Benjamin Schumacher, Michael D. Westmoreland
Alice and Bob share a correlated composite quantum system AB. If AB is used as the key for a one-time pad cryptographic system, we show that the maximum amount of information that Alice can send securely to Bob is the quantum mutual information of AB.
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Anyonic states, which are topologically robust originated from their peculiar structure of Hilbert space, have important applications in quantum computing and quantum communication. When an anyonic state is used as an information carrier of the deterministic quantum one-time pad (DQOTP), we find that the Fibonacci particle-antiparticle pair produced from vacuum can be used to asymptotically send $2\log_2 d_τ$ bits of classical information ($d_τ$ is the quantum dimension of a Fibonacci anyon $τ$), which equals to the anyonic mutual information of the pair. Furthermore, by studying the DQOTP via…
We postulate the existence of a universal uncertainty relation between the quantum and classical mutual informations between pairs of quantum systems. Specifically, we propose that the sum of the classical mutual information, determined by two mutually unbiased pairs of observables, never exceeds the quantum mutual information. We call this the complementary-quantum correlation (CQC) relation and prove its validity for pure states, for states with one maximally mixed subsystem, and for all states when one measurement is minimally disturbing. We provide results of a Monte Carlo simulation sugge…
One-time pad encrypted files can be sent through Internet channels using current Internet protocols. However, the need for renewing shared secret keys make this method unpractical. This work shows how users can use a fast physical random generator based on fluctuations of a light field and the Internet channel to directly boost key renewals. The transmitted signals are deterministic but carries imprinted noise that cannot be eliminated by the attacker. Thus, a one-time pad for Internet can be made practical. Security is achieved without third parties and not relying on the difficulty of factor…
We introduce and analyze an information theoretical task that we call the quantum multiple-access one-time pad. Here, a number of senders initially share a correlated quantum state with a receiver and an eavesdropper. Each sender performs a local operation to encode a classical message and sends their system to the receiver, who subsequently performs a measurement to decode the messages. The receiver will be able to decode the messages almost perfectly, while the eavesdropper must not be able to extract information about the messages even if they have access to the quantum systems transmitted.…
The previous work showed that the Y00 protocol could stay secure with the eavesdropper's guessing probability on the secret keys being strictly less than one under an unlimitedly long known-plaintext attack with quantum memory. However, an assumption that at least a fast correlation attack is completely disabled by irregular mapping. The present study shows that the Y00 protocol can be information-theoretic secure under any quantum-computational crypto-analyses if the Y00 system is well designed. The Y00 protocol directly encrypts messages with short secret keys expanded into pseudo-random run…
When elementary quantum systems, such as polarized photons, are used to transmit digital information, the uncertainty principle gives rise to novel cryptographic phenomena unachievable with traditional transmission media, e.g. a communications channel on which it is impossible in principle to eavesdrop without a high probability of being detected. With such a channel, a one-time pad can safely be reused many times as long as no eavesdrop is detected, and, planning ahead, part of the capacity of these uncompromised transmissions can be used to send fresh random bits with which to replace the on…
Suppose that Alice and Bob are located in distant laboratories, which are connected by an ideal quantum channel. Suppose further that they share many copies of a quantum state $ρ_{ABE}$, such that Alice possesses the $A$ systems and Bob the $BE$ systems. In our model, there is an identifiable part of Bob's laboratory that is insecure: a third party named Eve has infiltrated Bob's laboratory and gained control of the $E$ systems. Alice, knowing this, would like use their shared state and the ideal quantum channel to communicate a message in such a way that Bob, who has access to the whole of hi…
Quantum information is a valuable resource which can be encrypted in order to protect it. We consider the size of the one-time pad that is needed to protect quantum information in a number of cases. The situation is dramatically different from the classical case: we prove that one can recycle the one-time pad without compromising security. The protocol for recycling relies on detecting whether eavesdropping has occurred, and further relies on the fact that information contained in the encrypted quantum state cannot be fully accessed. We prove the security of recycling rates when authentication…
Entropic inequalities related to the quantum mutual information for bipartite system and tomographic mutual information is studied for Werner state of two qubits. Quantum correlations corresponding to entanglement properties of the qubits in Werner state are discussed.
