Einstein-Podolsky-Rosen steering paradox "2=1'' for $N$ qubits

TL;DR

This paper demonstrates a universal EPR steering paradox, expressed as '2=1', applicable to any N-qubit state under certain measurement conditions, revealing fundamental nonlocality in quantum mechanics.

Contribution

It introduces a general form of the EPR steering paradox for N-qubit states, extending the paradox to mixed states and broadening understanding of quantum nonlocality.

Findings

The paradox applies to all N-qubit states with specific measurement conditions.

The contradiction '2=1' signifies the incompatibility of local-hidden-state models with quantum mechanics.

Examples confirm the universality of the EPR steering paradox in N-qubit systems.

Abstract

Einstein-Podolsky-Rosen (EPR) paradox highlights the absence of a local realistic explanation for quantum mechanics, and shows the incompatibility of the local-hidden-state models with quantum theory. For $N$-qubit states, or more importantly, the $N$-qubit mixed states, we present the EPR steering paradox in the form of the contradictory equality "2=1". We show that the contradiction holds for any $N$-qubit state as long as both the pure state requirement and the measurement requirement are satisfied. This also indicates that the EPR steering paradox exists in more general cases. Finally, we give specific examples to demonstrate and analyze our arguments.