Negative Conditional Entropy Research Articles

Quantum channels that destroy negative conditional entropy

Quantum channels that destroy negative conditional entropy

Transferability-Guided Cross-Domain Cross-Task Transfer Learning.

We propose two novel transferability metrics fast optimal transport-based conditional entropy (F-OTCE) and joint correspondence OTCE (JC-OTCE) to evaluate how much the source model (task) can benefit the learning of the target task and to learn more generalizable representations for cross-domain cross-task transfer learning. Unlike the original OTCE metric that requires evaluating the empirical transferability on auxiliary tasks, our metrics are auxiliary-free such that they can be computed much more efficiently. Specifically, F-OTCE estimates transferability by first solving an optimal transport (OT) problem between source and target distributions and then uses the optimal coupling to compute the negative conditional entropy (NCE) between the source and target labels. It can also serve as an objective function to enhance downstream transfer learning tasks including model finetuning and domain generalization (DG). Meanwhile, JC-OTCE improves the transferability accuracy of F-OTCE by including label distances in the OT problem, though it incurs additional computation costs. Extensive experiments demonstrate that F-OTCE and JC-OTCE outperform state-of-the-art auxiliary-free metrics by 21.1% and 25.8% , respectively, in correlation coefficient with the ground-truth transfer accuracy. By eliminating the training cost of auxiliary tasks, the two metrics reduce the total computation time of the previous method from 43 min to 9.32 and 10.78 s, respectively, for a pair of tasks. When applied in the model finetuning and DG tasks, F-OTCE shows significant improvements in the transfer accuracy in few-shot classification experiments, with up to 4.41% and 2.34% accuracy gains, respectively.

A-unital Operations and Quantum Conditional Entropy

Negative quantum conditional entropy states are key ingredients for information theoretic tasks such as superdense coding, state merging and one-way entanglement distillation. In this work, we ask: how does one detect if a channel is useful in preparing negative conditional entropy states? We answer this question by introducing the class of A-unital channels, which we show are the largest class of conditional entropy non-decreasing channels. We also prove that A-unital channels are precisely the completely free operations for the class of states with non-negative conditional entropy. Furthermore, we study the relationship between A-unital channels and other classes of channels pertinent to the resource theory of entanglement. We then prove similar results for ACVENN: a previously defined, relevant class of states and also relate the maximum and minimum conditional entropy of a state with its von Neumann entropy. The definition of A-unital channels naturally lends itself to a procedure for determining membership of channels in this class. Thus, our work is valuable for the detection of resourceful channels in the context of conditional entropy.

Witnessing negative conditional entropy

Quantum states that possess negative conditional von Neumann entropy provide quantum advantage in several information-theoretic protocols including superdense coding, state merging, distributed private randomness distillation, and one-way entanglement distillation. While entanglement is an important resource, only a subset of entangled states have negative conditional von Neumann entropy. In this work, we characterize the class of density matrices having non-negative conditional von Neumann entropy as convex and compact. This allows us to prove the existence of a Hermitian operator (a witness) for the detection of states having negative conditional entropy for bipartite systems in arbitrary dimensions. We show two constructions of such witnesses. For one of the constructions, the expectation value of the witness in a state is an upper bound to the conditional entropy of the state. We pose the problem of obtaining a tight upper bound to the set of conditional entropies of states in which an operator gives the same expectation value. We solve this convex optimization problem numerically for a two qubit case and find that this enhances the usefulness of our witnesses. We also find that for a particular witness, the estimated tight upper bound matches the value of conditional entropy for Werner states. We explicate the utility of our work in the detection of useful states in several protocols.

Experimental Implications of Negative Quantum Conditional Entropy—H2 Mobility in Nanoporous Materials

During the last few decades, considerable advances in quantum information theory have shown deep existing connections between quantum correlation effects (like entanglement and quantum discord) and thermodynamics. Here the concept of conditional entropy plays a considerable role. In contrast to the classical case, quantum conditional entropy can take negative values. This counter-intuitive feature, already well understood in the context of information theory, was recently shown theoretically to also have a physical meaning in quantum thermodynamics [del Rio et al. Nature 2011, 474, 61]. Extending this existing work, here we provide evidence of the significance of negative conditional entropy in a concrete experimental context: Incoherent Neutron Scattering (INS) from protons of H2 in nano-scale environments; e.g., in INS from H2 in C-nanotubes, the data of the H2 translational motion along the nanotube axis seems to show that the neutron apparently scatters from a fictitious particle with mass of 0.64 atomic mass units (a.m.u.)—instead of the value of 2 a.m.u. as conventionally expected. An independent second experiment confirms this finding. However, taking into account the possible negativity of conditional entropy, we explain that this effect has a natural interpretation in terms of quantum thermodynamics. Moreover, it is intrinsically related to the number of qubits capturing the interaction of the two quantum systems H2 and C-nanotube. The considered effect may have technological applications (e.g., in H-storage materials and fuel cells).

