We investigate the structure and uniqueness of squeezed vacuum states defined by annihilation conditions of the form $(a-\alpha a^{†})|\psi ⟩=0$ and their multimode generalizations, with applications to the thermofield double (TFD) state in quantum field theory. For $N=1$ and $N=2$, we demonstrate that these conditions uniquely define the single- and two-mode squeezed vacua, generated by unitary squeezing operators. A key result is the unitary reformulation of the TFD state, expressed as a product of two-mode squeezing operators, ensuring invertibility and resolving the nonunitary paradox in the Minkowski-Rindler vacuum correspondence. Extending to cyclic annihilation conditions $(a_i-{\alpha }_i{a}_{i+1}^{†})|\psi ⟩=0$ with $a_{N+1}\equiv a_1$, we find that nontrivial squeezed states exist only for $N=2$. For $N>2$, we establish a no-go theorem, proving no normalizable, nontrivial solutions exist, revealing a fundamental limit on cyclic multimode entanglement. These results highlight the bipartite nature of TFD-like entanglement and constrain multipartite generalizations in multiregion quantum field theories.

Close

PrevNext

View figure in article

• Quantum formalism
• Quantum states of light
• Squeezing of quantum noise