Showing papers on "Coherent information published in 2013"
TL;DR: The derivation establishes a hierarchy of information quantities that can be used to investigate information theoretic tasks in the quantum domain: the one-shot entropies most accurately describe an operational quantity, yet they tend to be difficult to calculate for large systems.
Abstract: We consider two fundamental tasks in quantum information theory, data compression with quantum side information, as well as randomness extraction against quantum side information. We characterize these tasks for general sources using so-called one-shot entropies. These characterizations-in contrast to earlier results-enable us to derive tight second-order asymptotics for these tasks in the i.i.d. limit. More generally, our derivation establishes a hierarchy of information quantities that can be used to investigate information theoretic tasks in the quantum domain: The one-shot entropies most accurately describe an operational quantity, yet they tend to be difficult to calculate for large systems. We show that they asymptotically agree (up to logarithmic terms) with entropies related to the quantum and classical information spectrum, which are easier to calculate in the i.i.d. limit. Our technique also naturally yields bounds on operational quantities for finite block lengths.
297 citations
TL;DR: It is shown that the 'truly' work-like energy that can be extracted can be expressed in terms of a one-shot relative entropy measure introduced in information theory, suggesting that the relations between information theory and statistical mechanics, as illustrated by concepts like Maxwell's demon, Szilard engines and Landauer's principle, extends to the single-shot regime.
Abstract: The work content of non-equilibrium systems in relation to a heat bath is often analysed in terms of expectation values of an underlying random work variable. However, when optimizing the expectation value of the extracted work, the resulting extraction process is subject to intrinsic fluctuations, uniquely determined by the Hamiltonian and the initial distribution of the system. These fluctuations can be of the same order as the expected work content per se, in which case the extracted energy is unpredictable, thus intuitively more heat-like than work-like. This raises the question of the 'truly' work-like energy that can be extracted. Here we consider an alternative that corresponds to an essentially fluctuation-free extraction. We show that this quantity can be expressed in terms of a one-shot relative entropy measure introduced in information theory. This suggests that the relations between information theory and statistical mechanics, as illustrated by concepts like Maxwell's demon, Szilard engines and Landauer's principle, extends to the single-shot regime.
285 citations
TL;DR: It is shown that sandwiched α-Renyi divergence satisfies the data processing inequality for all values of α > 1, and it is proved that α-Holevo information, a variant of Holevo information defined in terms of sandwichedalpha-renyi divergence, is super-additive.
Abstract: Sandwiched (quantum) $\alpha$-Renyi divergence has been recently defined in the independent works of Wilde et al. (arXiv:1306.1586) and Muller-Lennert et al (arXiv:1306.3142v1). This new quantum divergence has already found applications in quantum information theory. Here we further investigate properties of this new quantum divergence. In particular we show that sandwiched $\alpha$-Renyi divergence satisfies the data processing inequality for all values of $\alpha> 1$. Moreover we prove that $\alpha$-Holevo information, a variant of Holevo information defined in terms of sandwiched $\alpha$-Renyi divergence, is super-additive. Our results are based on Holder's inequality, the Riesz-Thorin theorem and ideas from the theory of complex interpolation. We also employ Sion's minimax theorem.
277 citations
TL;DR: It is demonstrated that mutual information contains the quantum entanglement part of theEntanglement entropy, which is otherwise dominated by the thermal entropy at large temperatures.
Abstract: Using the Ryu-Takayanagi conjectured formula for entanglement entropy in the context of gauge-gravity duality, we investigate properties of mutual information between two disjoint rectangular sub-systems in nite temperature relativistic conformal eld theories in d-spacetime dimensions and non-relativistic scale-invariant theories in some generic examples. In all these cases mutual information undergoes a transition beyond which it is identically zero. We study this transition in detail and nd universal qualitative features for the above class of theories which has holographic dual descrip- tions. We also obtain analytical results for mutual information in the specic regime of the parameter space. This demonstrates that mutual information contains the quantum entanglement part of the entanglement entropy, which is otherwise dominated by the thermal entropy at large temperatures.
