Transmission Of Classical Information Research Articles

Quantum Limits on the Energy Consumption of Optical Transmission Systems

The search for schemes that minimize the energy associated with the transmission of information is a longstanding fundamental issue in communication theory. In this paper we extend fundamental limits to the energy consumption per unit of information, as given by Shannon's theory, to the quantum domain. Unlike previous studies, we address a scenario where the signal may be manipulated in an arbitrary way while propagating from the transmitter to the receiver. This situation characterizes many realistic scenarios, such as multi-span fiber-optic communication systems. We obtain the ultimate quantum limit on the energy consumption in this scenario and propose a simple binary energy modulation scheme that approaches this limit within one order of magnitude for practically relevant values of spectral efficiency. Under the same conditions, the quantum energy consumption limit of the standard optically amplified coherent communication scheme is three orders of magnitude above the ultimate identified limit. Throughout the paper we consider transmission of classical information over a quantum channel.

Classical information transmission capacity of quantum black holes

The fate of classical information incident on a quantum black hole has been the subject of an ongoing controversy in theoretical physics, because a calculation within the framework of semi-classical curved-space quantum field theory appears to show that the incident information is irretrievably lost, in contradiction to time-honored principles such as time-reversibility and unitarity. Here, we show within this framework embedded in quantum communication theory that signaling from past to future null infinity in the presence of a Schwarzschild black hole can occur with arbitrary accuracy, and thus that classical information is not lost in black hole dynamics. The calculation relies on a treatment that is manifestly unitary from the outset, where probability conservation is guaranteed because black holes stimulate the emission of radiation in response to infalling matter. This stimulated radiation is non-thermal and contains all of the information about the infalling matter, while Hawking radiation contains none of it.

Photon Information Efficient Communication Through Atmospheric Turbulence—Part II: Bounds on Ergodic Classical and Private Capacities

Vacuum-propagation optical communication with high photon efficiency (many bits/photon) and high spectral efficiency (many bits/s ·Hz) requires operation in the near-field power transfer regime with a large number of spatial modes. For terrestrial propagation paths, however, the effects of atmospheric turbulence must be factored into the photon and spectral efficiency assessments. In Part I of this study [N. Chandrasekaran and J. H. Shapiro, “Photon Information Efficient Communication Through Atmospheric Turbulence-Part I: Channel Model and Propagation Statistics,” J. Lightw. Technol., vol. 32, no. 6, pp. 1075-1087, Mar. 2014], modal-transmissivity statistics were derived for the turbulent channel that depend solely on the mutual coherence function of the atmospheric Green's function, and these bounds were evaluated for ~ 200 spatial-mode systems whose transmitters used either focused-beam (FB), Hermite-Gaussian (HG), or Laguerre-Gaussian (LG) modes and whose receivers either did or did not employ adaptive optics. This Part II paper derives upper and lower bounds for the ergodic Holevo capacities of classical and private information transmission over the multiple spatial-mode turbulent channel that can be evaluated from Part I's transmissivity statistics. Also included are bounds on the ergodic capacity for on-off keying encoding and direct detection. It is shown that: 1) adaptive optics are not necessary to realize high photon information efficiency and high spectral efficiency simultaneously; 2) an FB-mode system with perfect adaptive optics outperforms its HG-mode and LG-mode counterparts; and 3) the converse is true when adaptive optics are not employed.

Phase of the Quantum Bit wave function as a Resource for Information Storage and Transfer

We considered the phase of the quantum bit wave function as a resource for storage and transmission of classical information. We qualitatively evaluated the effectiveness of this resource. We considered use of this resource for the transmission of classical information through a quantum channel of communication with the help of technology of quantum teleportation.

The double-padlock problem: Is secure classical information transmission possible without key exchange?

