Shannon entropy and Fisher information functionals are known to quantify certain information-theoretic properties of continuous probability distributions of various origins. We carry out a systematic study of these functionals, while assuming that the pertinent probability density has a quantum mechanical appearance $ρ\doteq |ψ|^2$, with $ψ\in L^2(R)$. Their behavior in time, due to the quantum Schrödinger picture evolution-induced dynamics of $ρ(x,t)$ is investigated as well, with an emphasis on thermodynamical features of quantum motion.
We prove the difference between the minimal entanglement costs in quantum state merging under one-way and two-way communication in a one-shot scenario, whereas they have been known to coincide asymptotically. While the minimal entanglement cost in state merging under one-way communication is conventionally interpreted to characterize partial quantum information conditioned by quantum side information, we introduce a notion of spread quantum information evaluated by the corresponding cost under two-way communication. Spread quantum information quantitatively characterizes how nonlocally one-sho…
This is primarily a pedagogical paper. The paper re-visits some well-known quantum information theory inequalities. It does this from a quantum Bayesian networks perspective. The paper illustrates some of the benefits of using quantum Bayesian networks to discuss quantum SIT (Shannon Information Theory).
Quantum information is a useful resource to set up information processing. Despite physical components are normally two-level systems, their combination with entangling interactions becomes in a complex dynamics. Studied for piecewise field pulses, this work analyzes the modeling for quantum information operations with fields affordable technologically towards a universal quantum computation model.
Quantum Fisher information (QFI) and skew information (SI) plays a key role in the quantum resource theory. Understanding these measures in the physical system has practical significance in the state parameter estimation and quantum metrology. In this article, we consider a pair ofspin-1/2 particles coupled with dipolar and Dzyaloshinsky-Moriya (DM) interactions, serving as the physical carrier of quantum information. We examine the bipartite nonlocal correlations of pair of spin-1/2 particle system for the thermal equilibrium states, characterized by local quantum uncertainty (LQU) and local …
Quantum non Markovianity and quantum Darwinism are two phenomena linked by a common theme: the flux of quantum information between a quantum system and the quantum environment it interacts with. In this work, making use of a quantum collision model, a formalism initiated by Sudarshan and his school, we will analyse the efficiency with which the information about a single qubit gained by a quantum harmonic oscillator, acting as a meter, is transferred to a bosonic environment. We will show how, in some regimes, such quantum information flux is inefficient, leading to the simultaneous emergence …
State disturbance by a quantum measurement is at the core of foundational quantum physics and constitutes a fundamental basis of secure quantum information processing. While quantifying an information-disturbance relation has been a long-standing problem, recently verified reversibility of a quantum measurement requires to refine such a conventional information trade-off toward a complete picture of information conservation in quantum measurement. Here we experimentally demonstrate complete trade-off relations among all information contents, i.e., information gain, disturbance and reversibilit…
We first consider quantum communication protocols between a sender Alice and a receiver Bob, which transfer Alice's quantum information to Bob by means of non-local resources, such as classical communication, quantum communication, and entanglement. In these protocols, we assume that Alice and Bob may have quantum side information, not transferred. In this work, these protocols are called the state transfer with quantum side information. We determine the optimal costs for non-local resources in the protocols, and study what the effects of the use of quantum side information are. Our results ca…
A measurement is deemed successful, if one can maximize the information gain by the measurement apparatus. Here, we ask if quantum coherence of the system imposes a limitation on the information gain during quantum measurement. First, we argue that the information gain in a quantum measurement is nothing but the coherent information or the distinct quantum information that one can send from the system to apparatus. We prove that the maximum information gain from a pure state, using a mixed apparatus is upper bounded by the initial coherence of the system. Further, we illustrate the measurement…
We design a quantum probing protocol using Quantum Walks to investigate the Quantum Information spreading pattern. We employ Quantum Fisher Information, as a figure of merit, to quantify extractable information about an unknown parameter encoded within the Quantum Walk evolution. Although the approach is universal, we focus on the coherent static and dynamic disorder to investigate anomalous and classical transport as well as Anderson localization. Our results show that a Quantum Walk can be considered as a readout device of information about defects and perturbations occurring in complex netw…
We present a scheme of quantum information transmission, which transmits the quantum information contained in a single qubit via the quantum correlation shared by two parties (a two-qubit channel), whose quantum discord is non-zero. We demonstrate that the quantum correlation, which may have no entanglement, is sufficient to transmit the information of a quantum state. When the correlation matrix of the two-qubit channel is of full rank (rank three), the information of the qubit in either a mixed state or a pure state can be transmitted. The quantum discord of a channel with rank larger than o…
We show that contrary to the claim in Sci. Rep. 7, 15492 (2017), the quantum Fisher information itself is not a valid coherence measure based on the resource theory of coherence because it can increase via an incoherent operation.
