We study the Landau–Streater quantum channel Φ:B(Hd)↦B(Hd), whose Kraus operators are proportional to the irreducible unitary representation of SU(2) generators of dimension d. We establish SU(2) covariance for all d and U(3) covariance for d = 3. Using the theory of angular momentum, we explicitly find the spectrum and the minimal output entropy of Φ. Negative eigenvalues in the spectrum of Φ indicate that the channel cannot be obtained as a result of Hermitian Markovian quantum dynamics. Degradability and antidegradability of the Landau–Streater channel is fully analyzed. We calculate classical and entanglement-assisted capacities of Φ. Quantum capacity of Φ vanishes if d = 2, 3 and is strictly positive if d ⩾ 4. We show that the channel Φ ⊗ Φ does not annihilate entanglement and preserves entanglement of some states with Schmidt rank 2 if d ⩾ 3.
We study the Landau–Streater quantum channel Φ:B(Hd)↦B(Hd), whose Kraus operators are proportional to the irreducible unitary representation of SU(2) generators of dimension d. We establish SU(2) covariance for all d and U(3) covariance for d = 3. Using the theory of angular momentum, we explicitly find the spectrum and the minimal output entropy of Φ. Negative eigenvalues in the spectrum of Φ indicate that the channel cannot be obtained as a result of Hermitian Markovian quantum dynamics. Degradability and antidegradability of the Landau–Streater channel is fully analyzed. We calculate classical and entanglement-assisted capacities of Φ. Quantum capacity of Φ vanishes if d = 2, 3 and is strictly positive if d ⩾ 4. We show that the channel Φ ⊗ Φ does not annihilate entanglement and preserves entanglement of some states with Schmidt rank 2 if d ⩾ 3.
Two important classes of quantum channels, namely, the Werner-Holevo and the Landau-Streater channels, are known to be related only in three dimensions, i.e., when acting on qutrits. In this work, the definition of the Landau-Streater channel is extended in such a way that it retains its equivalence to the Werner-Holevo channel in all dimensions. This channel is then modified to be representable as a model of noise acting on qudits. We then investigate properties of the resulting noisy channel and determine the conditions under which it cannot be the result of a Markovian evolution. Furthermore, we investigate its different capacities for transmitting classical and quantum information with or without entanglement. In particular, while the pure (or high-noise) Landau-Streater or the Werner-Holevo channel is entanglement breaking and hence has zero capacity, by finding a lower bound for the quantum capacity, we show that when the level of noise is lower than a critical value the quantum capacity will be nonzero. Surprisingly, this value turns out to be approximately equal to 0.4 in all dimensions. Finally, we show that, in even dimensions, this channel has a decomposition in terms of unitary operations. This is in contrast with the three-dimensional, case where it has been proved that such a decomposition is impossible, even in terms of other quantum maps.
Two important classes of quantum channels, namly the Werner-Holevo and the Landau-Streater channels are known to be related only in three dimensions, i.e. when acting on qutrits. In this work, definition of the Landau-Streater channel is extended in such a way which retains its equivalence to the Werner-Holevo channel in all dimensions. This channel is then modified to be representable as a model of noise acting on qudits. We then investigate propeties of the resulting noisy channel and determine the conditions under which it cannot be the result of a Markovian evolution. Furthermore, we investigate its different capacities for transmitting classical and quantum information with or without entanglement. In particular, while the pure (or high noise) Landau-Streater or the Werner-Holevo channel is entanglement breaking and hence has zero capacity, by finding a lower bound for the quantum capacity, we show that when the level of noise is lower than a critical value the quantum capacity will be non-zero. Surprizingly this value turns out to be approximately equal to 0.4 in all dimensions. Finally we show that, in even dimension, this channel has a decomposition in terms of unitary operations. This is in contrast with the three dimensional case where it has been proved that such a decomposition is impossible, even in terms of other quantum maps.
