https://doi.org/10.1140/epjd/s10053-025-01061-3
Regular Article – Quantum Information
Local PT-symmetric evolutions on separable states and violation of no-signaling
1
Harish-Chandra Research Institute, A CI of Homi Bhabha National Institute, Chhatnag Road, Jhunsi, 211 019, Allahabad, India
2
S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, 700106, Kolkata, India
3
CSIR-National Physical Laboratory, Dr. K. S. Krishnan Road, 110012, New Delhi, India
Received:
9
September
2024
Accepted:
29
August
2025
Published online:
15
September
2025
Recently, it was shown that a violation of the no-signaling principle can be obtained by using local 
-symmetric evolutions on shared quantum states that are entangled and pure. The violation can be removed by using a 
inner product instead of the traditional one. We show that within the traditional inner product quantum mechanics, local -symmetric evolutions can lead to violation of the no-signaling principle for separable and even for classically correlated bipartite shared quantum states. For classically correlated states, specially chosen -symmetric operations from a set of zero volume can also preserve the principle. The classically correlated states used for the violation have the same correlation, when only a single basis is considered for measurements, as the maximally entangled states that were erstwhile used for the same purpose. This, along with the fact that states with no classical correlation cannot be used for violation of no-signaling within -symmetric evolutions, can potentially lead to the identification of minimal resources necessary for obtaining the violation. The violation obtained here can again be removed by using a inner product instead of the traditional one.
© The Author(s) 2025
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