Questions tagged [channel-capacity]

The highest rate at which quantum information can be communicated over many independent uses of a noisy quantum channel (e.g. a qubit) from a sender to a receiver.

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What is meant by a "single-letter" expression for the quantum channel capacity?

The quantity $Q_1(\Phi) = max_{\rho} I_C(\rho, \Phi)$, is called one-letter capacity of channel $\Phi$. I want to know, what is meant by the term "single-letter" capacity here, often used in ...
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What is the quantum capacity of the combined amplitude and phase damping channel?

Quantum capacity for the amplitude damping channel and the pure dephasing channel have closed-form formulas as it can be seen in section 24.7.2 of From Classical to Quantum Shannon Theory. However, I ...
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Optimality of teleportation for entanglement-assisted quantum channel coding

Setting: Consider a quantum channel $N_{A\rightarrow B}$ between Alice and Bob. Let Alice and Bob also share arbitrary amounts of entanglement assistance through the state $\phi_{A_EB_E}$ (these can ...
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2answers
146 views

Bounding diamond norm distance using probability of error in transmission of classical information

Let us consider an encode, noisy channel and a decoder such that classical messages $m\in\mathcal{M}$ can be transmitted with some small error. That is, for a message $m$ that is sent by Alice, Bob ...
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What was the meaning of Lossless Quantum compression?

I was reading few questions regarding lossless quantum compression on stack exchange, then out of curiosity, I started reading this article. After reading I end up being confused about what does ...
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211 views

Quantum capacity for serial composition of quantum channels

Recently, I have been working with quantum channel capacity for quantum-quantum channels and I was wondering if there exist some results for channel compositions. Specifically, I have been looking for ...
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79 views

What are examples of zero capacity quantum channels with Choi rank less than $d$?

All the currently known examples of quantum channels with zero quantum capacity are either PPT or anti-degradable. These notions can be conveniently defined in terms of the Choi matrix of the given ...
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82 views

How to compute the capacity of a quantum channel from its Kraus operators?

Is there a working rule to compute the capacity of a quantum channel described by a set of Kraus operators $\{K_i\}$?
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1answer
241 views

What exactly is the relation between the Holevo quantity and the mutual information?

On this page, it is stated that the Holevo quantity is an upper bound to the accessible information of a quantum state. In the scenario where Alice encodes classical information into a quantum state ...
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1answer
251 views

Understanding classical vs. quantum channel capacities

The classical channel capacity ($C_{ea}$) and the quantum channel capacity ($Q$) as defined here (eqs. 1 and 2) are given by \begin{equation} C_{ea} = \text{sup}_{\rho} \Big[S(\rho) + S(\Phi_t \rho) -...
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Experimental Realization of Superactivation of Quantum Capacity

The superactivation of quantum capacity is an effect that some quantum channels present such that is two of those channels with zero capacity are combined, a non-zero channel capacity can be achieved ...
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475 views

Advances in Quantum Channel Capacity

I have been reading about the Quantum Channel Capacity and it seems to be an open problem to find such capacity in general. Quantum capacity is the highest rate at which quantum information can be ...