Degradable quantum channels are among the only channels whose quantum and private classical capacities are known. As such, determining the structure of these channels is a pressing open question in quantum information theory. We give a comprehensive review of what is currently known about the structure of degradable quantum channels, including a number of new results as well as alternate proofs of some known results. In the case of qubits, we provide a complete characterization of all degradable channels with two dimensional output, give a new proof that a qubit channel with two Kraus operators is either degradable or anti-degradable, and present a complete description of anti-degradable unital qubit channels with a new proof. For higher output dimensions we explore the relationship between the output and environment dimensions (dB and dE, respectively) of degradable channels. For several broad classes of channels we show that they can be modeled with an environment that is “small” in the sense of ΦC. Such channels include all those with qubit or qutrit output, those that map some pure state to an output with full rank, and all those which can be represented using simultaneously diagonal Kraus operators, even in a non-orthogonal basis. Perhaps surprisingly, we also present examples of degradable channels with “large” environments, in the sense that the minimal dimension dE>dB. Indeed, one can have dE>14dB2. These examples can also be used to give a negative answer to the question of whether additivity of the coherent information is helpful for establishing additivity for the Holevo capacity of a pair of channels. In the case of channels with diagonal Kraus operators, we describe the subclasses that are complements of entanglement breaking channels. We also obtain a number of results for channels in the convex hull of conjugations with generalized Pauli matrices. However, a number of open questions remain about these channels and the more general case of random unitary channels.
Understanding the limits of quantum communication is a central problem in quantum information theory. Structural properties of quantum channels provide tools for analyzing these limits. In particular, approximate degradability links quantum-capacity bounds to the accuracy with which a channel's environment can be reconstructed from its output. We study this reconstruction problem for noisy Landau-Streater channels across finite-spin representations. For spin j and noise probability p, we construct an explicit degrading map with diamond-norm error at most [2+8/(j(j+1))]p2≤(38/3)p2 on the common interval 0≤p≤1/8. A lower bound establishes quadratic order for this construction at each fixed spin. Floating-point semidefinite optimization places its error within 2.48% of the numerical optimum on the sampled grid for four spins. Covariance and conditional-entropy concavity yield explicit two-sided quantum-capacity bounds for this family with a spin-uniform remainder. Building on the low-noise Pauli cancellation strategy, we formulate a sufficient condition based on a common scalar adjoint action on fixed, possibly nonunitary noise Kraus operators. The resulting reconstruction-error bound is uniform in system dimension and Kraus count. The criterion applies to irreducible SU(N) generator channels and noisy Werner-Holevo channels, with the SU(3) adjoint representation providing an example outside the mixed-unitary class.
We investigate information theoretic properties of low rank (less than or equal to 3) quantum channels with [Formula: see text]-symmetry, where we have a complete description. We prove that PPT property coincides with entanglement-breaking property and that degradability seldomly holds in this class. In connection with these results, we will demonstrate how we can compute Holevo and coherent information of those channels. In particular, we exhibit a strong form of additivity violation of coherent information, which resembles the superactivation of coherent information of depolarizing channels.
The quantum capacity captures the value of a quantum channel for transmitting quantum information, establishing the fundamental limits on quantum communication. In spite of its central role in quantum information theory, the quantum capacity of most channels is unknown, with wide gaps between the best upper and lower bounds. Even deciding whether a channel has nonzero capacity -- finding its capacity threshold -- is difficult. In this paper we report significant increases in the capacity thresholds of two prototypical noise models: the depolarizing channel and Pauli channels. In the case of the depolarizing channel, this is the first improvement in 18 years, giving a bigger increase beyond the hashing bound than all previous improvements combined. Our starting point is the representation theoretic framework recently proposed by Bhalerao and Leditzky (2025) to compute coherent information for special permutation invariant states. We generalize their framework to the full symmetric subspace, which allow us to optimize coherent information over rank two states in that space. A representation theoretic calculation shows that exponentially many Kraus operators of the channel annihilate the symmetric space, corresponding to a massive decrease in environment entropy for states on the symmetric space compared to the maximally mixed state. This explains the enhanced coherent information as a manifestation of degeneracy for the resulting codes.