Erasure of information stored in a quantum state requires energy cost and is inherently an irreversible operation. If quantumness of a system is physical, does erasure of quantum correlation as measured by discord also need some energy cost? Here, we show that change in quantum correlation is never larger than the total entropy change of the system and the environment. The entropy cost of erasing correlation has to be at least equal to the amount of quantum correlation erased. Hence, quantum correlation can be regarded as genuinely physical. We show that the new bound leads to the Landauer erasure. The physical cost of erasing quantum correlation is well respected in the case of bleaching of quantum information, thermalization, and can have potential application for any channel leading to erasure of quantum correlation.

The fidelity estimation between two quantum states is crucial for quantum computation and information science. However, an efficacious method for this, especially for mixed states and higher-dimensional density matrices, remains elusive. While there are many existing algorithms on computing the fidelity between two pure states, there is not much work on how to obtain the fidelity between two mixed states. Here, we propose an efficient quantum algorithm for the fidelity estimation, based primarily on the density matrix exponentiation and interferometeric scheme for mixed states, with a time complexity of O(N^2/ε^7), where N is the system size and ε is a precision error. Our algorithm may serve as a resource-efficient technique to deduce fidelity of any two (pure or mixed) unknown or known quantum states, when the density matrices of the quantum states commute with each other.

We investigate whether the inner product structure of quantum mechanics can be modified without violating fundamental physical principles. We consider a generalized inner product defined by a positive operator and assume local unitary dynamics, existence of entangled states and the no-signalling principle. We show that any nontrivial choice of inner product different from standard one inevitably leads to superluminal signalling, in contradiction with relativistic causality. Therefore, the standard Hilbert-space inner product is uniquely enforced by no-signalling.

The nature of quantum nonlocality, as exemplified by entanglement, remains one of the deepest mysteries in quantum physics, challenging classical notions of causality and locality. In this work, we introduce the concept of dark space-time, a hidden geometric structure that coexists with ordinary space-time but may allow superluminal information transfer. We propose a modified space-time metric for dark space-time, in which the speed of causal influences exceeds the speed of light, thereby permitting nonlocal correlations to be naturally mediated through an unobservable channel. The framework is developed through a two-space-time quantum formalism, where entangled states evolve via interactions between ordinary and dark space-time sectors. Furthermore, we discuss the implications of dark space-time for ER=EPR conjecture and black hole information paradox. The notion of dark space-time is more fundamental than the dark energy and dark matter. Our results provide a novel approach to reconciling quantum mechanics with a deeper geometric foundation, offering insights into the fundamental nature of reality.

It is known that non-unital noise such as the amplitude damping can sometimes increase quantum correlations, while unital noise such as the dephasing usually decreases quantum correlations. It is, therefore, important to delineate the conditions, when noise can enhance the quantumness of the system. Here, we show that if the noise acting on the system is unital (non-unital), then the noise acting on the environment must also be unital (non-unital), for the evolution to be unitary in the joint system-environment space. For example, if the first two qubits are treated as system and the third qubit is treated as environment, then both the system and the environment evolve unitally in case of a three-qubit GHZ state, and both of them evolve non-unitally in case of a three-qubit W state. Our result may be of interest in quantum information, and we anticipate it to be useful in various contexts, such as to better tackle noise in quantum computing and quantum information processing.

The speed limit provides an upper bound for the dynamical evolution time of a quantum system. Here, we introduce the notion of quantum acceleration limit for unitary time evolution of quantum systems under time-dependent Hamiltonian. We prove that the quantum acceleration is upper bounded by the fluctuation in the derivative of the Hamiltonian. This leads to a universal quantum acceleration limit (QAL) which answers the question: What is the minimum time required for a quantum system to be accelerated from arbitrary initial state to final state? We illustrate the quantum acceleration limit for a two-level quantum system and show that the bound is indeed tight. This notion can have important applications in adiabatic quantum computing, quantum control and quantum thermodynamics.

