arXiv subjects

Arun Kumar Pati

Publications and source records attributed to Arun Kumar Pati.

At least 55 records · Page 3Linked to original sources

arXiv2019

Super Quantum Search Algorithm with Weak Value Amplification and Postselection

We propose a new model of quantum computation which aims to speed up quantum algorithms assisted by the weak value amplification and ancillay quantum register with the pre- and postelection. Within this model, we show that a quantum computer can solve a data base search of N entries in one step with probability close to one for large N, provided the post-selection on the ancillary quantum register is successful. In this model, to search a data base of N entries, the number of qubits grows from n to 2n, but there is a huge reduction in time complexity. Physically, this can be understood as the effect of weak value amplification that arises due to the pre- and postselection of the ancillary register which interacts with the n qubit register where quantum search is performed. This effectively accelerates the computation and takes the state of quantum computer much ahead in time, compared to what one would obtain without weak value amplification and post-selection.

quant-ph↗

arXiv2019

Coherence of Purification

We introduce a quantity called the coherence of purification which can be a measure of total quantumness for a single system. We prove that coherence of purification is always more than the coherence of the system. For a pure state, the coherence of purification is same as the relative entropy of coherence. Furthermore, we show that the difference in the coherence of purification of a quantum state before and after the dephasing can capture residual quantumness. In addition, we show that the entanglement of purification that can be created by incoherent operation between two subsystems is upper bounded by the coherence of purification of the original system. We show that the coherence of purification is a resource in quantum state discrimination process. In the absence of coherence, entanglement and quantum correlations, the coherence of purification may play an important role in quantum information processing tasks.

quant-ph↗

arXiv2019

Quantum Coherence, Coherent Information and Information Gain in Quantum Measurement

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 scenario in the presence of environment. We argue that the information gain is upper bounded by the entropy exchange between the system and the apparatus. Also, to maximize the information gain, both the initial coherence of the apparatus, and the final entanglement between the system and apparatus should be maximum. Moreover, we find that for a fixed amount of coherence in the final apparatus state the more robust apparatus is, the more will be the information gain.

quant-ph↗

arXiv2019

Distinguishing two preparations for same pure state leads to signalling

Pure state of a physical system can be prepared in an infinite number of ways. Here, we prove that given a pure state of a quantum system it is impossible to distinguish two preparation procedures. Further, we show that if we can distinguish two preparation procedures for the same pure state then that can lead to signalling. This impossibility result is different than the no measurement without disturbance and the no-cloning. Extending this result for a pure bipartite entangled state entails that the impossibility of distinguishing two preparation procedures for a mixed state follows from the impossibility of distinguishing two preparations for a pure bipartite state.

physics.gen-ph↗

arXiv2019

Teleporting Grin of a Quantum Chesire Cat without cat

Quantum Chesire Cat is a counterintuitive phenomenon that provides a new window into the nature of the quantum systems in relation to multiple degrees of freedom associated with a single physical entity. Under suitable pre and postselections, a photon (the cat) can be decoupled from its circular polarization (its grin). In this paper, we explore whether the grin without the cat can be teleported to a distant location. This will be a totally disembodied teleportation protocol. Based on the original Quantum Chesire Cat setup, we design a protocol where the circular polarization is successfully teleported between two spatially separated parties even when the photon is not physically present with them. The process raises questions in our understanding about properties of quantum system. In particular it shows that question like ``whose polarization is it'' can prove to be vacuous in such scenario.

quant-ph↗

arXiv2019

Superposition of causal order enables perfect quantum teleportation with very noisy singlets

We show that the fidelity of the standard quantum teleportation protocol, which utilizes an impure resource state, applied successively, can be significantly improved, when used in conjunction with a quantum switch. In particular, we find that for two such teleportation channels conjugated with the superposition of causal order, teleportation fidelity beyond the classical threshold is achieved for significantly larger noise than would be possible conventionally. One can even make the effective teleportation channel perfectly faithful for very large noise. We also discuss the generalization of our scheme for more than two pathways, and define a figure of merit in that context.

quant-ph↗

arXiv2018

Superposition of causal order as a metrological resource for quantum thermometry

We propose a novel approach to qubit thermometry using a quantum switch, that introduces an indefinite causal order in the probe-bath interaction, to significantly enhance the thermometric precision. The resulting qubit probe shows improved precision in both low and high temperature regimes when compared to optimal qubit probes studied previously. It even performs better than a Harmonic oscillator probe, in spite of having only two energy levels rather than an infinite number of energy levels as that in a harmonic oscillator. We thereby show unambiguously that quantum resources such as the quantum switch can significantly improve equilibrium thermometry. We also derive a new form of thermodynamic uncertainty relation that is tighter and depends on the energy gap of the probe. The present work may pave the way for using indefinite causal order as a metrological resource.