The idealized Kish-Sethuraman (KS) cipher is theoretically known to offer perfect security through a classical information channel. However, realization of the protocol is hitherto an open problem, as the required mathematical operators have not been identified in the previous literature. A mechanical analogy of this protocol can be seen as sending a message in a box using two padlocks; one locked by the Sender and the other locked by the Receiver, so that theoretically the message remains secure at all times. We seek a mathematical representation of this process, considering that it would be very unusual if there was a physical process with no mathematical description. We select Clifford's geometric algebra for this task as it is a natural formalism to handle rotations in spaces of various dimension. The significance of finding a mathematical description that describes the protocol, is that it is a possible step toward a physical realization having benefits in increased security with reduced complexity.

A Smooth Entropy Approach to Quantum Hypothesis Testing and the Classical Capacity of Quantum Channels

We use the smooth entropy approach to treat the problems of binary quantum hypothesis testing and the transmission of classical information through a quantum channel. We provide lower and upper bounds on the optimal type II error of quantum hypothesis testing in terms of the smooth max-relative entropy of the two states representing the two hypotheses. Using then a relative entropy version of the Quantum Asymptotic Equipartition Property (QAEP), we can recover the strong converse rate of the i.i.d. hypothesis testing problem in the asymptotics. On the other hand, combining Stein's lemma with our bounds, we obtain a stronger ($\ep$-independent) version of the relative entropy-QAEP. Similarly, we provide bounds on the one-shot $\ep$-error classical capacity of a quantum channel in terms of a smooth max-relative entropy variant of its Holevo capacity. Using these bounds and the $\ep$-independent version of the relative entropy-QAEP, we can recover both the Holevo-Schumacher-Westmoreland theorem about the optimal direct rate of a memoryless quantum channel with product state encoding, as well as its strong converse counterpart.

Genuine multiparty quantum entanglement suppresses multiport classical information transmission

We establish a universal complementarity relation between the capacity of classical information transmission by employing a multiparty quantum state as a multiport quantum channel, and the genuine multipartite entanglement of the quantum state. The classical information transfer is from a sender to several receivers by using the quantum dense coding protocol with the multiparty quantum state shared between the sender and the receivers. The relation holds for arbitrary pure or mixed quantum states of an arbitrary number of parties in arbitrary dimensions.

Electromagnetic channel capacity for practical purposes

We give analytic upper bounds to the channel capacity C for transmission of classical information in electromagnetic channels (bosonic channels with thermal noise). In the practically relevant regimes of high noise and low transmissivity, by comparison with know lower bounds on C, our inequalities determine the value of the capacity up to corrections which are irrelevant for all practical purposes. Examples of such channels are radio communication, infrared or visible-wavelength free space channels. We also provide bounds to active channels that include amplification.

Achieving minimum-error discrimination of an arbitrary set of laser-light pulses

Laser light is widely used for communication and sensing applications, so the optimal discrimination of coherent states--the quantum states of light emitted by a laser--has immense practical importance. However, quantum mechanics imposes a fundamental limit on how well different coher- ent states can be distinguished, even with perfect detectors, and limits such discrimination to have a finite minimum probability of error. While conventional optical receivers lead to error rates well above this fundamental limit, Dolinar found an explicit receiver design involving optical feedback and photon counting that can achieve the minimum probability of error for discriminating any two given coherent states. The generalization of this construction to larger sets of coherent states has proven to be challenging, evidencing that there may be a limitation inherent to a linear-optics-based adaptive measurement strategy. In this Letter, we show how to achieve optimal discrimination of any set of coherent states using a resource-efficient quantum computer. Our construction leverages a recent result on discriminating multi-copy quantum hypotheses (arXiv:1201.6625) and properties of coherent states. Furthermore, our construction is reusable, composable, and applicable to designing quantum-limited processing of coherent-state signals to optimize any metric of choice. As illustrative examples, we analyze the performance of discriminating a ternary alphabet, and show how the quantum circuit of a receiver designed to discriminate a binary alphabet can be reused in discriminating multimode hypotheses. Finally, we show our result can be used to achieve the quantum limit on the rate of classical information transmission on a lossy optical channel, which is known to exceed the Shannon rate of all conventional optical receivers.