143 citations
TL;DR: This work gives a bound and uses it to give the first example where the reliability of sending quantum information at rates above the capacity decays exponentially to zero and shows that the framework can be used for proving generalized bounds on the reliability.
Abstract: Information theory tells us that if the rate of sending information across a noisy channel were above the capacity of that channel, then the transmission would necessarily be unreliable. For classical information sent over classical or quantum channels, one could, under certain conditions, make a stronger statement that the reliability of the transmission shall decay exponentially to zero with the number of channel uses, and the proof of this statement typically relies on a certain fundamental bound on the reliability of the transmission. Such a statement or the bound has never been given for sending quantum information. We give this bound and then use it to give the first example where the reliability of sending quantum information at rates above the capacity decays exponentially to zero. We also show that our framework can be used for proving generalized bounds on the reliability.
133 citations
TL;DR: It is proved that quantum theory can be formulated through four very simple postulates, each having a direct physical and intuitive meaning, and this constitutes a set of postulates for quantum theory with a simple and direct physical meaning, like the ones of special relativity or thermodynamics.
Abstract: Does information play a significant role in the foundations of physics? Information is the abstraction that allows us to refer to the states of systems when we choose to ignore the systems themselves. This is only possible in very particular frameworks, like in classical or quantum theory, or more generally, whenever there exists an information unit such that the state of any system can be reversibly encoded in a sufficient number of such units. In this work, we show how the abstract formalism of quantum theory can be deduced solely from the existence of an information unit with suitable properties, together with two further natural assumptions: the continuity and reversibility of dynamics, and the possibility of characterizing the state of a composite system by local measurements. This constitutes a set of postulates for quantum theory with a simple and direct physical meaning, like the ones of special relativity or thermodynamics, and it articulates a strong connection between physics and information.
117 citations
TL;DR: It is found that the engine can be driven by purely quantum information, expressed as the so-called quantum discord, forming a part of the quantum mutual information.
Abstract: The key question of this Letter is whether work can be extracted from a heat engine by using purely quantum mechanical information. If the answer is yes, what is its mathematical formula? First, by using a bipartite memory we show that the work extractable from a heat engine is bounded not only by the free energy change and the sum of the entropy change of an individual memory but also by the change of quantum mutual information contained inside the memory. We then find that the engine can be driven by purely quantum information, expressed as the so-called quantum discord, forming a part of the quantum mutual information. To confirm it, as a physical example we present the Szilard engine containing a diatomic molecule with a semipermeable wall.
91 citations
TL;DR: By deriving a general formula that decomposes the total entropy production into the thermodynamic and informational parts, this work obtains nonequilibrium equalities such as the fluctuation theorem in the presence of information processing.
Abstract: We relate the information exchange between two stochastic systems to the nonequilibrium entropy production in the whole system. By deriving a general formula that decomposes the total entropy production into the thermodynamic and informational parts, we obtain nonequilibrium equalities such as the fluctuation theorem in the presence of information processing. Our results apply not only to situations under measurement and feedback control but also to those under multiple information exchanges between two systems, giving the fundamental energy cost for information processing and elucidating the thermodynamic and informational roles of a memory in information processing. We point out a dual relationship between measurement and feedback.
74 citations
TL;DR: In this article, the authors show that information becomes objective only as quantum information is relegated to correlations with the global environment, and therefore, locally inaccessible. And they also prove an anti-symmetry property relating accessible information and discord, which explains why we perceive objective classical reality while flagrantly quantum superpositions are out of reach.
Abstract: The sum of the Holevo quantity (that bounds the capacity of quantum channels to transmit classical information about an observable) and the quantum discord (a measure of the quantumness of correlations of that observable) yields an observable-independent total given by the quantum mutual information. This split naturally delineates information about quantum systems accessible to observers – information that is redundantly transmitted by the environment – while showing that it is maximized for the quasi-classical pointer observable. Other observables are accessible only via correlations with the pointer observable. We also prove an anti-symmetry property relating accessible information and discord. It shows that information becomes objective – accessible to many observers – only as quantum information is relegated to correlations with the global environment, and, therefore, locally inaccessible. The resulting complementarity explains why, in a quantum Universe, we perceive objective classical reality while flagrantly quantum superpositions are out of reach.