quant-ph↗

arXiv2018

Quantum uncertainty relation based on the mean deviation

Traditional forms of quantum uncertainty relations are invariably based on the standard deviation. This can be understood in the historical context of simultaneous development of quantum theory and mathematical statistics. Here, we present alternative forms of uncertainty relations, in both state dependent and state independent forms, based on the mean deviation. We illustrate the robustness of this formulation in situations where the standard deviation based uncertainty relation is inapplicable. We apply the mean deviation based uncertainty relation to detect EPR violation in a lossy scenario for a higher inefficiency threshold than that allowed by the standard deviation based approach. We demonstrate that the mean deviation based uncertainty relation can perform equally well as the standard deviation based uncertainty relation as non-linear witness for entanglement detection.

quant-ph↗

arXiv2018

Evolution of coherence and non-classicality under global environmental interaction

A master equation has been constructed for a global system-bath interaction both in the absence as well as presence of non-Markovian noise. For the memoryless case, it has been exactly solved for a paradigmatic class of two qubit states in high and zero temperature thermal environment. For the non-Markovian model, it has been solved for zero temperature bath. The evolution of quantum coherence and entanglement has been observed in presence of the above mentioned interactions. We show that the global part of the system-bath interaction compensates for the decoherence, resulting in slow down of coherence and entanglement decay. For an appropriately defined limiting case, both coherence and entanglement show freezing behaviour for the high temperature bath. In case of zero temperature bath, the mentioned interaction not only stabilizes the non-classical correlations, but also enhances them for a finite period. For the memory dependent case, we have seen that the global interaction enhances the back-flow of information from environment to the system, as it enhances the regeneration of coherence and entanglement. Also we have studied the generation of Quantum Fisher information by the mentioned process. An intuitive measure of non-classicality based on non-commutativity of quantum states has been considered. Bounds on generated quantum Fisher information has been found in terms of quantumness and coherence. This gives us a novel understanding of Quantum Fisher information as a measure of non-classicality.

quant-ph↗

arXiv2018

Stronger classes of sum uncertainty and reverse uncertainy relations

Uncertainty relations are old, yet potentially rewarding to explore. By introducing a quantity called the uncertainty matrix, we provide a link between purity and observable incompatibility, and derive several stronger uncertainty relations in both forward and reverse directions for arbitrary quantum states, i.e., mixed as well as pure, and arbitrary incompatible quantum observables, none of which suffer from the problem of triviality. Besides the tightness, the interpretations of terms in these uncertainty relations may be of independent inter- est. We provide the possible generalization of stronger uncertainty relations to sum of variances of more than two observables. We also demonstrate applications of techniques used here to, firstly, obtain a simple reverse quantum speed limit for quantum states undergoing Markovian dynamical evolution, and secondly, to provide a lower bound for fidelity between two quantum states.

quant-ph↗

arXiv2018

Impossibility of Cloning of Quantum Coherence

It is well known that it is impossible to clone an arbitrary quantum state. However, this inability does not lead directly to no-cloning of quantum coherence. Here, we show that it is impossible to clone the coherence of an arbitrary quantum state which is a stronger statement than the 'no-cloning of quantum state'. In particular, with ancillary system as machine state, we show that it is impossible to clone the coherence of states whose coherence is greater than the coherence of the known states on which the transformations are defined. Also, we characterize the class of states for which coherence cloning will be possible for a given choice of machine. Furthermore, we find the maximum range of states whose coherence can be cloned perfectly. The impossibility proof also holds when we do not include machine states.

quant-ph↗

arXiv2018

Masking quantum information is impossible

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 in general. Our findings may have potential applications in secret sharing and future quantum communication protocols.

quant-ph↗

arXiv2018

Coherence makes quantum systems 'magical'

Two primary facets of quantum technological advancement that hold great promise are quantum communication and quantum computation. For quantum communication, the canonical resource is entanglement. For quantum gate implementation, the resource is 'magic' in an auxiliary system. It has already been shown that quantum coherence is the fundamental resource for the creation of entanglement. We argue on the similar spirit that quantum coherence is the fundamental resource when it comes to the creation of magic. This unifies the two strands of modern development in quantum technology under the common underpinning of existence of quantum superposition, quantified by the coherence in quantum theory. We also attempt to obtain magic monotones inspired from coherence monotones and vice versa. We further study the interplay between quantum coherence and magic in a qutrit system and that between quantum entanglement and magic in a qutrit-qubit setting.

