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Arvind

Publications and source records attributed to Arvind.

At least 109 records · Page 6Linked to original sources

Taming Weak Memory Models

Speculative techniques in microarchitectures relax various dependencies in programs, which contributes to the complexity of (weak) memory models. We show using WMM, a new weak memory model, that the model becomes simpler if it includes load-value speculation and thus, does not enforce any dependency! However, in the absence of good value-prediction techniques, a programmer may end up paying a price for the extra fences. Thus, we also present WMM-D, which enforces the dependencies captured by the current microarchitectures. WMM-D is still much simpler than other existing models. We also show that non-atomic multi-copy stores arise as a result of sharing write-through caches. We think restricting microarchitectures to write-back caches (and thus simpler weak memory models) will not incur any performance penalty. Nevertheless, we present WMM-S, another extension to WMM, which could model the effects of non-atomic multi-copy stores. WMM, WMM-D, and WMM-S are all defined using Instantaneous Instruction Execution (I^2E), a new way of describing memory models without explicit reordering or speculative execution.

cs.PL

Constructing valid density matrices on an NMR quantum information processor via maximum likelihood estimation

Estimation of quantum states is one of the most important steps in any quantum information processing experiment. A naive reconstruction of the density matrix from experimental measurements can often give density matrices which are not positive, and hence not physically acceptable. How do we ensure that at all stages of reconstruction, we keep the density matrix positive and normalized? Recently a method has been suggested based on maximum likelihood estimation, wherein the density matrix is guaranteed to be positive definite. We experimentally implement this protocol and demonstrate its utility on an NMR quantum information processor. We discuss several examples where we undertake such an estimation and compare it with the standard method of state estimation.

quant-ph

Weak measurement-based state estimation of Gaussian states of one-variable quantum systems

We present a scheme to estimate Gaussian states of one-dimensional continuous variable systems, based on weak (unsharp) quantum measurements. The estimation of a Gaussian state requires us to find position ($q$), momentum ($p$) and their second order moments. We measure $q$ weakly and follow it up with a projective measurement of $p$ on half of the ensemble, and on the other half we measure $p$ weakly followed by a projective measurement of $q$. In each case we use the state twice before discarding it. We compare our results with projective measurements and demonstrate that under certain conditions such weak measurement-based estimation schemes, where recycling of the states is possible, can outperform projective measurement-based state estimation schemes.

quant-ph

Experimental demonstration of quantum contextuality on an NMR qutrit

We experimentally test quantum contextuality of a single qutrit using NMR. The contextuality inequalities based on nine observables developed by Kurzynski et. al. are first reformulated in terms of traceless observables which can be measured in an NMR experiment. These inequalities reveal the contextuality of almost all single-qutrit states. We demonstrate the violation of the inequality on four different initial states of a spin-1 deuterium nucleus oriented in a liquid crystal matrix, and follow the violation as the states evolve in time. We also describe and experimentally perform a single-shot test of contextuality for a subclass of qutrit states whose density matrix is diagonal in the energy basis.

quant-ph

Quantum state estimation using weak measurements

We explore the possibility of using "weak measurements" without "weak value" for quantum state estimation. Since for weak measurements the disturbance caused during each measurement is small, we can rescue the state, unlike for the case of projective measurements. We use this property of weak measurements and design schemes for quantum state estimation for qubits and for Gaussian states. We show, via numerical simulations, that under certain circumstances, our method can outperform the estimation by projective measurements both for qubits and for Gaussian states. It turns out that ensemble size plays an important role and the scheme based on recycling works better for small ensembles.

quant-ph

Experimental construction of a W-superposition state and its equivalence to the GHZ state under local filtration

We experimentally construct a novel three-qubit entangled W-superposition ($\rm W \bar{\rm W}$) state on an NMR quantum information processor. We give a measurement-based filtration protocol for the invertible local operation (ILO) that converts the $\rm W \bar{\rm W}$ state to the GHZ state, using a register of three ancilla qubits. Further we implement an experimental protocol to reconstruct full information about the three-party $\rm W \bar{\rm W}$ state using only two-party reduced density matrices. An intriguing fact unearthed recently is that the $\rm W \bar{\rm W}$ state which is equivalent to the GHZ state under ILO, is in fact reconstructible from its two-party reduced density matrices, unlike the GHZ state. We hence demonstrate that although the $\rm W \bar{\rm W}$ state is interconvertible with the GHZ state, it stores entanglement very differently.