Experimental Implications of Negative Quantum Conditional Entropy—H2 Mobility in Nanoporous Materials

During the last few decades, considerable advances in quantum information theory have shown deep existing connections between quantum correlation effects (like entanglement and quantum discord) and thermodynamics. Here the concept of conditional entropy plays a considerable role. In contrast to the classical case, quantum conditional entropy can take negative values. This counter-intuitive feature, already well understood in the context of information theory, was recently shown theoretically to also have a physical meaning in quantum thermodynamics [del Rio et al. Nature 2011, 474, 61]. Extending this existing work, here we provide evidence of the significance of negative conditional entropy in a concrete experimental context: Incoherent Neutron Scattering (INS) from protons of H2 in nano-scale environments; e.g., in INS from H2 in C-nanotubes, the data of the H2 translational motion along the nanotube axis seems to show that the neutron apparently scatters from a fictitious particle with mass of 0.64 atomic mass units (a.m.u.)—instead of the value of 2 a.m.u. as conventionally expected. An independent second experiment confirms this finding. However, taking into account the possible negativity of conditional entropy, we explain that this effect has a natural interpretation in terms of quantum thermodynamics. Moreover, it is intrinsically related to the number of qubits capturing the interaction of the two quantum systems H2 and C-nanotube. The considered effect may have technological applications (e.g., in H-storage materials and fuel cells).

Quantumness of States and Unitary Operations

This paper investigates various properties that may by possessed by quantum states, which are believed to be specifically “quantum” (entanglement, nonlocality, steerability, negative conditional entropy, non-zero quantum discord, non-zero quantum super discord and contextuality) and their opposites. It also considers their “absolute” counterparts in the following sense: a given state has a given property absolutely if after an arbitrary unitary transformation it still possesses it. The known relations between the listed properties and between their absolute counterparts are summarized. It is proven that the only two-qubit state that has zero quantum discord absolutely is the maximally mixed state. Finally, related conceptual issues concerning the terms “classical” and “quantum” are discussed.

Non-negativity of conditional von Neumann entropy and global unitary operations

Conditional von Neumann entropy is an intriguing concept in quantum information theory. In the present work, we examine the effect of global unitary operations on the conditional entropy of the system. We start with the set containing states with non-negative conditional entropy and find that some states preserve the non-negativity under unitary operations on the composite system. We call this class of states as Absolute Conditional von Neumann entropy Non Negative class (\textbf{ACVENN}). We are able to characterize such states for $2\otimes 2$ dimensional systems. On a different perspective the characterization accentuates the detection of states whose conditional entropy becomes negative after the global unitary action. Interestingly, we are able to show that this \textbf{ACVENN} class of states forms a set which is convex and compact. This feature enables for the existence of hermitian witness operators the measurement of which could distinguish unknown states which will have negative conditional entropy after the global unitary operation. This has immediate application in super dense coding and state merging as negativity of conditional entropy plays a key role in both these information processing tasks. Some illustrations are also provided to probe the connection of such states with Absolute separable (AS) states and Absolute local (AL) states.

Geometry of two-qubit states with negative conditional entropy

We review the geometric features of negative conditional entropy and the properties of the conditional amplitude operator proposed by Cerf and Adami for two qubit states in comparison with entanglement and nonlocality of the states. We identify the region of negative conditional entropy in the tetrahedron of locally maximally mixed two-qubit states. Within this set of states, negative conditional entropy implies nonlocality and entanglement, but not vice versa, and we show that the Cerf–Adami conditional amplitude operator provides an entanglement witness equivalent to the Peres–Horodecki criterion. Outside of the tetrahedron this equivalence is generally not true.

Nonzero Classical Discord.

Quantum discord is the quantitative difference between two alternative expressions for bipartite mutual information, given respectively in terms of two distinct definitions for the conditional entropy. By constructing a stochastic model of shared states, classical discord can be similarly defined, quantifying the presence of some stochasticity in the measurement process. Therefore, discord can generally be understood as a quantification of the system's state disturbance due to local measurements, be it quantum or classical. We establish an operational meaning of classical discord in the context of state merging with noisy measurement and thereby show the quantum-classical separation in terms of a negative conditional entropy.

Negative conditional entropy of postselected states

We define a quantum entropy conditioned on post-selection which has the von Neumann entropy of pure states as a special case. This conditional entropy can take negative values which is consistent with part of a quantum system containing less information than the whole which can be in a pure state. The definition is based on generalised density operators for postselected ensembles. The corresponding density operators are consistent with the quantum generalisation of classical conditional probabilities following Dirac s formalism of quasiprobability distributions.

QUANTUM 1/f EFFECT BASED ON QUANTUM INFORMATION THEORY

The Quantum Information Theory Approach (QIT) explains for the first time the apparent lack of unitarity caused by the entropy increase in the Quantum 1/f Effect (Q1/fE). This allows for a deeper understanding of the quantum 1/f effect, showing no resultant entropy increase and therefore no violation of unitarity in the quantum-mechanical dynamical evolution. This new interpretation involves the von Neumann Quantum Entropy, including the negative conditional entropy concept for quantum entangled states introduced by QIT. The Q1/fE was applied to many high-tech systems, in particular to ultra small electronic devices in nanotechnology. The present paper explains how the additional entropy implied by the observed 1/f noise arises in spite of the entropy-conserving evolution of the system. On this basis, a derivation of the conventional and coherent quantum 1/f effect is given. The latter is derived from a non-relativistic form of the branch-point propagator derived by excluding the long range Coulomb interaction from the interaction hamiltonian. The paper concludes with examples of practical applications in various devices and systems, allowing for a new characterization of high technology.

Conditional entropies and their relation to entanglement criteria

We discuss conditional Rényi and Tsallis entropies for bipartite quantum systems of finite dimension. We investigate the relation between the positivity of conditional entropies and entanglement properties. It is in particular shown that any state having a negative conditional entropy with respect to any value of the entropic parameter is distillable since it violates the reduction criterion. Moreover, we show that the entanglement of Werner states in odd dimensions can neither be detected by entropic criteria nor by any other spectral criterion.