67 citations
TL;DR: It is shown that for an ensemble of semiconductor quantum dots that even in the presence of ultrafast dephasing, for suitably designed condensed matter systems quantum-coherent effects are robust enough to be observable at room temperature.
Abstract: Coherence in light-matter interaction is a necessary ingredient if light is used to control the quantum state of a material system. Coherent effects are firmly associated with isolated systems kept at low temperature. The exceedingly fast dephasing in condensed matter environments, in particular at elevated temperatures, may well erase all coherent information in the material at timescales shorter than a laser excitation pulse. Here we show for an ensemble of semiconductor quantum dots that even in the presence of ultrafast dephasing, for suitably designed condensed matter systems quantum-coherent effects are robust enough to be observable at room temperature. Our conclusions are based on an analysis of the reshaping an ultrafast laser pulse undergoes on propagation through a semiconductor quantum dot amplifier. We show that this pulse modification contains the signature of coherent light-matter interaction and can be controlled by adjusting the population of the quantum dots via electrical injection.
60 citations
TL;DR: In this paper, the authors provided tight bounds for the classical information capacity of a Bosonic thermal noise channel and compared these limits with the well-known lower bound of the channel and an upper bound first introduced by Holevo and Werner in their seminal work on the subject.
Abstract: Researchers provide tight bounds for the classical information capacity of a Bosonic thermal noise channel. They also compare these limits with the well-known lower bound of the channel and an upper bound first introduced by Holevo and Werner in their seminal work on the subject.
TL;DR: In this scheme, quantum Alice splits arbitrary two, three and N-qubit states with two classical parties in a way that both parties are sufficient to reconstruct Alice’s original states only under the condition of which she/he obtains the help from another one, but one of them cannot.
Abstract: By using a generalized Greenberger---Horne---Zeilinger (GHZ) state in which is locally unitarily connected with standard GHZ state as a communication channel, semi-quantum key distribution is extended to study semi-quantum information splitting protocols for secret sharing of quantum information. In our scheme, quantum Alice splits arbitrary two, three and N-qubit states with two classical parties, Bob and Charlie, in a way that both parties are sufficient to reconstruct Alice's original states only under the condition of which she/he obtains the help from another one, but one of them cannot. The presented protocols are helpful for both secure against certain eavesdropping attacks and economical in processing of quantum information.
TL;DR: This paper demonstrates how to construct quantum polar codes that achieve the symmetric private capacity of a degraded quantum wiretap channel with a classical eavesdropper, and has the desirable properties of being channel-adapted and symmetric capacity-achieving along with having an efficient encoder.
Abstract: Channel polarization is a phenomenon in which a particular recursive encoding induces a set of synthesized channels from many instances of a memoryless channel, such that a fraction of the synthesized channels becomes near perfect for data transmission and the other fraction becomes near useless for this task. Mahdavifar and Vardy have recently exploited this phenomenon to construct codes that achieve the symmetric private capacity for private data transmission over a degraded wiretap channel. In this paper, we build on their work and demonstrate how to construct quantum wiretap polar codes that achieve the symmetric private capacity of a degraded quantum wiretap channel with a classical eavesdropper. Due to the Schumacher-Westmoreland correspondence between quantum privacy and quantum coherence, we can construct quantum polar codes by operating these quantum wiretap polar codes in superposition, much like Devetak's technique for demonstrating the achievability of the coherent information rate for quantum data transmission. Our scheme achieves the symmetric coherent information rate for quantum channels that are degradable with a classical environment. This condition on the environment may seem restrictive, but we show that many quantum channels satisfy this criterion, including amplitude damping channels, photon-detected jump channels, dephasing channels, erasure channels, and cloning channels. Our quantum polar coding scheme has the desirable properties of being channel-adapted and symmetric capacity-achieving along with having an efficient encoder, but we have not demonstrated that the decoding is efficient. Also, the scheme may require entanglement assistance, but we show that the rate of entanglement consumption vanishes in the limit of large blocklength if the channel is degradable with classical environment.
