute, Chennai, India

CQIQC, Indian Institute of Science, Bangalore, India

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TABISH QURESHI

Centre for Theoretical Physics, Jamia Millia Islamia, New Delhi, India

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, and

ADITI SHEEL

Department of Physics, Jamia Millia Islamia, New Delhi, India

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https://doi.org/10.1142/S0217979213500689Cited by:5 (Source: Crossref)

Abstract

We address the question, does a system A being entangled with another system B, put any constraints on the Heisenberg uncertainty relation (or the Schrödinger–Robertson inequality)? We find that the equality of the uncertainty relation cannot be reached for any two noncommuting observables, for finite dimensional Hilbert spaces if the Schmidt rank of the entangled state is maximal. One consequence is that the lower bound of the uncertainty relation can never be attained for any two observables for qubits, if the state is entangled. For infinite-dimensional Hilbert space too, we show that there is a class of physically interesting entangled states for which no two noncommuting observables can attain the minimum uncertainty equality.

Keywords:

PACS: 03.65.Ud, 03.67.Mn

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