For any $n$-partite state $ρ_{A_{1}A_{2}\cdot\cdot\cdot A_{n}}$, we define its quantum mutual information matrix as an $n$ by $n$ matrix whose $(i,j)$-entry is given by quantum mutual information $I(ρ_{A_{i}A_{j}})$. Although each entry of quantum mutual information matrix, like its classical counterpart, is also used to measure bipartite correlations, the similarity ends here: quantum mutual information matrices are not always positive semidefinite even for collections of up to 3-partite states. In this work, we obtain necessary and sufficient conditions for the positive semidefinite quantum …
In quantum information theory it is generally accepted that quantum mutual information is an information-theoretic measure of total correlations of a bipartite quantum state. We argue that there exist quantum states for which quantum mutual information cannot be considered as a measure of total correlations. Moreover, for these states we propose a different way of quantifying total correlations.
In previous papers, we expressed the Entanglement of Formation in terms of Conditional Mutual Information (CMI). In this brief paper, we express the Entanglement of Distillation in terms of CMI.
In this paper, we study measures of quantum non-Markovianity based on the conditional mutual information. We obtain such measures by considering multiple parts of the total environment such that the conditional mutual information can be defined in this multipartite setup. The benefit of this approach is that the conditional mutual information is closely related to recovery maps and Markov chains; we also point out its relations with the change of distinguishability. We study along the way the properties of leaked information which is the conditional mutual information that can be back flowed, …
After Shannon, entropy becomes a fundamental quantity to describe not only uncertainity or chaos of a system but also information carried by the system. Shannon's important discovery is to give a mathematical expression of the mutual entropy (information), information transmitted from an input system to an output system, by which communication processes could be analyzed on the stage of mathematical science. In this paper, first we review the quantum mutual entropy and discuss its uses in quantum information theory, and secondly we show how the classical mutual entropy can be used to analyze g…
Quantum Mutual Information in Time
本文利用赝密度矩阵形式将量子互信息从类空系统扩展到时间域，证明其可作为类时关联的自然度量，并给出顺序测量下可提取经典信息的Holevo界。
We study the classical, classical-quantum, and quantum parts of conditional mutual information in the ``system-environment-ancilla'' setting of open quantum systems. We perform the separation of conditional mutual information by generalizing the classification of correlations of quantum states. The condition for identifying the classical part of conditional mutual information is given by adapting the no-local-broadcasting theorem to this setting, while the condition for classical-quantum part of conditional mutual information is obtained by considering the multipartite quantum discord and the …
Family of Quantum Mutual Information in Multiparty Quantum Systems
本文针对多方量子系统信息表征的复杂性问题，提出广义条件互信息概念及多方量子互信息族，通过阐释其性质与关联，为理解各类关联及推动量子信息理论基础研究提供新见解。
We study the relation between the quantum conditional mutual information and the quantum $α$-Rényi divergences. Considering the totally antisymmetric state we show that it is not possible to attain a proper generalization of the quantum conditional mutual information by optimizing the distance in terms of quantum $α$-Rényi divergences over the set of all Markov states. The failure of the approach considered arises from the observation that a small quantum conditional mutual information does not imply that the state is close to a quantum Markov state.