quant-ph↗

arXiv2018

Potent Value and Potent Operator with Pre- and Post-selected Quantum Systems

We introduce a novel concept which we call as potent value of system observable for pre- and post-selected quantum states. This describes, in general, how a quantum system affects the state of the apparatus during the time between two strong measurements corresponding to pre- and post-selections. The potent value can be realized for any interaction strength and for arbitrary coupling between the system and the apparatus observables. Most importantly, potent values generalize and unify the notion of the weak values and modular values of observables in quantum theory. Furthermore, we define a potent operator which describes the action of one system on the another and show that superposition of time-evolutions and time-translation machines are potent operators. These concepts may find useful applications in quantum information processing and can lead to technological benefits.

quant-ph↗

arXiv2018

Quantum speed limit constraints on a nanoscale autonomous refrigerator

Quantum speed limit, furnishing a lower bound on the required time for the evolution of a quantum system through the state space, imposes an ultimate natural limitation to the dynamics of physical devices. Quantum absorption refrigerators, on the other hand, have attracted a great deal of attention in the last few years. In this article, we discuss the effects of quantum speed limit on the performance of a quantum absorption refrigerator. In particular, we show that there exists a trade-off relation between the steady cooling rate of the refrigerator and the minimum time taken to reach the steady state. Based on this, we define a figure of merit called "bounding second order cooling rate" and show that this scales linearly with the unitary interaction strength among the constituent qubits. We also study the increase of bounding second order cooling rate with the thermalization strength. We subsequently demonstrate that coherence in the initial three qubit system can significantly increase the bounding second order cooling rate. We study the efficiency of the refrigerator at maximum bounding second order cooling rate and, in a limiting case, we show that the efficiency at maximum bounding second order cooling rate is given by a simple formula reminiscent of the Curzon-Ahlborn relation.

quant-ph↗

arXiv2018

Quantifying coherence with quantum addition

Quantum addition channels have been recently introduced in the context of deriving entropic power inequalities for finite dimensional quantum systems. We prove a reverse entropy power equality which can be used to analytically prove an inequality conjectured recently for arbitrary dimension and arbitrary addition weight. We show that the relative entropic difference between the output of such a quantum additon channel and the corresponding classical mixture quantitatively captures the amount of coherence present in a quantum system. This new coherence measure admits an upper bound in terms of the relative entropy of coherence and is utilized to formulate a state-dependent uncertainty relation for two observables. Our results may provide deep insights to the origin of quantum coherence for mixed states that truly come from the discrepancy between quantum addition and the classical mixture.

quant-ph↗

arXiv2018

Quantum no-go theorems in causality respecting systems in presence of closed timelike curves: Tweaking the Deutsch condition

We consider causality respecting (CR) quantum systems interacting with closed timelike curves (CTCs), within the Deutsch model. We introduce the concepts of popping up and elimination of quantum information and use them to show that no-cloning and no-deleting, which are true in CR quantum systems, are no more valid in the same that are interacting with CTCs. We also find limits on the possibility of creation of entanglement between a CR system and a CTC, and the same between two CR systems in the presence of a CTC. We prove that teleportation of quantum information, even in its approximate version, from a CR region to a CTC is disallowed. Interestingly, we find that tweaking the Deutsch model, by allowing the input and output to be not the same, leads to a nontrivial approximate teleportation beyond the classical limit.

quant-ph↗

arXiv2018

Max- relative entropy of coherence: an operational coherence measure

The operational characterization of quantum coherence is the corner stone in the development of resource theory of coherence. We introduce a new coherence quantifier based on max-relative entropy. We prove that max-relative entropy of coherence is directly related to the maximum overlap with maximally coherent states under a particular class of operations, which provides an operational interpretation of max-relative entropy of coherence. Moreover, we show that, for any coherent state, there are examples of subchannel discrimination problems such that this coherent state allows for a higher probability of successfully discriminating subchannels than that of all incoherent states. This advantage of coherent states in subchannel discrimination can be exactly characterized by the max-relative entropy of coherence. By introducing suitable smooth max-relative entropy of coherence, we prove that the smooth max-relative entropy of coherence provides a lower bound of one-shot coherence cost, and the max-relative entropy of coherence is equivalent to the relative entropy of coherence in asymptotic limit. Similar to max-relative entropy of coherence, min-relative entropy of coherence has also been investigated. We show that the min-relative entropy of coherence provides an upper bound of one-shot coherence distillation, and in asymptotic limit the min-relative entropy of coherence is equivalent to the relative entropy of coherence.

quant-ph↗