Sending classical information through relativistic quantum channels

We investigate how special relativity influences the transmission of classical information through quantum channels by evaluating the Holevo bound when the sender and the receiver are in (relativistic) relative motion. By using the spin degrees of freedom of spin-1/2 fermions to encode the classical information we show that, for some configurations, the accessible information in the receiver can be increased when the spin detector moves fast enough. This is possible by allowing the momentum wave packet of one of the particles to be wide enough while the momentum wave packets of other particles are kept relatively narrow. In this way, one can take advantage of the fact that boosts entangle the spin and momentum degrees of freedom of spin-1/2 fermions to increase the accessible information in the former. We close the paper with a discussion of how this relativistic quantum channel cannot in general be described by completely positive quantum maps.

Maximally-dense-coding-capable quantum states

A complementarity relation is established between the capacity of multiport classical information transmission via quantum states and multiparty quantum correlation measures for three-qubit pure states. The multiparty quantum correlation measures considered are the generalized geometric measure, the tangle, and the discord monogamy score. The complementarity relation is revealed by the identification of a one-parameter family of pure three-qubit states, which we call the maximally dense coding capable family of states. These states have the maximal multiport dense coding capacity among all three-qubit pure states with an arbitrary fixed amount of the multiparty quantum correlations.

Experimental achievement of the entanglement-assisted capacity for the depolarizing channel

We experimentally demonstrate the achievement of the entanglement-assisted capacity for classical information transmission over a depolarizing channel. The implementation is based on the generation and local manipulation of two-qubit Bell states, which are finally measured at the receiver by realizing projective measurements in the Bell basis. The depolarizing channel is realized by introducing quantum noise in a controlled way on one of the two qubits. This work represents an investigation into the amount of information that can be shared in the presence of noise.

Quantum communication and quantum computing

The subject of quantum computing brings together ideas from classical information theory, computer science, and quantum physics. This review aims to summarize not just quantum computing, but the whole subject of quantum information theory. Information can be identified as the most general thing which must propagate from a cause to an effect. It therefore has a fundamentally important role in the science of physics. However, the mathematical treatment of information, especially information processing, is quite recent, dating from the mid-20th century. This has meant that the full significance of information as a basic concept in physics is only now being discovered. This is especially true in quantum mechanics. The theory of quantum information and computing puts this significance on a firm footing, and has led to some profound and exciting new insights into the natural world. Among these are the use of quantum states to permit the secure transmission of classical information (quantum cryptography), the use of quantum entanglement to permit reliable transmission of quantum states (teleportation), the possibility of preserving quantum coherence in the presence of irreversible noise processes (quantum error correction), and the use of controlled quantum evolution for efficient computation (quantum computation). The common theme of all these insights is the use of quantum entanglement as a computational resource.

On classical capacities of infinite-dimensional quantum channels

A coding theorem for entanglement-assisted communication via an infinite-dimensional quantum channel with linear constraints is extended to a natural degree of generality. Relations between the entanglement-assisted classical capacity and ?-capacity of constrained channels are obtained, and conditions for their coincidence are given. Sufficient conditions for continuity of the entanglement-assisted classical capacity as a function of a channel are obtained. Some applications of the obtained results to analysis of Gaussian channels are considered. A general (continuous) version of the fundamental relation between coherent information and the measure of privacy of classical information transmission via an infinite-dimensional quantum channel is proved.

Polar Codes for Private and Quantum Communication Over Arbitrary Channels

We construct new polar coding schemes for the transmission of quantum or private classical information over arbitrary quantum channels. In the former case, our coding scheme achieves the symmetric coherent information and in the latter the symmetric private information. Both schemes are built from a polar coding construction capable of transmitting classical information over a quantum channel [Wilde and Guha, IEEE Transactions on Information Theory, in press]. Appropriately merging two such classical-quantum schemes, one for transmitting "amplitude" information and the other for transmitting "phase," leads to the new private and quantum coding schemes, similar to the construction for Pauli and erasure channels in [Renes, Dupuis, and Renner, Physical Review Letters 109, 050504 (2012)]. The encoding is entirely similar to the classical case, and thus efficient. The decoding can also be performed by successive cancellation, as in the classical case, but no efficient successive cancellation scheme is yet known for arbitrary quantum channels. An efficient code construction is unfortunately still unknown. Generally, our two coding schemes require entanglement or secret-key assistance, respectively, but we extend two known conditions under which the needed assistance rate vanishes. Finally, although our results are formulated for qubit channels, we show how the scheme can be extended to multiple qubits. This then demonstrates a near-explicit coding method for realizing one of the most striking phenomena in quantum information theory: the superactivation effect, whereby two quantum channels which individually have zero quantum capacity can have a non-zero quantum capacity when used together.