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 …
Quantum measurement is a basic tool to manifest intrinsic quantum effects from fundamental tests to quantum information applications. While a measurement is typically performed to gain information on a quantum state, its role in quantum technology is indeed manifold. For instance, quantum measurement is a crucial process element in measurement-based quantum computation. It is also used to detect and correct errors thereby protecting quantum information in error-correcting frameworks. It is therefore important to fully characterize the roles of quantum measurement encompassing information gain,…
Masking quantum information, which is impossible without randomness as a resource, is a task that encodes quantum information into bipartite quantum state while forbidding local parties from accessing to that information. In this work, we disprove the geometric conjecture about unitarily maskable states [K. Modi et al., Phys. Rev. Lett. 120, 230501 (2018)], and make an algebraic analysis of quantum masking. First, we show a general result on quantum channel mixing that a subchannel's mixing probability should be suppressed if its classical capacity is larger than the mixed channel's capacity. …
We study the existence of the maximal quantum Fisher information matrix in multi-parameter quantum estimation, which bounds the ultimate precision limit. We show that when the maximal quantum Fisher information matrix exists, it can be directly obtained from the underlying dynamics. Examples are then provided to demonstrate the usefulness of the maximal quantum Fisher information matrix by deriving various tradeoff relations in multi-parameter quantum estimation and obtaining the bounds for the scalings of the precision limit.
I draw attention to previous work that shows that the observables corresponding to relativistic quantum field modes commonly employed in papers on "relativistic quantum information" cannot be measured by ideal measurements.
Classical information encoded in composite quantum states can be completely hidden from the reduced subsystems and may be found only in the correlations. Can the same be true for quantum information? If quantum information is hidden from subsystems and spread over quantum correlation, we call it as masking of quantum information. We show that while this may still be true for some restricted sets of non-orthogonal quantum states, it is not possible for arbitrary quantum states. This result suggests that quantum qubit commitment -- a stronger version of the quantum bit commitment is not possible…
The accessible information and the informational power quantify the amount of information extractable from a quantum ensemble and by a quantum measurement, respectively. So-called spherical quantum 2-designs constitute a class of ensembles and measurements relevant in testing entropic uncertainty relations, quantum cryptography, and quantum tomography. We provide lower bounds on the entropy of 2-design ensembles and measurements, from which upper bounds on their accessible information and informational power follow, as a function of the dimension only. We show that the statistics generated by …
In this work we will study the Local quantum Fisher information and the local quantum uncertainty in two-qubit Heisenberg XYZ spin chain model with Dzyaloshinskii Moriya (DM) interaction in z direction. Here we show that the DM interaction and spin interactions along the x, y, and z axis can increase and maintain local quantum Fisher information and local quantum uncertainty. It is also shown that because of thermal fluctuations local quantum Fisher information and local quantum uncertainty are decreased by increasing temperature. They are equal to one at very low temperature and starts to dec…
In this paper we investigate the dynamics of a spin chain whose two end spins interact with two independent non-Markovian baths by using the non-Markovian quantum state diffusion (QSD) equation approach. Specifically two issues about quantum information scrambling in open quantum system are addressed. The first issue is that tripartite mutual information (TMI) can quantify information scrambling properly via its negative value in closed system, whether it is still suitable to indicate quantum scrambling in open quantum system. However we find that negative TMI is not an suitable quantifier of …
Quantum error correction (QEC) is one of the central concepts in quantum information science and also has wide applications in fundamental physics. The capacity theorems provide solid foundations of QEC. We here provide a general and highly applicable form of capacity theorem for both classical and quantum information, i.e., hybrid information, with assistance of a limited resource of entanglement in one-shot scenario, which covers broader situations than the existing ones. Harnessing the wide applicability of the theorem, we show that a demonstration of QEC by short random quantum circuits is…
In this paper, a kind of quantum dialogue (QD) protocols without information leakage assisted by quantum operation is proposed. The participant in charge of preparation can automatically know the collapsed states after quantum operation performed on the prepared quantum states. The other participant is able to know the collapsed states derived from the prepared quantum states through quantum measurement. The information leakage problem is avoided by means of imposing auxiliary quantum operation on the prepared quantum states.
A deeply rooted view in classical and quantum information is that "information is physical", i.e., to store and process information, we need a physical body. Here we ask whether quantum information can remain without a physical body. We answer this question in the affirmative, i.e., we argue that quantum information can exist without a physical body in volatile form. We introduce the notion of the volatility of quantum information and show that indeed the conditions for it are naturally satisfied in the quantum teleportation protocol. We argue that even if special relativity principles are not…
The advantages of quantum information processing are in many cases obtained as consequences of quantum interactions, especially for computational tasks where two-qubit interactions are essential. In this work, we establish the framework of analyzing and quantifying loss or gain of information on a quantum system when the system interacts with its environment. We show that the information flow, the theoretical method of characterizing (non-)Markovianity of quantum dynamics, corresponds to the rate of the minimum uncertainty about the system given quantum side information. Thereafter, we analyze…
By studying quantum information masking in non-Hermitian quantum systems, we show that mutually orthogonal quantum states can be deterministically masked, while an arbitrary set of quantum states cannot be masked in non-Hermitian quantum systems. We further demonstrate that a set of linearly independent states which are mutually $η$-orthogonal can be deterministically masked by a pseudo-unitary operator. Moreover, we study robustness of quantum information masking against noisy environments. The robustness of deterministic and probabilistic quantum information masking under different quantum n…