TL;DR: The Shannon mutual information of subsystems of critical quantum chains in their ground states is considered and it is indicated that for relatively small lattice sizes, its finite-size behavior already detects the universality class of quantum critical behavior.
Abstract: We consider the Shannon mutual information of subsystems of critical quantum chains in their ground states. Our results indicate a universal leading behavior for large subsystem sizes. Moreover, as happens with the entanglement entropy, its finite-size behavior yields the conformal anomaly $c$ of the underlying conformal field theory governing the long-distance physics of the quantum chain. We study analytically a chain of coupled harmonic oscillators and numerically the $Q$-state Potts models ($Q=2$, 3, and 4), the $XXZ$ quantum chain, and the spin-1 Fateev-Zamolodchikov model. The Shannon mutual information is a quantity easily computed, and our results indicate that for relatively small lattice sizes, its finite-size behavior already detects the universality class of quantum critical behavior.
TL;DR: The origin of information entropy is discussed, the difference between information entropy and thermodynamic entropy is explained, the role of Information entropy in complexity theories, including chaos theory and fractal theory, and new fields in which information entropy may play important roles are speculated.
Abstract: What is information? What role does information entropy play in this information exploding age, especially in understanding emergent behaviors of complex systems? To answer these questions, we discuss the origin of information entropy, the difference between information entropy and thermodynamic entropy, the role of information entropy in complexity theories, including chaos theory and fractal theory, and speculate new fields in which information entropy may play important roles.
TL;DR: In this paper, the smooth entropy approach was used to treat the problems of binary quantum hypothesis testing and the transmission of classical information through a quantum channel, and lower and upper bounds on the optimal type II error of binary hypothesis testing in terms of the smooth max-relative entropy of the two states representing the two hypotheses were derived.
Abstract: 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. Then using 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 ( e-independent) version of the relative entropy-QAEP. Similarly, we provide bounds on the one-shot e-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 e-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.
TL;DR: 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.
Abstract: 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.
TL;DR: It is shown that quantum Fisher information cannot be cloned, whilst it might be broadcast even when the input states are non-commuting, and indicates a hybrid way of information broadcasting which is of particular significance from both practical and theoretical perspectives.
Abstract: It is well known that classical information can be cloned, but nonorthogonal quantum states cannot be cloned, and noncommuting quantum states cannot be broadcast. We conceive a scenario in which the object we want to broadcast is the statistical distinguishability, as quantified by quantum Fisher information, about a signal parameter encoded in quantum states. We show that quantum Fisher information cannot be cloned, while it might be broadcast even when the input states are noncommuting. This situation interpolates between cloning of classical information and no broadcasting of quantum information, and indicates a hybrid way of information broadcasting which is of particular significance from both practical and theoretical perspectives.
TL;DR: It is demonstrated that after removing a logarithmic-sized quantum system from one half of a pair of perfectly correlated bitstrings, even the most sensitive pair of measurements might yield only outcomes essentially independent of each other, which is a form of information locking.
Abstract: It is known that the maximum classical mutual information, which can be achieved between measurements on pairs of quantum systems, can drastically underestimate the quantum mutual information between them. In this article, we quantify this distinction between classical and quantum information by demonstrating that after removing a logarithmic-sized quantum system from one half of a pair of perfectly correlated bitstrings, even the most sensitive pair of measurements might yield only outcomes essentially independent of each other. This effect is a form of information locking but the definition we use is strictly stronger than those used previously. Moreover, we find that this property is generic, in the sense that it occurs when removing a random subsystem. As such, the effect might be relevant to statistical mechanics or black hole physics. While previous works had always assumed a uniform message, we assume only a min-entropy bound and also explore the effect of entanglement. We find that classical information is strongly locked almost until it can be completely decoded. Finally, we exhibit a quantum key distribution protocol that is ‘secure’ in the sense of accessible information but in which leakage of even a logarithmic number of bits compromises the secrecy of all others.
TL;DR: In this paper, an information-theoretic description of electron probabilities is extended to cover the complex amplitudes (wave functions) of quantum mechanics, and a complementary character of the Fisher and Shannon information measures is explored and the relationship between these classical information densities is derived.
