Abstract Superdense coding is a fundamental protocol in quantum information theory that facilitates the transmission of classical information at capacities exceeding classical limits by exploiting quantum entanglement. However, the presence of noise in communication channels, particularly in the case of Pauli channels, poses a significant challenge to the efficiency of superdense coding. In this paper, we explore an active protocol designed for scenarios involving two distinct, addressable noisy channels. We investigate how a quantum switch, by actively composing these two channels in an indefinite causal order, can construct a new composite channel with significantly enhanced capacity. Our findings indicate that, when confronted with the same type of Pauli channels which are commutative, the quantum switch offers no advantage over classical strategies constrained by definite causal order. Remarkably, when two different channels are composed, the quantum switch can exploit the non-commutativity of their underlying operators to coherently cancel their noise effects. This vividly illustrates the ‘different is more’ principle: using the quantum switch to actively compose two different non-commuting channels yields a significant capacity gain over composing two identical commutative channels. This underscores the potential of the quantum switch as a tool for active noise-aware protocol design, where the difference itself is a resource, rather than as a tool for passive noise mitigation.
Abstract Superdense coding is a fundamental protocol in quantum information theory that facilitates the transmission of classical information at capacities exceeding classical limits by exploiting quantum entanglement. However, the presence of noise in communication channels, particularly in the case of Pauli channels, poses a significant challenge to the efficiency of superdense coding. In this paper, we explore an active protocol designed for scenarios involving two distinct, addressable noisy channels. We investigate how a quantum switch, by actively composing these two channels in an indefinite causal order, can construct a new composite channel with significantly enhanced capacity. Our findings indicate that, when confronted with the same type of Pauli channels which are commutative, the quantum switch offers no advantage over classical strategies constrained by definite causal order. Remarkably, when two different channels are composed, the quantum switch can exploit the non-commutativity of their underlying operators to coherently cancel their noise effects. This vividly illustrates the ‘different is more’ principle: using the quantum switch to actively compose two different non-commuting channels yields a significant capacity gain over composing two identical commutative channels. This underscores the potential of the quantum switch as a tool for active noise-aware protocol design, where the difference itself is a resource, rather than as a tool for passive noise mitigation.
Abstract The quantum switch is known to remove noise probabilistically, but whether this constitutes an advantage over causally ordered processing has remained contentious: postselection, weak classical benchmarks, and task-dependent comparisons have all drawn criticism. Here we give an exact analysis of the question for a qubit under Pauli noise. For any two qubit Pauli channels, measuring the switch’s control qubit implements a commutation syndrome : it sorts each noise realization by whether the two Kraus errors commuted, syndrome information that an unencoded qubit does not otherwise possess, and the optimal measure-and-feed-forward protocol has a closed form. The analytical results have two levels of generality. For the exactly solvable pair, an isotropic depolarizing channel and a flip channel along an arbitrary axis, we prove a complete ceiling theorem: every definite-order protocol using each channel once, with arbitrary memoryless intermediate operations and receiver-side post-processing, deterministic or heralded, has entanglement fidelity at most ma x P c P , and the switch exceeds this ceiling deterministically , by p q / 3 over most of parameter space. For arbitrary qubit Pauli pairs, the ceiling is proven against arbitrary receiver-side post-processing, and the gain is strictly positive if and only if the two syndrome branches call for different Pauli corrections, confining the exceptions to error-dominated noise. Side systems are covered whenever they are non-signaling about the message. Beyond these theorems the evidence is numerical: strict gain in 99.8 % of 5000 random Pauli pairs, and no case, within a 200 -pair sample, in which an optimized midpoint echo overturns the gain. The state-resolved gain obeys an exact geometric law, Δ F = 2 p q / 3 | r ^ ⋅ n ^ | 2 : alignment is the condition under which the degenerate two-error syndrome becomes perfectly correctable. The separation survives control dephasing down to a threshold visibility that falls with noise strength, and at strong noise it outperforms coherent control of the two orderings even with twice the channel uses.
In a recent series of works [Ebler et al., Phys. Rev. Lett. 120, 120502 (2018); arXiv:1809.06655v2; arXiv:1810.10457v2], it has been shown that the quantum superposition of causal order---the quantum switch---offers an enhancement of classical and quantum channel capacity through noisy channels, a phenomenon that was coined ``causal activation.'' In this paper, we attempt to clarify the nature of the advantage, by comparing the quantum switch to a class of processes that can be interpreted as quantum superposition of processes with the same causal order. We show that some of these processes can match or even outperform the quantum switch at enhancing classical and quantum channel capacity, and argue that they require the same resources as the switch. We conclude, in agreement with Abbott et al. [arXiv:1810.09826v1], that the aforementioned advantages appear to be attributable to the ability to coherently control quantum operations, and not to indefinite causal order per se.