Mutual information and swap operation in the two-qubit Heisenberg model with the Dzyaloshinskii-Moriya (DM) anisotropic antisymmetric interaction are investigated. It is found that the mutual information I of such a quantum channel is sensitive to the initial conditions and declines with the increase of the temperature. The DM interaction can lead to a higher mutual information, especially for the ferromagnetic case. The entanglement quality of input states cannot enhance the mutual information of the quantum channel. When the DM interaction is large, the mutual information will be the maximum…
The importance of using the averaged mutual information when quantifying quantum objectivity
本文强调在量化量子客观性时，必须使用平均互信息而非非平均量子互信息，以避免在信息非均匀编码时产生误导，确保结果具有清晰的操作解释。
Using the relative entropy of total correlation, we derive an expression relating the mutual information of $n$-partite pure states to the sum of the mutual informations and entropies of its marginals and analyze some of its implications. Besides, by utilizing the extended strong subadditivity of von Neumann entropy, we obtain generalized monogamy relations for the total correlation in three-partite mixed states. These inequalities lead to a tight lower bound for this correlation in terms of the sum of the bipartite mutual informations. We use this bound to propose a measure for residual three…
Mutual information harvesting for circularly accelerated detectors
研究两个圆周加速探测器在反射边界附近与无质量标量场相互作用时的互信息采集行为，分析不同加速和半径下互信息的震荡特性及最大值变化。
One-time-pad (OTP) encryption simply cannot be cracked, even by a quantum computer. The need of sharing in a secure way supplies of symmetric random keys turned the method almost obsolete as a standing-alone method for fast and large volume telecommunication. Basically, this secure sharing of keys and their renewal, once exhausted, had to be done through couriers, in a slow and costly process. This paper presents a solution for this problem providing a fast and unlimited renewal of secure keys: An untappable key distribution system is presented and detailed. This fast key distribution system u…
Cryptographic random number generation is critical for any quantum safe encryption. Based on the natural uncertainty of some quantum processes, variety of quantum random number generators or QRNGs have been created with physical quantum processes. They generally generate random numbers with good unpredictable randomness. Of course, physical QRNGs are costic and require physical integrations with computing systems. This paper proposes a pseudo quantum random number generator with a quantum algorithm called quantum permutation pad or QPP, leveraging the high entropy of quantum permutation space …
We investigate a two-qubit system to understand the relationship between concurrence and mutual information, where the former determines the amount of quantum entanglement, whereas the latter is its classical residue after performing local projective measurement. For a given ensemble of random pure states, in which the values of concurrence are uniformly distributed, we calculate the joint probability of concurrence and mutual information. Although zero mutual information is the most probable in the uniform ensemble, we find positive correlation between the classical information and concurrenc…
Entanglement entropy in free scalar field theory at its ground state is dominated by an area law term. However, when mixed states are considered this property ceases to exist. We show that in such cases the mutual information obeys an "area law". The proportionality constant connecting the area to the mutual information has an interesting dependence on the temperature. At infinite temperature it tends to a finite value which coincides with the classical calculation.
The total many-body correlations present in finite temperature classical spin systems are studied using the concept of mutual information. As opposed to zero-temperature quantum phase transitions, the total correlations are not maximal at the phase transition, but reach a maximum in the high temperature paramagnetic phase. The Shannon and Renyi mutual information in both Ising and Potts models in 2 dimensions are calculated numerically by combining matrix product states algorithms and Monte Carlo sampling techniques.
In this paper, we try to establish a connection between a quantum information concept, i.e. the mutual information, and the conventional order parameter in condensed matter physics. We show that a non-vanishing mutual information at a long distance means the existence of long-range order. By analyzing the entanglement spectra of the reduced density matrix that are used to calculate the mutual information, we show how to find the local order operator used to identify various phases with long-rang order.