quant-ph

Measurement-based local quantum filters and their ability to transform quantum entanglement

We introduce local filters as a means to detect the entanglement of bound entangled states which do not yield to detection by witnesses based on positive (P) maps which are not completely positive (CP). We demonstrate how such non-detectable bound entangled states can be locally filtered into detectable bound entangled states. Specifically, we show that a bound entangled state in the orthogonal complement of the unextendible product bases (UPB), can be locally filtered into a another bound entangled state that is detectable by the Choi map. We reinterpret these filters as local measurements on locally extended Hilbert spaces. We give explicit constructions of a measurement-based implementation of these filters for $2 \otimes 2$ and $3 \otimes 3$ systems. This provides us with a physical mechanism to implement such local filters.

quant-ph

Quantum Private Comparison over noisy channels

Quantum Private Comparison (QPC) allows us to protect private information during its comparison. In the past various three-party quantum protocols have been proposed that claim to work well under noisy conditions. Here we tackle the problem of QPC under noise. We analyze the EPR-based protocol under depolarizing noise, bit flip and phase flip noise. We show how noise affects the robustness of the EPR-based protocol. We then present a straightforward protocol based on CSS codes to perform QPC which is robust against noise and secure under general attacks.

quant-ph

Implementation of the quantum Fourier transform on a hybrid qubit-qutrit NMR quantum emulator

The quantum Fourier transform (QFT) is a key ingredient of several quantum algorithms and a qudit-specific implementation of the QFT is hence an important step toward the realization of qudit-based quantum computers. This work develops a circuit decomposition of the QFT for hybrid qudits based on generalized Hadamard and generalized controlled-phase gates, which can be implemented using selective rotations in NMR. We experimentally implement the hybrid qudit QFT on an NMR quantum emulator, which uses four qubits to emulate a single qutrit coupled to two qubits.

quant-ph

Experimental construction of generic three-qubit states and their reconstruction from two-party reduced states on an NMR quantum information processor

We experimentally explore the state space of three qubits on an NMR quantum information processor. We construct a scheme to experimentally realize a canonical form for general three-qubit states up to single-qubit unitaries. This form involves a non-trivial combination of GHZ and W-type maximally entangled states of three qubits. The general circuit that we have constructed for the generic state reduces to those for GHZ and W states as special cases. The experimental construction of a generic state is carried out for a nontrivial set of parameters and the good fidelity of preparation is confirmed by complete state tomography. The GHZ and W-states are constructed as special cases of the general experimental scheme. Further, we experimentally demonstrate a curious fact about three-qubit states, where for almost all pure states, the two-qubit reduced states can be used to reconstruct the full three-qubit state. For the case of a generic state and for the W-state, we demonstrate this method of reconstruction by comparing it with the directly tomographed three-qubit state.

quant-ph

Experimental protection against evolution of states in a subspace via a super-Zeno scheme on an NMR quantum information processor

We experimentally demonstrate the freezing of evolution of quantum states in one- and two-dimensional subspaces of two qubits, on an NMR quantum information processor. State evolution was frozen and leakage of the state from its subspace to an orthogonal subspace was successfully prevented using super-Zeno sequences, comprising of a set of inverting radio frequency (rf) pulses punctuated by pre-selected time intervals. We demonstrate the efficacy of the scheme by preserving different types of states, including separable and maximally entangled states in one- and two-dimensional subspaces of two qubits. The change in the experimental density matrices was tracked by carrying out full state tomography at several time points. We use the fidelity measure for the one-dimensional case and the leakage (fraction) into the orthogonal subspace for the two-dimensional case, as qualitative indicators to estimate the resemblance of the density matrix at a later time to the initially prepared density matrix. For the case of entangled states, we additionally compute an entanglement parameter to indicate the presence of entanglement in the state at different times. We experimentally demonstrate that the super-Zeno scheme is able to successfully confine state evolution to the one- or two-dimensional subspace being protected.

quant-ph

Entanglement properties of positive operators with ranges in completely entangled subspaces