Quantum compositions of channels can grant advantages over classical compositions in quantum information processing or thermodynamical tasks. One of such quantum composition is one with indefinite causal order, where multiple quantum channels are placed in a superposition of different causal or operation orders. The advantages of indefinite causal order were demonstrated in an experimentally realizable setup known as the quantum switch and were often attributed to this new quantum resource of indefinite causality, but some doubts and disagreements still remains as compositions without indefinite causal order can achieve the same advantages. In this work, we proposed that the quantum switch's uniqueness lies in its ability to exhibit coherent non-Markovianity, where memory effects acts across different paths of superposition. We showed that the quantum switch violates completely positive or CP-divisibility and thus has intrinsic non-Markovianity in its evolution, which allows for non-Markovian backflow of information from the environment. This backflow of information can then play a role in the many advantages seen in the quantum switch, and by extending the quantum switch operation such that the non-Markovianity is controllable, we showed that these advantages depend on the presence and amount of non-Markovianity, achieving the quantum switch case when the system is fully non-Markovian. Particularly, we demonstrated this for the quantum switch's advantages in communication capacities, work extraction via daemonic ergotropy, and refrigeration via heat extraction. Other quantum compositions that are often compared to indefinite causal order, such as the superposition of independent channels and superposition of trajectories, are also captured by this extended construction of the quantum switch, and we showed that their difference with the quantum switch lies in the presence or absence of non-Markovianity. Our work suggests that non-Markovianity is an important recipe for the quantum switch or indefinite causal order, and is a nonnegligible factor for its advantages.
Recent studies have shown that quantum information may be effectively transmitted by a finite collection of completely depolarizing channels in a coherent superposition of different orders, via an operation known as the quantum SWITCH. Such results are quite remarkable, as completely depolarizing channels taken in isolation and in a definite order can only output white noise. For general channels, however, little is known about the potential communication enhancement provided by the quantum SWITCH. In this work, we define an easily computable quantity Pn associated with the quantum SWITCH of n copies of a fixed channel, and we conjecture that Pn>0 is both a necessary and sufficient condition for communication enhancement via the quantum SWITCH. In support of our conjecture, we derive a simple analytic expression for the classical capacity of the quantum SWITCH of n copies of an arbitrary Pauli channel in terms of the quantity Pn, which we then use to show that our conjecture indeed holds in the space of all Pauli channels. Utilizing such results, we then formulate a communication protocol involving the quantum SWITCH which enhances the private capacity of the BB84 channel.
Classical communication capacity of a channel can be enhanced either through a device called a ``quantum switch'' or by putting the channel in a quantum superposition. The gains in the two cases, although different, have their origin in the use of a quantum resource, but is it the same resource? Here this question is explored through simulating large sets of random channels. We find that quantum superposition always provides an advantage, while the quantum switch does not: it can either increase or decrease communication capacity. The origin of this discrepancy can be attributed to a subtle combination of superposition and noncommutativity.
Entanglement certification is often performed on states that have already undergone noisy transmission or processing. Noise can reduce the surviving entanglement and can also cause a given criterion to fail even when entanglement remains. In this context, the quantum switch, a paradigmatic realization of indefinite causal order (ICO), coherently controls the orders in which two channels act and has been shown to offer advantages across a range of quantum information-processing tasks. Here we ask whether this coherent control enlarges the noise-parameter region in which entanglement remains certifiable. We regard the two order branches as the arms of a causal-order interferometer and insert a local unitary between the channel uses to tune their interference. For stochastic Pauli noise, a postselected ICO output can exhibit greater entanglement negativity than any classical mixture of the two definite orders; in particular, we identify regimes where its negativity remains nonzero while that of every classical mixture vanishes. A suitable local Pauli unitary substantially enlarges this ICO-only region, while an input-dependent path-difference indicator qualitatively links operator noncommutativity to the postselected negativity gain. Numerical examples extend the advantage to local amplitude-damping noise and two-qutrit Weyl noise. At a representative Weyl-noise point for the 3×3 positive-partial-transpose (PPT) Tiles bound-entangled state, a nondecomposable witness detects the postselected ICO output, whereas an analytic bound excludes detection of the definite-order outputs and their mixtures by the entire locally rotated witness family. These results identify causal-order interferometry as a strategy for enhancing entanglement certification across distinct noise models and dimensions.