Searcharxiv⌕ Search

arXiv subjects

S. Omkar

Publications and source records attributed to S. Omkar.

16 recordsLinked to original sources
arXiv2020

Highly photon loss tolerant quantum computing using hybrid qubits

We investigate a scheme for topological quantum computing using optical hybrid qubits and make an extensive comparison with previous all-optical schemes. We show that the photon loss threshold reported by Omkar {\it et al}. [Phys. Rev. Lett. 125, 060501 (2020)] can be improved further by employing postselection and multi-Bell-state-measurement based entangling operation to create a special cluster state, known as Raussendorf lattice for topological quantum computation. In particular, the photon loss threshold is enhanced up to $5.7\times10^{-3}$, which is the highest reported value given a reasonable error model. This improvement is obtained at the price of consuming more resources by an order of magnitude, compared to the scheme in the aforementioned reference. Neverthless, this scheme remains resource-efficient compared to other known optical schemes for fault-tolerant quantum computation.

quant-ph↗
arXiv2020

Resource-efficient and fault-tolerant topological quantum computation with hybrid entanglement of light

We propose an all-linear-optical scheme to ballistically generate a cluster state for measurement-based topological fault-tolerant quantum computation using hybrid photonic qubits entangled in a continuous-discrete domain. Availability of near-deterministic Bell-state measurements on hybrid qubits is exploited for the purpose. In the presence of photon losses, we show that our scheme leads to a significant enhancement in both tolerable photon-loss rate and resource overheads. More specifically, we report a photon-loss threshold of $\sim3.3\times 10^{-3}$, which is higher than those of known optical schemes under a reasonable error model. Furthermore, resource overheads to achieve logical error rate of $10^{-6} (10^{-15})$ is estimated to be $\sim8.5\times10^{5} (1.7\times10^{7})$ which is significantly less by multiple orders of magnitude compared to other reported values in the literature.

quant-ph↗
arXiv2019

Quantum error correction assisted quantum metrology without entanglement

In this article we study the role that quantum resources play in quantum error correction assisted quantum metrology (QECQM) schemes. We show that there exist classes of such problems where entanglement is not necessary to retrieve noise free evolution and Heisenberg scaling in the long time limit. Over short time scales, noise free evolution is also possible even without any form of quantum correlations. In particular, for qubit probes, we show that whenever noise free quantum metrology is possible via QECQM, entanglement free schemes over long time scales and correlation free schemes over short time scales are always possible.

quant-ph↗
arXiv2017

Quantum Critical Environment Assisted Quantum Magnetometer

A central qubit coupled to an Ising ring of $N$ qubits, operating close to a critical point is investigated as a potential precision quantum magnetometer for estimating an applied transverse magnetic field. We compute the Quantum Fisher information for the central, probe qubit with the Ising chain initialized in its ground state or in a thermal state. The non-unitary evolution of the central qubit due to its interaction with the surrounding Ising ring enhances the accuracy of the magnetic field measurement. Near the critical point of the ring, Heisenberg-like scaling of the precision in estimating the magnetic field is obtained when the ring is initialized in its ground state. However, for finite temperatures, the Heisenberg scaling is limited to lower ranges of $N$ values.

quant-ph↗
arXiv2017

Coherence as a Unit Resource for Quantum Error Correction

In this paper we study an error correcting protocol that specifically derives its error correcting properties from elementary units of coherence. The entire protocol from beginning to end is performed using non-coherence increasing operations, resulting in the consumption of the input coherence, thus necessitating further quantum resources if one wishes to perform the protocol again. We show that even when the input quantum resource is just 1 coherent qubit, one may acquire partial protection from phase flip errors, and that this can be scaled up to protect against arbitrary qubit errors with 6 ancillary coherent qubits as input. The work presented strengthens the operational interpretation of a single unit of coherence by providing a useful information theoretic task that one may perform when such elementary units of coherence are available.

