Information capacity formula of quantum optical channels
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Abstract:
The applications of the general formulae of channel capacity developed in the quantum information theory to evaluation of information transmission capacity of optical channel are interesting subjects. In this review paper, we will point out that the formulation based on only classical-quantum channel mapping model may be inadequate when one takes into account a power constraint for noisy channel. To define the power constraint well, we should explicitly consider how quantum states are conveyed through a transmission channel. Basing on such consideration, we calculate a capacity formula for an attenuated noisy optical channel with genreral Gaussian state input; this gives certain progress beyond the example in our former paper.Keywords:
Classical capacity
We introduce a proper framework of coding problems for a quantum memoryless channel and derive an asymptotic formula for the channel capacity having an operational significance. Some general lower and upper bounds for the quantum channel capacity are also derived.
Classical capacity
Quantum capacity
Amplitude damping channel
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Coding theorems in quantum Shannon theory express the ultimate rates at which a sender can transmit information over a noisy quantum channel. More often than not, the known formulas expressing these transmission rates are intractable, requiring an optimization over an infinite number of uses of the channel. Researchers have rarely found quantum channels with a tractable classical or quantum capacity, but when such a finding occurs, it demonstrates a complete understanding of that channel's capabilities for transmitting classical or quantum information. Here we show that the three-dimensional capacity region for entanglement-assisted transmission of classical and quantum information is tractable for the Hadamard class of channels. Examples of Hadamard channels include generalized dephasing channels, cloning channels, and the Unruh channel. The generalized dephasing channels and the cloning channels are natural processes that occur in quantum systems through the loss of quantum coherence or stimulated emission, respectively. The Unruh channel is a noisy process that occurs in relativistic quantum information theory as a result of the Unruh effect and bears a strong relationship to the cloning channels. We give exact formulas for the entanglement-assisted classical and quantum communication capacity regions of these channels. The coding strategy for each of these examples is superior to a na\"{\i}ve time-sharing strategy, and we introduce a measure to determine this improvement.
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Classical capacity
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Unruh effect
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Quantum information processing exploits the quantum nature of information. It offers fundamentally new solutions in the field of computer science and extends the possibilities to a level that cannot be imagined in classical communication systems. For quantum communication channels, many new capacity definitions were developed in comparison to classical counterparts. A quantum channel can be used to realize classical information transmission or to deliver quantum information, such as quantum entanglement. In this paper we overview the properties of the quantum communication channel, the various capacity measures and the fundamental differences between the classical and quantum channels.
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Noisy quantum channels may be used in many information carrying applications. We show that different applications may result in different channel capacities. Upper bounds on several of these capacities are proved. These bounds are based on the coherent information, which plays a role in quantum information theory analogous to that played by the mutual information in classical information theory. Many new properties of the coherent information and entanglement fidelity are proved. Two non-classical features of the coherent information are demonstrated: the failure of subadditivity, and the failure of the pipelining inequality. Both properties arise as a consequence of quantum entanglement, and give quantum information new features not found in classical information theory. The problem of a noisy quantum channel with a classical observer measuring the environment is introduced, and bounds on the corresponding channel capacity proved. These bounds are always greater than for the unobserved channel. We conclude with a summary of open problems.
Classical capacity
Coherent information
Amplitude damping channel
Subadditivity
Quantum capacity
Information Theory
Quantum mutual information
Observer (physics)
Information transmission
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The transmission of classical information over a classical channel gave rise to the classical capacity theorem with the optimal rate in terms of the classical mutual information. Despite classical information being a subset of quantum information, the rate of the quantum capacity problem is expressed in terms of the coherent information, which does not mathematically generalize the classical mutual information. Additionally, there are multiple capacity theorems with distinct formulas when dealing with transmitting information over a noisy quantum channel. This leads to the question of what constitutes a mathematically accurate quantum generalization of classical mutual information and whether there exists a quantum task that directly extends the classical capacity problem. In this paper, we address these inquiries by introducing a quantity called the generalized information, which serves as a mathematical extension encompassing both classical mutual information and coherent information. We define a transmission task, which includes as specific instances both classical information and quantum information capacity problems, and show that the transmission capacity of this task is characterized by the generalized information.
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Amplitude damping channel
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Information Theory
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Parameter Regime Giving Zero Quantum Coherent Information of A Non-Pauli Quantum Channel Author: Advisors: Tong (Mary) Liu Dr. Bei Zeng, Dr. David Kribs In quantum information theory, in order for two (or more) parties to communicate, there must be a communication channel. The two central quantities that must be considered are quantum channel capacity and the quantum coherent information. The first describes the capability for a given channel to communicate the required quantum information and the latter describes the amount of information that has been successfully transmitted through the corresponding quantum channel. The capacity of a quantum channel is actually a function of the coherent information, and so the basic step for getting the channel capacity is to calculate its coherent information which serves as a lower bound on the capacity. Generally speaking, it is hard to find the capacity of a given quantum channel, this is because of regularization which is to introduce additional process to solve an ill-conditioned problem. Comparing to general quantum channels, the capacity is easily achieved for the two fundamental classes of quantum channels, degradable and antidegradable, in such a way that degradable channels have capacity given exactly by the coherent information and antidegradable channels have zero coherent information. However, this is not true for general quantum channels, by all means that, under certain restrictions, it is possible to find a non-Pauli quantum channel such that its coherent information is zero but its capacity is non-zero.
Quantum capacity
Coherent information
Pauli exclusion principle
Classical capacity
Amplitude damping channel
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The applications of the general formulae of channel capacity developed in the quantum information theory to evaluation of information transmission capacity of optical channel are interesting subjects. In this review paper, we will point out that the formulation based on only classical-quantum channel mapping model may be inadequate when one takes into account a power constraint for noisy channel. To define the power constraint well, we should explicitly consider how quantum states are conveyed through a transmission channel. Basing on such consideration, we calculate a capacity formula for an attenuated noisy optical channel with genreral Gaussian state input; this gives certain progress beyond the example in our former paper.
Classical capacity
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Citations (1)
In Shannon information theory the capacity of a memoryless communication channel cannot be increased by the use of feedback. The use of classical feedback is shown to provide no increase in the classical capacity of a memoryless quantum channel when feedback is used across nonentangled input states, or when the channel is an entanglement-breaking channel
Classical capacity
Amplitude damping channel
Quantum capacity
Information Theory
Shannon–Hartley theorem
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We study the communication capabilities of a quantum channel under the most general channel model known as the one-shot model. Unlike classical channels that can only be used to transmit classical information (bits), a quantum channel can be used for transmission of classical information, quantum information (qubits) and simultaneous transmission of classical and quantum information. In this work, we investigate the one-shot capabilities of a quantum channel for simultaneously transmitting of bits and qubits. This problem was studied in the asymptotic regime for a memoryless channel and a regularized characterization of the capacity region was reported. It is known that the transmission of private classical information is closely related to the problem of quantum information transmission. We resort to this idea and find achievable and converse bounds on the simultaneous transmission of the public and private classical information. then by shifting the classical private rate to the quantum information rate, the obtained rate regions will be translated into rate regions of thThis in turn, leads to a rate region for simulttaneous transmission of classical and quantum information. In the case of asymptotic i.i.d. setting, our one-shot result is evaluated to the known results in the literature. Our main tools used in the achievability proofs are position-based decoding and convex-split lemma.
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Amplitude damping channel
Converse
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Quantum capacity
Communication source
Classical capacity
Amplitude damping channel
Coherent information
Operator (biology)
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