The nonadditivity of channel capacity is a defining feature that distinguishes quantum communication from classical communication. In the quantum realm, the channel capacity is determined by coherent information, which is defined through the von Neumann entropies of the output and its environment. Despite its fundamental importance, experimental evidence of such nonadditive quantum communication has been elusive because of the complexity of the required quantum channel. Here, we experimentally observe entropic-singularity-induced coherent-information nonadditivity using the qutrit platypus channel implemented on a photonic platform. By preparing six-dimensional photonic entanglement, we directly measure the coherent information of a platypus channel, a qubit amplitude damping channel, and their joint uses, revealing a clear violation of additivity. Quantum process tomography further reveals the entropic singularity responsible for this effect, demonstrating how singular entropy landscapes in low-dimensional channels can enhance quantum communication beyond additive limits.
The nonadditivity of channel capacity is a defining feature that distinguishes quantum communication from classical communication. In the quantum realm, the channel capacity is determined by coherent information, which is defined through the von Neumann entropies of the output and its environment. Despite its fundamental importance, experimental evidence of such nonadditive quantum communication has been elusive because of the complexity of the required quantum channel. Here, we experimentally observe entropic-singularity-induced coherent-information nonadditivity using the qutrit platypus channel implemented on a photonic platform. By preparing six-dimensional photonic entanglement, we directly measure the coherent information of a platypus channel, a qubit amplitude damping channel, and their joint uses, revealing a clear violation of additivity. Quantum process tomography further reveals the entropic singularity responsible for this effect, demonstrating how singular entropy landscapes in low-dimensional channels can enhance quantum communication beyond additive limits.
When can noiseless quantum information be sent across noisy quantum devices? And at what maximum rate? These questions lie at the heart of quantum technology, but remain unanswered because of non-additivity- a fundamental synergy which allows quantum devices (aka quantum channels) to send more information than expected. Previously, non-additivity was known to occur in very noisy channels with coherent information much smaller than that of a perfect channel; but, our work shows non-additivity in a simple low-noise channel. Our results extend even further. We prove a general theorem concerning positivity of a channel's coherent information. A corollary of this theorem gives a simple dimensional test for a channel's capacity. Applying this corollary solves an open problem by characterizing all qubit channels whose complement has non-zero capacity. Another application shows a wide class of zero quantum capacity qubit channels can assist an incomplete erasure channel in sending quantum information. These results arise from introducing and linking logarithmic singularities in the von-Neumann entropy with quantum transmission: changes in entropy caused by this singularity are a mechanism responsible for both positivity and non-additivity of the coherent information. Analysis of such singularities may be useful in other physics problems.
Determining capacities of quantum channels is a fundamental question in quantum information theory. Despite having rigorous coding theorems quantifying the flow of information across quantum channels, their capacities are poorly understood due to superadditivity effects. Studying these phenomena is important for deepening our understanding of quantum information, yet simple and clean examples of superadditive channels are scarce. Here we study a family of channels called platypus channels. Its simplest member, a qutrit channel, is shown to display superadditivity of coherent information when used jointly with a variety of qubit channels. Higher-dimensional family members display superadditivity of quantum capacity together with an erasure channel. Subject to the "spin-alignment conjecture" introduced in our companion paper [F. Leditzky, D. Leung, V. Siddhu, G. Smith, and J. A. Smolin, The platypus of the quantum channel zoo, IEEE Transactions on Information Theory (IEEE, 2023), 10.1109/TIT.2023.3245985], our results on superadditivity of quantum capacity extend to lower-dimensional channels as well as larger parameter ranges. In particular, superadditivity occurs between two weakly additive channels each with large capacity on their own, in stark contrast to previous results. Remarkably, a single, novel transmission strategy achieves superadditivity in all examples. Our results show that superadditivity is much more prevalent than previously thought. It can occur across a wide variety of channels, even when both participating channels have large quantum capacity.