Traditional quantum speed limits formulated in density matrix space are generally unattainable for a wide class of dynamics and it is difficult to characterize the fastest possible dynamics. To address this, we present two distinct quantum speed limits in Liouville space for completely positive and trace-preserving (CPTP) dynamics. The first bound saturates for time-optimal CPTP dynamics, while the second bound is exact for all states and all CPTP dynamics. Our bounds have a clear physical and geometric interpretation arising from the uncertainty relations for operators acting on Liouville space, and the geometry of quantum evolution in Liouville space. We also obtain the form of the Liouvillian, which generates the time-optimal CPTP dynamics that connects the given initial and target states. To illustrate our findings, we show that the speed of evolution in Liouville space bounds the growth of the spectral form factor and Krylov complexity of states, which are crucial for studying information scrambling and quantum chaos. In another important application, we show that our results can help us understand the counterintuitive phenomenon of the Mpemba effect in nonequilibrium open quantum dynamics, as the minimal relaxation time scale obtained by speed limits is dictated by the eigenmodes of the Liouvillian.

Quantum coherence, a fundamental resource in quantum computing and quantum information, often competes with localization effects that affect quantum states in disordered systems. In this work, we prove exact trade-off relations between quantum coherence and a measure of localization and many-body localization, namely, the inverse participation ratio (IPR). We prove that for a pure quantum state, the l1 norm of quantum coherence and the relative entropy of coherence satisfy complementarity relations with IPR. For a mixed state, IPR and the l2 norm of quantum coherence as well as relative entropy of coherence satisfy trade-off inequalities. We further explore the applicability of these general relations between quantum coherence and measure of localization in the context of delocalization to many-body localization transition in a disordered interacting quantum manybody system and demonstrate that quantum coherence is also an ideal characterization of the delocalization to many-body localization transition. Our numerical analysis shows that though the full system loses coherence in the many-body localization phase, coherence of a subsystem can increase with the combined effect of disorder and interactions. We believe that these trade-off relations can help in better understanding of how coherence can be preserved or lost in realistic many-body quantum systems, which is vital for developing robust quantum technologies and uncovering new phases of quantum matter.

Quantum key distribution (QKD) enables secure key sharing between distant parties, with several protocols proven resilient against conventional eavesdropping strategies. Here, we introduce a new attack scenario where an eavesdropper, Eve, exploits a quantum switch using the indefinite causal order to intercept and manipulate quantum communication channel. Using multiple metrics such as the information gain, mutual information, and Bell violation, we demonstrate that the presence of a quantum switch significantly compromises QKD security. Our results highlight a previously overlooked vulnerability, emphasizing the need for countermeasures against quantum-controlled adversarial strategies.

The traditional quantum speed limits are not attainable for many physical processes, as they tend to be loose and fail to determine the exact time taken by quantum systems to evolve. To address this, we derive exact quantum speed limits for the unitary dynamics of pure-state quantum system that outperform the existing quantum speed limits. Using these exact quantum speed limits, we can precisely estimate the evolution time for two- and higher-dimensional quantum systems. Additionally, for both finite- and infinite-dimensional quantum systems, we derive an improved Mandelstam-Tamm bound for pure states and show that this bound always saturates for any unitary generated by self-inverse Hamiltonians. Furthermore, we show that our speed limits establish an upper bound on the quantum computational circuit complexity. These results will have a significant impact on our understanding of quantum physics as well as rapidly developing quantum technologies, such as quantum computing, quantum control and quantum thermal machines.

The fundamental division of the total quantum evolution phase into geometric and dynamical components is a central problem in quantum physics. Here, we prove a remarkably simple and universal law demonstrating that this partitioning is governed, at every instant, solely by a single geometric quantity: the Bargmann angle (Bures angle). This result provides a universally applicable and rigorous way to define the exact fraction of the total phase that is geometric versus dynamical in origin, thereby establishing a new quantitative link between the dynamics of quantum evolution and the geometry of the state space. This finding has immediate practical consequences, furnishing a real-time measure of the geometricity of an evolution for designing high-fidelity geometric quantum gates with optimized robustness, and opening new avenues for quantum speed limit and coherent control.

