Quantum computations without definite causal structure

Abstract

We show that quantum theory allows for transformations of black boxes that cannot be realized by inserting the input black boxes within a circuit in a pre-defined causal order. The simplest example of such a transformation is the classical switch of black boxes, where two input black boxes are arranged in two different orders conditionally on the value of a classical bit. The quantum version of this transformation-the quantum switch-produces an output circuit where the order of the connections is controlled by a quantum bit, which becomes entangled with the circuit structure. Simulating these transformations in a circuit with fixed causal structure requires either postselection, or an extra query to the input black boxes.

Causally nonseparable processes admitting a causal model

“…The proof that the process (10) cannot be used to violate any causal inequalities, for any local strategy 6 consists of two steps: (i)we show that the set of correlations compatible with W is the same as the set of correlations achievable with W T B (where T B denotes the partial transpose of the systems B B…”

“…For three and more parties, there are causally nonseparable processes whose physical realization is knownone instance is the 'quantum switch' [6], where the causal order between two parties A and B is controlled by a quantum system belonging to a third party C. Processes of this kind, however, cannot violate causal inequalities [7,8]: they admit a 'causal model', i.e., a causally separable process is capable of reproducing their correlations. Their causal nonseparability can only be certified through device-dependent 'causal tomography' or 'causal witnesses' [7].…”

“…Since W T B is causally separable, it can be 6 Note that our proof guarantees the existence of a causal model, which means that the correlations belong to every causal polytope, without restriction on the number of inputs and outputs for each party. 7 The condition on the CJ representation of a CPTP map is that , which is strictly smaller.…”

Functional quantum computing: An optical approach

“…This is best illustrated by the N − switch operation [4,5] which coherently permutes the orderings of N black box operators based on the value of control qubits and applies them to a target qubit register. In addition to being an interesting example of the differences between quantum functions and quantum circuits, arbitrary control over causal orderings is a useful mechanism for investigating the fundamental role of causality in quantum systems [10][11][12][13] and enhancing the efficiency of certain quantum information processing tasks [14,15].…”

“…Investigations into quantum functions find that while physical systems are capable of arbitrarily controlling the use and ordering of black box unitaries, quantum circuits cannot represent this [4][5][6][7][8][9] without significantly increased resources. Though this doesn't mean that quantum functions will necessarily lead to more physically resource efficient experiments, the functions can provide different and more compact formalism for * timothyrambo2017@u.northwestern.edu † JBA is currently affiliated with Berberian & Company, LLC, but his authorship here reflects work performed before joining that company.…”