# Increasing quantum channel capacity

I have a few confusions regarding quantum communication. Please bear with me as I ask what might appear to be basic or naive questions:

In the case of classical communication the capacity of wireless channel is given by: \begin{align} C_c= B \log_2\left(1+\dfrac{P h}{\sigma^2}\right) \end{align}
where $$B$$ is the bandwidth, $$P$$ is the transmission power, $$h$$ is the channel gain and $$\sigma^2$$ is the variance of AWGN. So we can increase the per second capacity by increasing the transmission power and/or the bandwidth.

Now in the case of amplitude dampening quantum channel the capacity is given by: \begin{align} Q=\max_{\tau}[H(\tau(1-\gamma))-H(\tau(\gamma))] \end{align} where $$\tau\in [0,1]$$, $$H$$ is the Shannon entropy function and $$\gamma$$ is the damping parameter. I think this is also referred to one-shot capacity of the channel at some places.

I have the following questions/confusions:

1. It appears that the capacity of the quantum channel is inherently limited to $$\leq$$ 1. Unlike classical communication where we can enhance capacity by increasing transmission power or bandwidth, I wonder if a quantum channel's bandwidth has a similar impact on the capacity. Is there an analogous method in the realm of quantum communication that could potentially boost its capacity?

2. If what we have is one-shot capacity (capacity per channel use). Does that mean we can transmit on the channel multiple times in a second? As the amplitude dampening channel is degradable, the capacity will be N*Q qbits/second? Where N is the number of transmission per second. Is there an upper bound to the value of N (maximum number of transmissions per second)?

3. What if we need to transmit hundreds of qbits per-second? Can we assume multiple quantum channels between the sender and the receiver over the same optical fiber? Or is there some other resource that can help in increasing the capacity?

I understand that these questions might appear elementary, and I have attempted to search for answers online; however, I am facing some challenges in finding the information I need. If you have any familiarity with the field, I would greatly appreciate your insights, even if you cannot provide a definitive answer. Additionally, if you could suggest any references or resources that I could explore to deepen my understanding, that would be immensely helpful. Thank you for your support!

• I think part of the confusion is that you're comparing a continuous classical channel to a discrete'' (finite dimensional) quantum channel. This is why you see the quantum channel has a capacity bounded by $1$, note this bound on the capacity would be the same if you considered a classical channel with a 1-bit output. To get a fairer comparison you probably want to look at infinite-dimensional quantum systems. Jul 26 at 9:46