Non-classical features of quantum systems can degrade when subjected to environment and noise. Here, we ask a fundamental question: What is the minimum amount of time it takes for a quantum system to exhibit non-classical features in the presence of noise? Here, we prove distinct speed limits on the quantumness of observable as the norm of the commutator of two given observables. The speed limit on such quantumness measures sets the fundamental upper bound on the rate of change of quantumness, which provides the lower bound on the time required to change the quantumness of a system by a given amount. Additionally, we have proved speed limit for the non-classical features such as quantum coherence that captures the amount of superposition in the quantum systems. We have demonstrated that obtained speed limits are attainable for physical processes of interest, and hence, these bounds can be considered to be tight.

Grover's quantum search algorithm promises a quadratic speedup for unstructured search over its classical counterpart. But this advantage is affected by noise acting on the search space. Here, we show that a quantum switch can act as a resource to mitigate the effects of noise. In this scenario, the noise is modeled by a depolarizing channel, which coherently acts on the entire quantum register. We show that a quantum switch can significantly reduce the error in Grover's search algorithm. We consider the success probability of finding the marked item as the sole quantifier of diminishing the effect of noise in the search space in the presence of quantum switch. We propose two frameworks for the application of quantum switches. In the first framework, we apply the superposition of channel's orders in the form of a switch and do a post-selection at every iteration of the applications of the Grover operator. In the second framework, we delay this measurement and post-selection until the very end. The number of post selections is minimal in the second scenario, and hence the noise reduction can be attributed more to the presence of quantum switch. We illustrate with an example of significant advantage in the success probability of Grover's algorithm using quantum switch.

Given the initial and final states of a quantum system, the speed of transportation of state vector in the projective Hilbert space governs the quantum speed limit. Here, we ask the question what happens to the quantum speed limit under continuous measurement process. We model the continuous measurement process by a non-Hermitian Hamiltonian which keeps the evolution of the system Schrödinger-like even under the process of measurement. Using this specific measurement model, we prove that under continuous measurement, the speed of transportation of a quantum system tends to zero. Interestingly, we also find that for small time scale, there is an enhancement of quantum speed even if the measurement strength is finite. Our findings can have applications in quantum computing and quantum control where dynamics is governed by both unitary and measurement processes.

We consider a scenario of remote state preparation (RSP) of qubits in the context of sequential network scenario. A single copy of an entangled state is shared between Alice on one side, and several Bobs on the other, who sequentially perform unsharp single-particle measurements in order to prepare a specific state. In the given scenario without any shared randomness between the various Bobs, we first determine the classical bound of fidelity for the preparation of remote states by the Bobs. We then show that there can be at most 6 number of Bobs who can sequentially and independently prepare the remote qubit state in Alice's lab with fidelity exceeding the classical bound in the presence of shared quantum correlations. The upper bound is achieved when the singlet state is initially shared between Alice and the first Bob and every Bob prepares a state chosen from the equatorial circle of the Bloch sphere. Then we introduce a new RSP protocol for non-equatorial ensemble of states. The maximum number of Bobs starts to decrease from six when either the choice of remote states is shifted from the equatorial circle towards the poles of the Bloch sphere, or when the initial state shifts towards non-maximally entangled pure and mixed states.

The no-masking theorem for quantum information proves that it is impossible to encode an arbitrary input state into a larger bipartite entangled state such that the full information is stored in the correlation but the individual subsystems have no information about the input state. Here, we ask the question: Is it possible to mask an observable such that the information about the observable is available in the joint system, but individual subsystems reveal nothing about the imprints of the observable? This generalizes the notion of masking to observables. We show that a universal unitary that can mask an arbitrary observable in any dimension does not exist. For a qubit system, we show that the masking operation for a given observable is locally unitarily connected to the swap operation. This suggests a conservation law for information content of observables that goes beyond the conservation laws under symmetry operations. Furthermore, we prove that the unconditional no-bit commitment result follows from the no-masking theorem for observables. Our results can have important applications in quantum information and quantum communication where we encode information not in states but in observables.

