Quantum state reconstruction via sequential optimization algorithm reducing optimizable parameters

Abstract Quantum state reconstruction is an important tool in quantum information science. Based on the idea of sequential disentanglement, we propose a quantum state reconstruction algorithm that reduces the number of parameters to be optimized. For transforming the arbitrary quantum state into a tensor product of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mfenced close="〉" open="∣"> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:mfenced> </mml:math> states in the computational basis, we give the conclusion that it is not necessary to apply a global unitary transformation in the optimization of sequential disentanglement. In detail, for disentangling arbitrary n -qubit pure state <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mfenced close="〉" open="∣"> <mml:mrow> <mml:mi>ψ</mml:mi> </mml:mrow> </mml:mfenced> </mml:math> into <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mfenced close="〉" open="∣"> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi>ψ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>˜</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> </mml:mfenced> <mml:mfenced close="〉" open="∣"> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:mfenced> </mml:math> , we simply apply the quantum operator U to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>n</mml:mi> <mml:mo>−</mml:mo> <mml:mfenced close="⌋" open="⌊"> <mml:mrow> <mml:mfrac> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:mfrac> </mml:mrow> </mml:mfenced> </mml:math> qubits. This means that the number of parameters that need to be optimized has been further reduced, thereby saving quantum resources. Finally, numerical simulations verify the feasibility of the proposed algorithm.