Abstract: The entropic perspective on the molecular electronic structure is investigated. Information-theoretic description of electron probabilities is extended to cover the complex amplitudes (wave functions) of quantum mechanics. This analysis emphasizes the entropic concepts due to the phase part of electronic states, which generates the probability current density, thus allowing one to distinguish the information content of states generating the same electron density and differing in their current densities. The classical information measures of Fisher and Shannon, due to the probability/density distributions themselves, are supplemented by the nonclassical terms generated by the wave-function phase or the associated probability current. A complementary character of the Fisher and Shannon information measures is explored and the relationship between these classical information densities is derived. It is postulated to characterize also their nonclassical (phase/current-dependent) contributions. The continuity equations of the generalized information densities are examined and the associated nonclassical information sources are identified. The variational rules involving the quantum-generalized Shannon entropy, which generate the stationary and time-dependent Schrodinger equations from the relevant maximum entropy principles, are discussed and their implications for the system “thermodynamic” equilibrium states are examined. It is demonstrated that the lowest, stationary “thermodynamic” state differs from the true ground state of the system, by exhibiting the space-dependent phase, linked to the modulus part of the wave function, and hence also a nonvanishing probability current.
TL;DR: An introduction to a collection of recent papers revisit how to quantify the relationship between information and work in the light of modern information theory, so-called single-shot information theory.
Abstract: A collection of recent papers revisit how to quantify the relationship between information and work in the light of modern information theory, so-called single-shot information theory This is an introduction to those papers, from the perspective of the author Many of the results may be viewed as a quantification of how much work a generalized Maxwell’s daemon can extract as a function of its extra information These expressions do not in general involve the Shannon/von Neumann entropy but rather quantities from single-shot information theory In a limit of large systems composed of many identical and independent parts the Shannon/von Neumann entropy is recovered
TL;DR: In this paper, the authors present the full characterization of phase-randomized or phase-averaged coherent states, a class of states exploited in communication channels and in decoy state-based quantum key distribution protocols.
Abstract: We present the full characterization of phase-randomized or phase-averaged coherent states, a class of states exploited in communication channels and in decoy state-based quantum key distribution protocols. We report on the suitable formalism to analytically describe the main features of these states and on their experimental investigation, that results in agreement with theory. In particular, we consider a recently proposed non-Gaussianity measure based on the quantum fidelity, that we compare with previous ones, and we use the mutual information to investigate the amount of correlations one can produce by manipulating this class of states.
TL;DR: This work considers a time-energy measure for quantum channels and compute lower and upper bounds of it using the channel Kraus operators, and can obtain the exact value of the time- energy measure for a special class of channels.
Abstract: Quantum mechanics sets limits on how fast quantum processes can run given some system energy through time-energy uncertainty relations, and they imply that time and energy are tradeoffs against each other. Thus, we propose to measure the time energy as a single unit for quantum channels. We consider a time-energy measure for quantum channels and compute lower and upper bounds of it using the channel Kraus operators. For a special class of channels (which includes the depolarizing channel), we can obtain the exact value of the time-energy measure. One consequence of our result is that erasing quantum information requires $\sqrt{(n+1)/n}$ times more time-energy resource than erasing classical information, where $n$ is the system dimension.
TL;DR: It is demonstrated that coherent measurements are optimal and strictly more powerful than conventional one-at-a-time measurements for the task of discriminating quantum states, including certain entangled many-body states (e.g., matrix product states).
Abstract: Measurement of a quantum system – the process by which an observer gathers information about it – provides a link between the quantum and classical worlds. The nature of this process is the central issue for attempts to reconcile quantum and classical descriptions of physical processes. Here, we show that the conventional paradigm of quantum measurement is directly responsible for a well-known disparity between the resources required to extract information from quantum and classical systems. We introduce a simple form of quantum data gathering, “coherent measurement”, that eliminates this disparity and restores a pleasing symmetry between classical and quantum statistical inference. To illustrate the power of quantum data gathering, we demonstrate that coherent measurements are optimal and strictly more powerful than conventional one-at-a-time measurements for the task of discriminating quantum states, including certain entangled many-body states (e.g., matrix product states).
