Unambiguous arbitrary high-dimensional Bell states analyzer via indefinite causal order

Abstract High-dimensional quantum systems greatly outperform their two-dimensional counterparts in channel capacity, quantum complexity and efficiency, quantum communication security, etc. Bell-state analyzer (BSA) is a crucial prerequisite for a number of quantum communication protocols. We propose an approach for completely and deterministically distinguishing a set of arbitrary d -dimensional ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>d</mml:mi> <mml:mtext>⩾</mml:mtext> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> ) Bell states via indefinite causal order (ICO). In previous schemes, bit and phase information are discriminated in succession. Exploiting the gravitational ICO as the sole resource, we propose some high-dimensional BSA schemes. Independent of the dimensions, a set of generalized Bell states are completely and deterministically discriminated by adjusting the form of the embedded local single-qudit gates within ICO switch and measuring each qudit in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo fence="false" stretchy="false">{</mml:mo> <mml:mrow> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mn>0</mml:mn> <mml:mo fence="false" stretchy="false">⟩</mml:mo> <mml:mo>,</mml:mo> <mml:mrow> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mn>1</mml:mn> <mml:mo fence="false" stretchy="false">⟩</mml:mo> <mml:mo>,</mml:mo> <mml:mo>⋯</mml:mo> <mml:mo>,</mml:mo> <mml:mrow> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mi>d</mml:mi> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> <mml:mo fence="false" stretchy="false">⟩</mml:mo> <mml:mo fence="false" stretchy="false">}</mml:mo> </mml:mrow> </mml:math> basis. Notably, in our high-dimensional BSA process, the indefinite causal structure is not consumed. Hence a completely nondestructive high-dimensional BSA can be achieved by iterating the indefinite causal structure process for two rounds.