Multiqubit quantum teleportation

We provide a class of six-qubit states for three-qubit perfect teleportation. These states include the six-qubit cluster states as a special class. We generalize this class of six-qubit states to 2n-qubit pure states for n-qubit teleportation, n ⩾ 1. These states can be also used for 2n-bit classical information transmission in dense coding.

Transmission of classical and quantum information through a quantum memory channel with damping

We consider the transfer of classical and quantum information through a memory amplitude damping channel. Such a quantum channel is modeled as a damped harmonic oscillator, the interaction between the information carriers — a train of qubits — and the oscillator being of the Jaynes-Cummings kind. We prove that this memory channel is forgetful, so that quantum coding theorems hold for its capacities. We analyze entropic quantities relative to two uses of this channel. We show that memory effects improve the channel aptitude to transmit both classical and quantum information, and we investigate the mechanism by which memory acts in changing the channel transmission properties.

Conditions for coincidence of the classical capacity and entanglement-assisted capacity of a quantum channel

Several relations between the Holevo capacity and entanglement-assisted classical capacity of a quantum channel are proved; necessary and sufficient conditions for their coincidence are obtained. In particular, it is shown that these capacities coincide if (respectively, only if) the channel (respectively, the ?-essential part of the channel) belongs to the class of classical-quantum channels (the ?-essential part is a restriction of a channel obtained by discarding all states that are useless for transmission of classical information). The obtained conditions and their corollaries are generalized to channels with linear constraints. By using these conditions it is shown that the question of coincidence of the Holevo capacity and entanglement-assisted classical capacity depends on the form of a constraint. Properties of the difference between quantum mutual information and the ?-function of a quantum channel are explored.

On quantum advantage in dense coding

The quantum advantage of dense coding—the increase in the rate of classical information transmission due to shared entanglement—is studied. General encoding quantum operations are considered. Particular attention is devoted to the case of many senders and one receiver. It is shown that restrictions on the possible operations among the many senders can strongly affect the usefulness of a shared quantum state for dense coding. It is shown, e.g., that there are states that do not provide any quantum advantage if communication among the senders is not allowed, but are useful for dense coding as soon as the senders can communicate classically. These results are actually independent of the particular quantification of the quantum advantage, being valid for any reasonable definition of such a rate increase. It is further shown that the quantum advantage of dense coding satisfies a monogamy relation with the so-called entanglement of purification.

Schemes of transmission of classical information via quantum channels with many senders: Discrete- and continuous-variable cases

Superadditivity effects in the classical capacity of discrete multi-access channels (MACs) and continuous variable (CV) Gaussian MACs are analysed. New examples of the manifestation of superadditivity in the discrete case are provided including, in particular, a channel which is fully symmetric with respect to all senders. Furthermore, we consider a class of channels for which {\it input entanglement across more than two copies of the channels is necessary} to saturate the asymptotic rate of transmission from one of the senders to the receiver. The 5-input entanglement of Shor error correction codewords surpass the capacity attainable by using arbitrary two-input entanglement for these channels. In the CV case, we consider the properties of the two channels (a beam-splitter channel and a "non-demolition" XP gate channel) analyzed in [Czekaj {\it et al.}, Phys. Rev. A {\bf 82}, 020302 (R) (2010)] in greater detail and also consider the sensitivity of capacity superadditivity effects to thermal noise. We observe that the estimates of amount of two-mode squeezing required to achieve capacity superadditivity are more optimistic than previously reported.