Experimental Quantum Switching for Exponentially Superior Quantum Communication Complexity

Abstract

Finding exponential separation between quantum and classical information tasks is like striking gold in quantum information research. Such an advantage is believed to hold for quantum computing but is proven for quantum communication complexity. Recently, a novel quantum resource called the quantum switch-which creates a coherent superposition of the causal order of events, known as quantum causality-has been harnessed theoretically in a new protocol providing provable exponential separation. We experimentally demonstrate such an advantage by realizing a superposition of communication directions for a two-party distributed computation. Our photonic demonstration employs d-dimensional quantum systems, qudits, up to d = 2 13 dimensions and demonstrates a communication complexity advantage, requiring less than (0.696 ± 0.006) times the communication of any causally ordered protocol. These results elucidate the crucial role of the coherence of communication direction in achieving the exponential separation for the one-way processing task, and open a new path for experimentally exploring the fundamentals and applications of advanced features of indefinite causal structures.Computation by separated parties with minimal communication is the focus of communication complexity, which has applications to distributed computing, very-large-scale integration, streaming algorithms, and more [1]. For quantum information, communication complexity is especially exciting as exponential quantum-classical gaps can be proven [2][3][4][5][6][7][8][9]. By contrast, exponential quantum-classical gaps for computation tasks such as factorization [10] depend on the best-known classical algorithm, and thus are strongly believed but not rigorously proven. Experimentally, quantum communication complexity has been studied in proof of principle for the quantum fingerprinting protocol [11][12][13] and beyond [1,14,15].The quantum switch provides a new communication complexity tool that leads to another instance of exponential quantum advantage [16]. The quantum switch is a device where a control qubit determines the order in which two transformations are performed on a target system [17,18]. When the control is in a superposition of logical states, the order of the operations is causally indefinite; i.e., there is a superposition of the ordering of target operations. The quantum switch has broad relevance in the context of quantum causality [19] including applications to studies of quantum gravity [19][20][21][22], communication complexity [16, * These authors contributed equally to this work.2 23], witnessing causality [17,[24][25][26][27][28] and deciding whether a given indefinite causal order is physical [29,30]. In quantum computing, the quantum switch can reduce the query complexity for some tasks compared to causally ordered protocols [18,31] -this advantage has been demonstrated for single-qubit control and single-qubit target circuits [32]. In quantum communication, the quantum switch enhances the communication rate beyond the limits of ...

Sending classical information via three noisy channels in superposition of causal orders

“…(iii) As the number of operations N grows, the experiment requires coherent control in a robust and scalable manner of dimension d c × d which a priori grows as N !×N !. In the existing experiments [5,17,19,20], the control system has been realized using either the path or polarization degrees of freedom of a single photon, and for the target system, it has been implemented using either the polarization or the transverse spatial mode of the same photon. In all these implementations, fibered or in free space, the quantum switch is limited due to the encoding of the control system in a two dimensional space and thus does not scale up to more than N = 2 quantum channels, although in [20] the arrival time encodes a d-dimensional target system.…”

“…We propose frequency encoding using off-the-shelf and mature telecom components. time-bin [20] degree of freedom of the same photon going through the superposition of the channels.…”

Experimental Two‐Way Communication with One Photon

“…In terms of efficiency, it has been demonstrated, both theoretically and experimentally, that quantum protocols reduce the information transfer required to perform some specific distributed computational tasks . Some of these schemes provide an exponential advantage with respect to their classical counterparts while, at the same time, quantum systems also allow for a decrease in the amount of physical resources necessary for communication …”

Quantum superpositions of causal orders as an operational resource

“…There, C coherently controls the causal order in which the target qudit passes through A and B. Quantum control of causal orders constitutes a stronger form of causal nonseparbility in the sense of requiring not only coherence but also entanglement. Interestingly, in addition, it admits clear physical interpretations in terms of interferometers [15,[19][20][21]. Somewhat surprisingly though, even though the terminology quantum control of causal orders appears quite frequently in the literature, a precise formal definition of this notion has -to our knowledge -not been provided yet.…”

“…In turn, from an applied viewpoint, it has been recently shown to be a useful resource for a number of interesting information-processing tasks [5,14,16,18]. Moreover, it has already been subject of experimental investigations [15,[19][20][21]. Curiously, even though quantum control of causal orders is the rule-of-thumb terminology evoked to discuss the quantum switch, a precise formal definition of this notion is -to our knowledge -still missing.…”