Abstract When can noiseless quantum information be sent across noisy quantum devices? And at what maximum rate? These questions lie at the heart of quantum technology, but remain unanswered because of non-additivity— a fundamental synergy which allows quantum devices (aka quantum channels) to send more information than expected. Previously, non-additivity was known to occur in very noisy channels with coherent information much smaller than that of a perfect channel; but, our work shows non-additivity in a simple low-noise channel. Our results extend even further. We prove a general theorem concerning positivity of a channel’s coherent information. A corollary of this theorem gives a simple dimensional test for a channel’s capacity. Applying this corollary solves an open problem by characterizing all qubit channels whose complement has non-zero capacity. Another application shows a wide class of zero quantum capacity qubit channels can assist an incomplete erasure channel in sending quantum information. These results arise from introducing and linking logarithmic singularities in the von-Neumann entropy with quantum transmission: changes in entropy caused by this singularity are a mechanism responsible for both positivity and non-additivity of the coherent information. Analysis of such singularities may be useful in other physics problems.
A small linear increase from zero in some eigenvalue of a density operator makes the derivative of its von-Neumann entropy logarithmic. We call this logarithmic derivative a log-singularity and use it develop methods for checking non-additivity and positivity of the coherent information Q(1) of a noisy quantum channel. One concrete application of our method leads to a novel type of non-additivity where a zero quantum capacity qubit amplitude damping channel in parallel with a simple qutrit channel is shown to have larger Q(1) than the sum of Q(1)'s of the two individual channels. Another application shows that any noisy quantum channel has positive Q(1) if its output dimension is larger than its complementary output (environment) dimension and this environment dimension equals the rank of some output state obtained from a pure input state. Special cases of this result prove Q(1) is positive for a variety of channels, including the complement of a qubit channel, and a large family of incomplete erasure channels where the positivity of Q(1) comes as a surprise.
Understanding quantum channels and the strange behavior of their capacities is a key objective of quantum information theory. Here we study a remarkably simple, low-dimensional, single-parameter family of quantum channels with exotic quantum information-theoretic features. As the simplest example from this family, we focus on a qutrit-to-qutrit channel that is intuitively obtained by hybridizing together a simple degradable channel and a completely useless qubit channel. Such hybridizing makes this channel’s capacities behave in a variety of interesting ways. For instance, the private and classical capacity of this channel coincide and can be explicitly calculated, even though the channel does not belong to any class for which the underlying information quantities are known to be additive. Moreover, the quantum capacity of the channel can be computed explicitly, given a clear and compelling conjecture is true. This “spin alignment conjecture,” which may be of independent interest, is proved in certain special cases and additional numerical evidence for its validity is provided. Finally, we generalize the qutrit channel in two ways, and the resulting channels and their capacities display similarly rich behavior. In the companion paper [1], we further show that the qutrit channel demonstrates superadditivity when transmitting quantum information jointly with a variety of assisting channels, in a manner unknown before.
A key objective of quantum information theory is to understand quantum channels and their capacities. Here we study a remarkably simple, low-dimensional, single-parameter family of quantum channels with exotic quantum information-theoretic features. We focus on the simplest example from this family, a qutrit-to-qutrit channel intuitively obtained by hybridizing together a simple degradable channel with a completely useless qubit channel. Such hybridizing makes this channel’s capacities behave in a variety of interesting ways. For instance, the private and classical capacity of this channel coincide and can be explicitly calculated, even though the channel lies outside any previous class with calculable capacities. Moreover, the quantum capacity of the channel can be computed explicitly, given a clear and compelling conjecture is true. This "spin alignment conjecture", which may be of independent interest, is proved in certain special cases and backed numerically in certain other cases. Finally, we generalize the qutrit channel; the resulting channels and their capacities display similarly rich behavior. Our companion paper [22] demonstrates superadditivity when transmitting quantum information jointly across our qutrit channel used with a variety of assisting channels, in a manner unknown before.