Related papers: Query Complexity of Classical and Quantum Channel …
Quantum query complexity is a fundamental model for analyzing the computational power of quantum algorithms. It has played a key role in characterizing quantum speedups, from early breakthroughs such as Grover's and Simon's algorithms to…
In our previous work, we presented a Blahut-Arimoto type algorithm for computing the discrete memoryless (DM) classical-quantum channel capacity. And the speed of convergence is analyzed. In this paper, we present numerical experiment to…
The quantum channel capacity gives the ultimate limit for the rate at which quantum data can be reliably transmitted through a noisy quantum channel. Degradable quantum channels are among the few channels whose quantum capacities are known.…
Quantum state discrimination is an important problem in many information processing tasks. In this work we are concerned with finding its best possible sample complexity when the states are preprocessed by a quantum channel that is required…
Divergence chain rules for channels relate the divergence of a pair of channel inputs to the divergence of the corresponding channel outputs. An important special case of such a rule is the data-processing inequality, which tells us that if…
We study the query complexity of computing a function f:{0,1}^n-->R_+ in expectation. This requires the algorithm on input x to output a nonnegative random variable whose expectation equals f(x), using as few queries to the input x as…
We consider the process consisting of preparation, transmission through a quantum channel, and subsequent measurement of quantum states. The communication complexity of the channel is the minimal amount of classical communication required…
The discrimination of quantum processes, including quantum states, channels, and superchannels, is a fundamental topic in quantum information theory. It is often of interest to analyze the optimal performance that can be achieved when…
We investigate the classical communication over quantum channels when assisted by no-signaling (NS) and positive-partial-transpose-preserving (PPT) codes, for which both the optimal success probability of a given transmission rate and the…
Alternative exact expressions are derived for the minimum error probability of a hypothesis test discriminating among $M$ quantum states. The first expression corresponds to the error probability of a binary hypothesis test with certain…
To decide whether a quantum channel is degradable is relatively easy: one has to find at least one example of a degrading quantum channel. But in general, no conclusive criterion exists to show the opposite. Using elementary methods we…
We consider a setting where a stream of qubits is processed sequentially. We derive fundamental limits on the rate at which classical information can be transmitted using qubits that decohere as they wait to be processed. Specifically, we…
Certifying the correct functioning of a unitary channel is a critical step toward reliable quantum information processing. In this work, we investigate the query complexity of the unitary channel certification task: testing whether a given…
Query complexity measures the amount of information an algorithm needs about a problem to compute a solution. On a quantum computer there are different realizations of a query and we will show that these are not always equivalent. Our…
We connect two key concepts in quantum information: compatibility and divisibility of quantum channels. Two channels are compatible if they can be both obtained via marginalization from a third channel. A channel divides another channel if…
Quantum hypothesis testing is an important tool for quantum information processing. Two main strategies have been widely adopted: in a minimum error discrimination strategy, the average error probability is minimized; while in an…
We determine both the quantum and the private capacities of low-noise quantum channels to leading orders in the channel's distance to the perfect channel. It has been an open problem for more than 20 years to determine the capacities of…
We develop a theory for finding quantum error correction (QEC) procedures which are optimized for given noise channels. Our theory accounts for uncertainties in the noise channel, against which our QEC procedures are robust. We demonstrate…
The quantum capacity of a memoryless channel is often used as a single figure of merit to characterize its ability to transmit quantum information coherently. The capacity determines the maximal rate at which we can code reliably over…
We study the complexity of testing properties of quantum channels. First, we show that testing identity to any channel $\mathcal N: \mathbb C^{d_{\mathrm{in}} \times d_{\mathrm{in}}} \to \mathbb C^{d_{\mathrm{out}} \times d_{\mathrm{out}}}$…