07 Jul 2013
TL;DR: An explicit entanglement distillation scheme is constructed which achieves the coherent information when used to send quantum information over a noisy quantum channel and how the scheme can be used for secret key distillation and private channel coding is discussed.
Abstract: We construct an explicit entanglement distillation scheme which achieves the coherent information when used to send quantum information over a noisy quantum channel. For Pauli and erasure channels we present efficient encoding and decoding algorithms based on polar codes. Unlike previous constructions, this scheme does not require the sender and receiver to share noiseless entanglement before the protocol begins. It is possible, but still unproven, that the scheme even achieves a rate beyond the coherent information, due to degeneracies of certain error correcting codes. Finally we discuss how the scheme can be used for secret key distillation and private channel coding.
TL;DR: In this paper, a system of two two-level atoms interacting with a single-mode quantized electromagnetic field in a lossless resonant cavity via a multi-photon transition is considered.
Abstract: In this article, a system of two two-level atoms interacting with a single-mode quantized electromagnetic field in a lossless resonant cavity via a multi-photon transition is considered. The quantum Fisher information, negativity, classical Fisher information, and reduced von Neumann entropy for the two atoms are investigated. We found that the number of photon transitions plays an important role in the dynamics of different information quantifiers in the cases of two symmetric and two asymmetric atoms. Our results show that there is a close relationship between the different quantifiers. Also, the quantum and classical Fisher information can be useful for studying the properties of quantum states which are important in quantum optics and information.
TL;DR: In this article, the use of probabilistic noiseless amplification in entangled coherent state-based schemes for the test of quantum nonlocality has been shown to provide substantial advantages.
Abstract: We show that the use of probabilistic noiseless amplification in entangled coherent state-based schemes for the test of quantum nonlocality provides substantial advantages. The threshold amplitude to falsify a Bell-CHSH nonlocality test, in fact, is significantly reduced when amplification is embedded into the test itself. Such a beneficial effect holds also in the presence of detection inefficiency. Our study helps in affirming noiseless amplification as a valuable tool for coherent information processing and the generation of strongly nonclassical states of bosonic systems.
TL;DR: In this paper, a connection between mutual information and the conventional order parameter in condensed matter physics is established, and it is shown that non-vanishing mutual information between two subsystems separated by a long distance means the existence of long-range orders in the system.
TL;DR: It is demonstrated that fundamental aspects of quantum theory can be applied to work in information studies (IS), and the non‐ or extra‐mathematical components of quantum Theory offer ontological and epistemic modes of thought which apply to information.
Abstract: Purpose – This paper aims to demonstrate that fundamental aspects of quantum theory can be applied to work in information studies (IS).Design/methodology/approach – The field of information studies is so broad and extensive that it requires similar breadth of epistemic and methodological features in order to fulfill its inherent promise as a human enterprise. Quantum theory holds promise as a way to shape questions and inquiry in information studies (IS).Findings – The revolutionary elements of quantum theory, such as entanglement, nonlocality, etc. can be applied to information, especially language‐based communication.Research limitations/implications – Perhaps most especially, the non‐ or extra‐mathematical components of quantum theory offer ontological and epistemic modes of thought which apply to information. Those modes of thought are ripe with conceptual promise for examination of, for example, information as objective entity and as complex material substance. This paper explores some of the potenti...
TL;DR: In this article, an explicit quantum coding scheme which achieves a communication rate not less than the coherent information when used to transmit quantum information over a noisy quantum channel is presented. But it does not require the sender and receiver to share any entanglement before the protocol begins.
Abstract: We construct an explicit quantum coding scheme which achieves a communication rate not less than the coherent information when used to transmit quantum information over a noisy quantum channel. For Pauli and erasure channels we also present efficient encoding and decoding algorithms for this communication scheme based on polar codes (essentially linear in the blocklength), but which do not require the sender and receiver to share any entanglement before the protocol begins. Due to the existence of degeneracies in the involved error-correcting codes it is indeed possible that the rate of the scheme exceeds the coherent information. We provide a simple criterion which indicates such performance. Finally we discuss how the scheme can be used for secret key distillation as well as private channel coding.