quant-ph↗
arXiv2016

Quasiprobability distributions in open quantum systems: spin-qubit systems

Quasiprobability distributions (QDs) in open quantum systems are investigated for $SU(2)$, spin like systems, having relevance to quantum optics and information. In this work, effect of both quantum non-demolition (QND) and dissipative open quantum systems, on the evolution of a number of spin QDs are investigated. Specifically, compact analytic expressions for the $W$, $P$, $Q$, and $F$ functions are obtained for some interesting single, two and three qubit states, undergoing general open system evolutions. Further, corresponding QDs are reported for an N qubit Dicke model and a spin-1 system. The existence of nonclassical characteristics are observed in all the systems investigated here. The study leads to a clear understanding of quantum to classical transition in a host of realistic physical scenarios. Variation of the amount of nonclassicality observed in the quantum systems, studied here,are also investigated using nonclassical volume.

quant-ph↗
arXiv2016

The Unruh effect interpreted as a quantum noise channel

We make use of the tools of quantum information theory to shed light on the Unruh effect. A modal qubit appears as if subjected to quantum noise that degrades quantum information, as observed in the accelerated reference frame. The Unruh effect experienced by a mode of a free Dirac field, as seen by a relativistically accelerated observer, is treated as a noise channel, which we term the Unruh channel. We characterize this channel by providing its operator-sum representation, and study various facets of quantum correlations, such as, Bell inequality violations, entanglement, teleportation and measurement-induced decoherence under the effect. We compare and contrast this channel from conventional noise due to environmental decoherence. We show that the Unruh effect produces an amplitude-damping-like channel, associated with zero temperature, even though the Unruh effect is associated with a non-zero temperature. Asymptotically, the Bloch sphere subjected to the channel does not converge to a point, as would be expected by fluctuation-dissipation arguments, but contracts by a finite factor. We construct for the Unruh effect the inverse channel, a non-completely-positive map, that formally reverses the effect, and offer some physical interpretation.

quant-ph↗
arXiv2016

Characterization of Unruh Channel in the context of Open Quantum Systems

We show through the Choi matrix approach that the effect of Unruh acceleration on a qubit is similar to the interaction of the qubit with a vacuum bath, despite the finiteness of the Unruh temperature. Thus, rather counterintuitvely, from the perspective of decoherence in this framework, the particle experiences a vacuum bath with a temperature-modified interaction strength, rather than a thermal bath. We investigate how this "relativistic decoherence" is modified by the presence of environmentally induced decoherence, by studying the degradation of quantum information, as quantified by parameters such as nonlocality, teleportation fidelity, entanglement, coherence and quantum measurement-induced disturbance (a discord-like measure). Also studied are the performance parameters such as gate and channel fidelity. We highlight the distinction between dephasing and dissipative environmental interactions, by considering the actions of quantum non-demolition and squeezed generalized amplitude damping channels, respectively, where, in particular, squeezing is shown to be a useful quantum resource.

quant-ph↗
arXiv2015

The two-qubit amplitude damping channel: characterization using quantum stabilizer codes

A protocol based on quantum error correction based characterization of quantum dynamics (QECCD) is developed for quantum process tomography on a two-qubit system interacting dissipatively with a vacuum bath. The method uses a 5-qubit quantum error correcting code that corrects arbitrary errors on the first two qubits, and also saturates the quantum Hamming bound. The dissipative interaction with a vacuum bath allows for both correlated and independent noise on the two-qubit system. We study the dependence of the degree of the correlation of the noise on evolution time and inter-qubit separation.

quant-ph↗
arXiv2015

Quantum Fisher and Skew information for Unruh accelerated Dirac qubit

We develop a Bloch vector representation of Unruh channel for a Dirac field mode. This is used to provide a unified, analytical treatment of quantum Fisher and Skew information for a qubit subjected to the Unruh channel, both in its pure form as well as in the presence of experimentally relevant external noise channels. The time evolution of Fisher and Skew information is studied along with the impact of external environment parameters such as temperature and squeezing. The external noises are modelled by both purely dephasing phase damping as well as the squeezed generalized amplitude damping channels. An interesting interplay between the external reservoir temperature and squeezing on the Fisher and Skew information is observed, in particular, for the action of the squeezed generalized amplitude damping channel. It is seen that for some regimes, squeezing can enhance the quantum information against the deteriorating influence of the ambient environment. Similar features are also observed for the analogous study of Skew information, highlighting the similar origin of the Fisher and Skew information.

