Quantum informational properties of the Landau–Streater channel

Abstract

We study the Landau-Streater quantum channel Φ : B(H d ) → B(H d ), 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.

On Quantum Operations of Photon Subtraction and Photon Addition

“…Finally, the multiple photon addition and subtraction operations can be treated in the same way because Interestingly, in contrast to the quantum channels [32][33][34][35], the quantum informational properties of quantum operations such as capacities and entanglement degradation remain essentially unstudied. From this viewpoint, the fair quantum operations (4) and (5) can be analyzed as paradigmatic examples of operations on continuousvariable quantum states.…”

Capacity of trace decreasing quantum operations and superadditivity of coherent information for a generalized erasure channel

“…The regularized capacity C(Φ) may exceed the Holevo capacity C χ (Φ) [3]; however, it is hard to evaluate C(Φ) explicitly for a given channel Φ, so many recent studies are devoted to the search of lower and upper bounds for C(Φ) (see, e.g., Refs. [28][29][30]). Below in this section we find the lower and upper bounds for classical capacity of the generalized erasure channel.…”

Realization of the Werner–Holevo and Landau–Streater Quantum Channels for Qutrits on Quantum Computers

“…Moreover, such qutrit channels are extremal, exhibit the global unitary covariance, and violate the multiplicativity of the maximal p-norm 7 . Quantum informational properties of these channels are reviewed 8 . It is of great interest to physically implement the specific interaction of a qutrit with environment that would produce the Landau-Streater and Werner-Holevo channels.…”

“…where U are unitary operators. They have been subject of extensive recent study 5,6,8 . In terms of applications in quantum physics, the QCs can be used to describe the time evolution of a spin-1 quantum particles, which interacts with another one.…”