Subcategory: Physics (not Nanoscience)
Sarah Hagen - Southern Illinois University Carbondale
Co-Author(s): Eric Chitambar, University of Illinois at Urbana-Champaign, Urbana, IL; Brian Doolittle, University of Illinois at Urbana-Champaign, Urbana, IL
Quantum nonlocality describes the way that two or more quantum systems can be correlated in a manner that defies a classical explanation. Nonlocality can be detected using separated measurements on an entangled quantum system. If the measurement statistics violate a so-called Bell inequality, then nonlocal correlations are detected [Bell, Physics, 1, 195–200 (1964)]. The quantum resource theory of nonlocality provides an understanding of the physical dynamics that are possible under local quantum operations [Chitambar and Gour, Rev. Mod. Phys., 91, 025001 (2019)]. This has applications within quantum cryptography, as nonlocal correlations provide a way for distributed parties to establish private key in an untrustworthy environment [Vazirani and Vidick, Phys. Rev. Lett., 113, 140501 (2014)]. Here we consider the problem of distributing nonlocal correlations using a quantum channel and establish that two initially local systems can exhibit nonlocal correlations after exchanging a third system that shares only local correlations with both of them. We restrict attention to the CHSH Inequality in two-qubit systems [Horodecki et al. Phys. Lett. A, 200, 340 (1995)] and our protocol involves two parties, Alice and Bob, who initially share some local Bell-diagonal state. Alice introduces an ancilla system and couples it to one-half of the Bell-diagonal state by performing a controlled-NOT (CNOT) gate before sending the system to Bob. To demonstrate the effect of distributing nonlocality using local quantum resources, we perform numerical maximizations of the correlations that can be generated across different bipartitions of the three-part quantum state. The effect is achieved when the ancilla system is locally correlated with Alice and Bob’s system, and yet Bob and the ancilla system share nonlocal correlations with Alice. This task is analogous to the distribution of entanglement using separable states [T.S. Cubitt, F. Verstraete, W. Dur, and J.I. Cirac, Phys. Rev. Lett. 91, 037902 (2003)]. However, the ability to distribute entanglement using separable states does not necessarily imply that nonlocality can be distributed using local states. Moreover, we show that nonlocality distribution is possible for a set of Bell-diagonal states in which entanglement distribution is not possible, as shown in [A. Kay, Phys. Rev. Lett. 109, 080503 (2012)]. When considering a Bell-diagonal state, ρ = (1/4)*(I4 + s01σxσx + s10σzσz + s11σyσy), this is the set of states where s11 = 0. We conclude with an analysis of the two-qubit state space for which nonlocality distribution using local states is possible: Nonlocality distribution is not possible for Bell-diagonal states in which s11 = 0 and s01 = 0 or s10 = 0 for our choice of gate operation. Further research seeks to characterize to a greater extent this state space by looking at states that are not Bell-diagonal.
Funder Acknowledgement(s): This research is supported by the National Science Foundation under grant NSF PHY-1659598, extended to the University of Illinois at Urbana-Champaign.
Faculty Advisor: Eric Chitambar, firstname.lastname@example.org
Role: I wrote the program for calculating and ultimately conducted the numerical maximization of the correlations generated across the three bisections of our quantum system for this initial Bell-diagonal state and the CNOT operation. I also produced the computational analysis of the state space of Bell-diagonal states for which nonlocality distribution is possible with our choice of operator.