How fast an observable can evolve in time is answered by so-called observable speed limit. Here, we prove a stronger version of the observable speed limit and show that the previously obtained bound is a special case of the new bound. The stronger quantum speed limit for the state also follows from the stronger quantum speed limit for observables (SQSLO). We apply this to prove a stronger bound for the entanglement rate using the notion of capacity of entanglement (the quantum information theoretic counterpart of the heat capacity) and show that it outperforms previous bounds. Furthermore, we apply the SQSLO for the rate of modular Hamiltonian and in the context of interacting qubits in a quantum battery. These illustrative examples reveal that the speed limit for the modular energy and the time required to charge the battery can be exactly predicted using the new bound. This shows that for estimating the charging time of quantum battery SQSLO is actually tight, i.e., it saturates. Our findings can have important applications in quantum thermodynamics, the complexity of operator growth, predicting the time rate of quantum correlation growth, and quantum technology, in general.

The quantum speed limit describes how quickly a quantum system can evolve in time from an initial state to a final state under a given dynamics. Here, we derive a generalised quantum speed limit (GQSL) for arbitrary time-continuous evolution using the geometrical approach of quantum mechanics. The GQSL is applicable for quantum systems undergoing unitary, non-unitary, completely positive, non-completely positive and relativistic quantum dynamics. This reduces to the well known standard quantum speed limit (QSL), i.e., the Mandelstam-Tamm bound when the quantum system undergoes unitary time evolution. Using our formalism, we then obtain a quantum speed limit for non-Hermitian quantum systems. To illustrate our findings, we have estimated the quantum speed limit for a time-independent non-Hermitian system as well as for a time-dependent non-Hermitian system namely the Bethe-Lamb Hamiltonian for general two-level system.

The notions of predictability and visibility are essential in the mathematical formulation of wave particle duality. The work of Jakob and Bergou [Phys. Rev. A 76, 052107] generalises these notions for higher-dimensional quantum systems, which were initially defined for qubits, and subsequently proves a complementarity relation between predictability and visibility. By defining the single-party information content of a quantum system as the addition of predictability and visibility, and assuming that entanglement in a bipartite system in the form of concurrence mutually excludes the single-party information, the authors have proposed a complementarity relation between the concurrence and the single-party information content. We show that the information content of a quantum system defined by Jakob and Bergou is nothing but the Hilbert-Schmidt distance between the state of the quantum system of our consideration and the maximally mixed state. Motivated by the fact that the trace distance is a good measure of distance as compared to the Hilbert-Schmidt distance from the information theoretic point of view, we, in this work, define the information content of a quantum system as the trace distance between the quantum state and the maximally mixed state. We then employ the quantum Pinsker's inequality and the reverse Pinsker's inequality to derive a new complementarity and a reverse complementarity relation between the single-party information content and the entanglement present in a bipartite quantum system in a pure state. As a consequence of our findings, we show that for a bipartite system in a pure state, its entanglement and the predictabilities and visibilities associated with the subsystems cannot be arbitrarily small as well as arbitrarily large.

The possibility of a quantum system to exhibit properties that are akin to both the classically held notions of being a particle and a wave, is one of the most intriguing aspects of the quantum description of nature. These aspects have been instrumental in understanding paradigmatic natural phenomena as well as to provide nonclassical applications. A conceptual foundation for the wave nature of a quantum state has recently been presented, through the notion of quantum coherence. We introduce here a parallel notion for the particle nature of a quantum state of an arbitrary physical system. We provide elements of a resource theory of particleness, and give a quantification of the same. Finally, we provide evidence for a complementarity between the particleness thus introduced, and the coherence of an arbitrary quantum state.