Rényi and Shannon mutual information in critical and decohered critical system
本文引入Rényi广义互信息研究临界TFIM系统，证明其在环境退相干下仍保持Ising CFT的标度律和中心荷，且Rényi-2中心荷对局部退相干具有强鲁棒性。
The work is devoted to study of quantum mutual information and coherent information -- the two important characteristics of quantum communication channel. Appropriate definitions of these quantities in the infinite-dimensional case are given and their properties are studied in detail. Basic identities relating quantum mutual information and coherent information of a pair of complementary channels are proved. An unexpected continuity property of quantum mutual information and coherent information following from the above identities is observed. An upper bound for the coherent information is obt…
Universal Decay of Mutual Information and Conditional Mutual Information in Gapped Pure- and Mixed-State Quantum Matter
研究证明有隙纯态和混合态量子物质中互信息和条件互信息呈现超多项式衰减，且在多种相中验证，同时强化了混合态相的概念。
We prove decomposition rules for quantum Rényi mutual information, generalising the relation $I(A:B) = H(A) - H(A|B)$ to inequalities between Rényi mutual information and Rényi entropy of different orders. The proof uses Beigi's generalisation of Reisz-Thorin interpolation to operator norms, and a variation of the argument employed by Dupuis which was used to show chain rules for conditional Rényi entropies. The resulting decomposition rule is then applied to establish an information exclusion relation for Rényi mutual information, generalising the original relation by Hall.
We investigate the correlation harvesting protocol for mutual information between two Unruh-DeWitt detectors in a static BTZ black hole spacetime. Here, the effects coming from communication and change in proper separation of the detectors are set to be negligible so that only a black hole affects the extracted mutual information. We find that, unlike the entanglement harvesting scenario, harvested mutual information is zero only when a detector reaches an event horizon, and that although the Hawking effect and gravitational redshift both affect the extraction of mutual information, it is extr…
I study the mutual information between spatial subsystems in a variety of scale invariant quantum field theories. While it is derived from the bare entanglement entropy, the mutual information offers a more refined probe of the entanglement structure of quantum field theories because it remains finite in the continuum limit. I argue that the mutual information has certain universal singularities that are a manifestation of the idea of "entanglement per scale". Moreover, I propose a method, based on an ansatz for higher dimensional twist operators, to compute the entanglement entropy, Renyi ent…
We study formal properties of smooth max-information, a generalization of von Neumann mutual information derived from the max-relative entropy. Recent work suggests that it is a useful quantity in one-shot channel coding, quantum rate distortion theory and the physics of quantum many-body systems. Max-information can be defined in multiple ways. We demonstrate that different smoothed definitions are essentially equivalent (up to logarithmic terms in the smoothing parameters). These equivalence relations allow us to derive new chain rules for the max-information in terms of min- and max-entropi…
We study corner contributions to holographic mutual information for entangling regions composed of a set of disjoint sectors of a single infinite circle in three-dimensional conformal field theories. In spite of the UV divergence of holographic mutual information, it exhibits a first order phase transition. We show that tripartite information is also divergent for disjoint sectors, which is in contrast with the well-known feature of tripartite information being finite even when entangling regions share boundaries. We also verify the locality of corner effects by studying mutual information bet…
A simpler approach to the characterization of vanishing conditional mutual information is presented. Some remarks are given as well. More specifically, relating the conditional mutual information to a commutator is a very promising approach towards the approximate version of SSA. That is, it is conjectured that small conditional mutual information implies small perturbation of quantum Markov chain.
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 finite temperature relativistic conformal field 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 find universal qualitative features for the above class of theories which has holographic dual descri…
Exact characterizations for quantum conditional mutual information and some other entropies
通过将熵的定义转化为显式构造项的求和，给出了量子条件互信息及其他熵的精确等式刻画，这些等式在互信息大小下均成立且不可改进。
We study the generic scaling properties of the mutual information between two disjoint intervals, in a class of one-dimensional quantum critical systems described by the c=1 bosonic field theory. A numerical analysis of a spin-chain model reveals that the mutual information is scale-invariant and depends directly on the boson radius. We interpret the results in terms of correlation functions of branch-point twist fields. The present study provides a new way to determine the boson radius, and furthermore demonstrates the power of the mutual information to extract more refined information of con…
Two quantum measurements sequentially acting one after the other, if they are mutually unbiased, will lead to a complete removal of information encoded in the input quantum state. We find that if the order of the two sequential measurements can be superposed, with a quantum switch, then the information encoded in the input can still be retained in the output state.
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