quant-ph↗
arXiv2015

Quantum code for quantum error characterization

A quantum error correcting code is a subspace $\mathcal{C}$ such that allowed errors acting on any state in $\mathcal{C}$ can be corrected. A quantum code for which state recovery is only required up to a logical rotation within $\mathcal{C}$, can be used for detection of errors, but not for quantum error correction. Such a code with stabilizer structure, which we call an "ambiguous stabilizer code" (ASC), can nevertheless be useful for the characterization of quantum dynamics (CQD). The use of ASCs can help lower the size of CQD probe states used, but at the cost of increased number of operations.

quant-ph↗
arXiv2015

Characterization of quantum dynamics using quantum error correction

Characterizing noisy quantum processes is important to quantum computation and communication (QCC), since quantum systems are generally open. To date, all methods of characterization of quantum dynamics (CQD), typically implemented by quantum process tomography, are \textit{off-line}, i.e., QCC and CQD are not concurrent, as they require distinct state preparations. Here we introduce a method, "quantum error correction based characterization of dynamics", in which the initial state is any element from the code space of a quantum error correcting code that can protect the state from arbitrary errors acting on the subsystem subjected to the unknown dynamics. The statistics of stabilizer measurements, with possible unitary pre-processing operations, are used to characterize the noise, while the observed syndrome can be used to correct the noisy state. Our method requires at most $2(4^n-1)$ configurations to characterize arbitrary noise acting on $n$ qubits.

quant-ph↗
arXiv2012

The operator sum-difference representation for quantum maps: application to the two-qubit amplitude damping channel

On account of the Abel-Galois no-go theorem for the algebraic solution to quintic and higher order polynomials, the eigenvalue problem and the associated characteristic equation for a general noise dynamics in dimension $d$ via the Choi-Jamiolkowski approach cannot be solved in general via radicals. We provide a way around this impasse by decomposing the Choi matrix into simpler, not necessarily positive, Hermitian operators that are diagonalizable via radicals, which yield a set of `positive' and `negative' Kraus operators. The price to pay is that the sufficient number of Kraus operators is $d^4$ instead of $d^2$, sufficient in the Kraus representation. We consider various applications of the formalism: the Kraus repesentation of the 2-qubit amplitude damping channel, the noise resulting from a 2-qubit system interacting dissipatively with a vacuum bath; defining the maximally dephasing and purely dephasing components of the channel in the new representation, and studying their entanglement breaking and broadcast properties.

quant-ph↗
arXiv2012

Dissipative and Non-dissipative Single-Qubit Channels: Dynamics and Geometry

Single-qubit channels are studied under two broad classes: amplitude damping channels and generalized depolarizing channels. A canonical derivation of the Kraus representation of the former, via the Choi isomorphism is presented for the general case of a system's interaction with a squeezed thermal bath. This isomorphism is also used to characterize the difference in the geometry and rank of these channel classes. Under the isomorphism, the degree of decoherence is quantified according to the mixedness or separability of the Choi matrix. Whereas the latter channels form a 3-simplex, the former channels do not form a convex set as seen from an ab initio perspective. Further, where the rank of generalized depolarizing channels can be any positive integer upto 4, that of amplitude damping ones is either 2 or 4. Various channel performance parameters are used to bring out the different influences of temperature and squeezing in dissipative channels. In particular, a noise range is identified where the distinguishability of states improves inspite of increasing decoherence due to environmental squeezing.

quant-ph↗
arXiv2012

Libertarian free will and quantum indeterminism

The basic question in the long-standing debate about free will (FW) is not whether FW can be demonstrated to exist nor even whether it exists, but instead how to define it scientifically. If FW is not dismissed as an illusion nor identified with a variety of unpredictability, then logical paradoxes arise that make FW elusive to define. We resolve these paradoxes through a model of FW, in which FW is a new causal primitive empowered to override physical causality under guidance. We develop a simple mathematical realization of this model, that when applied to quantum theory, suggests that the exercise of FW corresponds to a nonlinear POVM causing deviations from the Born rule. In principle, these deviations would stand in conflict with known conservation laws and invariance principles, implying that the brain, the presumed seat of FW, may be an arena of exotic, non-standard physics. However, in practice it will be difficult to distinguish these deviations from quantum and neural noise, and statistical fluctuations. We indicate possible neurobiological and neurological tests, implications and applications of our proposed model.

quant-ph↗