Quantum correlations with a gap between the sequential and spatial cases

We address the problem of whether parties who cannot communicate but share nonsignaling quantum correlations between the outcomes of sharp measurements can distinguish, just from the value of a correlation observable, whether their outcomes were produced by sequential compatible measurements on single systems or by measurements on spatially separated subsystems. We show that there are quantum correlations between the outcomes of sequential measurements which cannot be attained with spatially separated systems. We present examples of correlations between spatially separated systems whose quantum maximum tends to the sequential maximum as the number of parties increases and examples of correlations between spatially separated systems whose quantum maximum fails to violate the noncontextual bound while its corresponding sequential version does.

Figure 1

(a) Scenario in which two parties, Alice and Bob, perform measurements on two subsystems of a composite system. The measurement setting is indicated by the yellow button that is pressed. The measurement outcome is the light (red or blue) that flashes when the button is pressed. (b) Scenario in which two parties perform sequential compatible measurements on a single system.

Figure 2

(a) Scenario in which three parties perform spatially or spacelike separated measurements on three systems prepared in an entangled state. (b) Scenario in which three parties perform sequential timelike separated compatible measurements on a single quantum system.

Figure 3

(a) Compatibility graph of the observables in $S_3$ defined in Eq. (4). Nodes in the same straight line represent mutually compatible observables. Observables $A_i,B_j,C_k,...$ are Alice's, Bob's, Charlie's,..., respectively. (b) Compatibility graph of the observables in $S_4$. (c) Compatibility graph of the observables in $T_5$ defined in Eq. (8). (d) Compatibility graph of the observables in $T_7$. Assuming that these observables are, in addition, local observables in a Bell inequality scenario implies the appearance of additional compatibility relations, which, in terms of resources, means the disappearance of incompatibilities and therefore the reduction of the maximum quantum value.