We prove that the projection on a completely entangled subspace S of maximum dimension in a multipartite quantum system obtained by Parthasarathy is not positive under partial transpose. We next show that several positive operators with range in S also have the same property. In this process we construct an orthonormal basis of S and provide a linking theorem to link the constructions of completely entangled subspaces due to Parthasarthy, Bhat and Johnston.

quant-ph

Estimation of quantum states by weak and projective measurements

We explore the possibility of using "weak" measurements to carry out quantum state tomography. Given a certain fixed number of copies of identically prepared states of a qubit, we simulate state tomography using weak as well as projective measurements. Due to the collapse of the state after measurement, we cannot re-use the state after a projective measurement. If the coupling strength between the quantum system and the measurement device is made weaker, the disturbance caused to the state can be lowered. This then allows us to re-use the same member of the ensemble for further measurements and thus extract more information from the system. However, this happens at the expense of getting imprecise information from the first measurement. We simulate this scheme for a single qubit and show that under certain circumstances, it can outperform the projective measurement-based tomography scheme. This opens up the possibility of new ways of extracting information from quantum ensembles. We study the efficacy of this scheme for different coupling strengths.

quant-ph

Determining the parity of a permutation using an experimental NMR qutrit

We present the NMR implementation of a recently proposed quantum algorithm to find the parity of a permutation. In the usual qubit model of quantum computation, speedup requires the presence of entanglement and thus cannot be achieved by a single qubit. On the other hand, a qutrit is qualitatively more quantum than a qubit because of the existence of quantum contextuality and a single qutrit can be used for computing. We use the deuterium nucleus oriented in a liquid crystal as the experimental qutrit. This is the first experimental exploitation of a single qutrit to carry out a computational task.

quant-ph

Extremal extensions of entanglement witnesses and their connection with UPB

In this paper we describe a new connection between UPB (unextendable product bases) and P (positive) maps which are not CP (completely positive). We show that inner automorphisms of the set of P maps which are not CP, produce extremal extensions of these maps that help in entanglement detection. By constructing such an extension of the well-known Choi map, we strengthen its power to unearth PPT (positive under partial transpose) entangled states. We further show that the class of maps generated from the Choi map via an inner automorphism naturally detects the entanglement of states in the orthogonal complement of certain UPB. This brings out a hitherto undiscovered connection between the Choi map and UPB. We also show that certain other recently considered extremal extensions are obtainable by such extensions of the Choi map.

quant-ph

Extremal extensions of entanglement witnesses: Unearthing new bound entangled states

In this paper, we discuss extremal extensions of entanglement witnesses based on Choi's map. The constructions are based on a generalization of the Choi map due to Osaka, from which we construct entanglement witnesses. These extremal extensions are powerful in terms of their capacity to detect entanglement of positive under partial transpose (PPT) entangled states and lead to unearthing of entanglement of new PPT states. We also use the Cholesky-like decomposition to construct entangled states which are revealed by these extremal entanglement witnesses.

quant-ph

Simulating a single qubit channel using a mixed state environment

We analyze the class of single qubit channels with the environment modeled by a one-qubit mixed state. The set of affine transformations for this class of channels is computed analytically, employing the canonical form for the two-qubit unitary operator. We demonstrate that, 3/8 of the generalized depolarizing channels can be simulated by the one-qubit mixed state environment by explicitly obtaining the shape of the volume occupied by this class of channels within the tetrahedron representing the generalized depolarizing channels. Further, as a special case, we show that the two-Pauli Channel cannot be simulated by a one-qubit mixed state environment.

quant-ph

Optical implementations, oracle equivalence, and the Bernstein-Vazirani algorithm

We describe a new implementation of the Bernstein-Vazirani algorithm which relies on the fact that the polarization states of classical light beams can be cloned. We explore the possibility of computing with waves and discuss a classical optical model capable of implementing any algorithm (on $n$ qubits) that does not involve entanglement. The Bernstein-Vazirani algorithm (with a suitably modified oracle), wherein a hidden $n$ bit vector is discovered by one oracle query as against $n$ oracle queries required classically, belongs to this category. In our scheme, the modified oracle is also capable of computing $f(x)$ for a given $x$, which is not possible with earlier versions used in recent NMR and optics implementations of the algorithm.

quant-ph