arXiv subjects

A. R. P. Rau

Publications and source records attributed to A. R. P. Rau.

At least 19 recordsLinked to original sources

arXiv2026

Temporal steering of entanglement decay with single-shot control

Entanglement in open quantum systems can vanish abruptly through entanglement sudden death (ESD) under dissipative evolution, posing a challenge for quantum technologies. Here, we show that the timing of a single local unitary operation can deterministically steer the trajectory of entanglement decay. This introduces temporal steering of dissipative quantum dynamics as a control resource. We develop a time-dependent open-system framework in which a time-shift operator generates a family of effective conditional maps parametrized by $x \in [0,1]$, connecting independent and correlated amplitude damping. Within this framework, we derive analytic conditions for ESD and show that a single intermediate local $σ_x$ operation can avoid, delay, or hasten ESD by redirecting the dissipative trajectory rather than modifying the environment. We further prove that this single-shot protocol is optimal within a broad class of local control strategies. Experimentally, a displaced-Sagnac interferometer realizes the correlated-damping-like regime and, for the first time in one photonic platform, demonstrates avoidance, delay, and hastening of the separability transition. Our results establish temporal steering of open-system dynamics as a practical paradigm for decoherence control, and demonstrate operational advantages in use cases such as teleportation, illustrating that in dissipative quantum systems knowing \textit{when} to act can be as important as knowing \textit{what} operation to perform.

quant-ph↗

arXiv2025

Phase amplitude separation of wave function as local gauge transformation

A quantum-mechanical wave function is complex, but all observations are real, expressible through expectation values and transition matrix elements that involve the wave functions. It can be useful to separate at the outset the amplitude and phase as real quantities that together carry the same information that is contained in the complex wave function. Two main avenues for doing so go way back in the history of the subject and have been used both for scattering and bound states. A connection is made here to gauge transformations of electrodynamics where the advent of quantum mechanics and later quantum field theory showed the central role that local gauge transformations play in physics.

quant-ph↗

arXiv2024

Second Born electrons, born again seamen

The multiple puns in the title play on a curiosity, that the rescue of a person overboard at sea and the dominance of the second Born term in charge transfer in atomic collisions share common elements of physics. Essentials and commonality in the two are explained.

physics.pop-ph↗

arXiv2021

Symmetries and Geometries of Qubits, and their Uses

The symmetry SU(2) and its geometric Bloch Sphere rendering are familiar for a qubit (spin-1/2) but extension of symmetries and geometries have been investigated far less for multiple qubits, even just a pair of them, that are central to quantum information. In the last two decades, two different approaches with independent starting points and motivations have come together for this purpose. One was to develop the unitary time evolution of two or more qubits for studying quantum correlations, exploiting the relevant Lie algebras and especially sub-algebras of the Hamiltonians involved, and arriving at connections to finite projective geometries and combinatorial designs. Independently, geometers studying projective ring lines and associated finite geometries have come to parallel conclusions. This review brings together both the Lie algebraic and group representation perspective of quantum physics and the geometric algebraic one, along with connections to complex quaternions. Together, all this may be seen as further development of Felix Klein's Erlangen Program for symmetries and geometries. In particular, the fifteen generators of the continuous SU(4) Lie group for two-qubits can be placed in one-to-one correspondence with finite projective geometries, combinatorial Steiner designs, and finite quaternionic groups. The very different perspectives may provide further insight into problems in quantum information. Extensions are considered for multiple qubits and higher spin or higher dimensional qudits.

quant-ph↗

arXiv2021

A Tale of Two Representations: Energy and Time in Photoabsorption

This essay is based on a talk at Advances in Atomic, Molecular, and Optical Sciences 2020 (AAMOS20) in a symposium honoring Prof. S. T. Manson's decades-long contribution to photoabsorption studies. Quantum physics introduced into physics pairs of conjugate quantities bearing a specific complementary relationship, energy and time being one such pair. This gives rise to two alternative representations, a time-dependent and a time-independent one, seemingly very different but both capable of embracing the same physics. They give complementary descriptions and insight, with technical questions, theoretical and experimental, determining which may be the more convenient and practicable at any juncture. Two recent topics, Cooper minima in photoabsorption in Cl$^-$ and Ar, and angular-momentum barrier tunneling of $f$ photoelectrons from Se in WSe$_2$, provide illustrative examples, also of the role that technological developments over the past five decades played in our approach to and understanding of phenomena.

quant-ph↗

arXiv2019

Placing Kirkman's Schoolgirls and Quantum Spin Pairs on the Fano Plane: A Rainbow of Four Primary Colors, A Harmony of Fifteen Tones

A recreational problem from nearly two centuries ago has featured prominently in recent times in the mathematics of designs, codes, and signal processing. The number 15 that is central to the problem coincidentally features in areas of physics, especially in today's field of quantum information, as the number of basic operators of two quantum spins ("qubits"). This affords a 1:1 correspondence that we exploit to use the well-known Pauli spin or Lie-Clifford algebra of those fifteen operators to provide specific constructions as posed in the recreational problem. An algorithm is set up that, working with four basic objects, generates alternative solutions or designs. The choice of four base colors or four basic chords can thus lead to color diagrams or acoustic patterns that correspond to realizations of each design. The Fano Plane of finite projective geometry involving seven points and lines and the tetrahedral three-dimensional simplex of 15 points are key objects that feature in this study.

quant-ph↗

arXiv2018

Inevitability of the Lagrangian and gauge potentials

In seeking a minimal variational formulation of Maxwell's equations, one is led naturally to the scalar and vector potentials as "adjoint" functions in a well-defined sense and to the crucial minus sign that defines the Lagrangian.

physics.class-ph↗

arXiv2018

Calculation of quantum discord in arbitrary dimensions, especially for X- and other specialized states

Quantum discord, a kind of quantum correlation based on entropic measures, is defined as the difference between quantum mutual information and classical correlation in a bipartite system. Procedures are available for analytical calculation of discord when one of the parties is a qubit with dimension two and measurements made on it to get that one-way discord. We extend now to systems when both parties are of larger dimension, of interest to qudit-quDit with d, D > 2 or spin chains of spins > 1/2. While recognizing that no universal scheme is feasible, applicable to all density matrices, nevertheless a procedure similar to that for d=2 that works for many mixed-state density matrices remains of interest as shown by recent such applications. We focus on this method that uses unitary operations to describe measurements, reducing them to a compact form so as to minimize the number of variables needed for extremizing the classical correlation, often the most difficult part of the discord calculation. Results are boiled down to a simple recipe for that extremization; for some classes of density matrices, the procedure even gives trivially the final value of the classical correlation without that extremization. A qutrit-qutrit (d=D=3) system is discussed in detail with specific applications to density matrices for whom other calculations involved difficult numerics. Special attention is given to the so-called X-states and Werner and isotropic states when the calculations become particularly simple. An appendix discusses an independent but related question of the systematics of X-states of arbitrary dimension. It forms a second, separate, part of this paper, extending our previous group-theoretic considerations of systematics for qubits now to higher d.

quant-ph↗

arXiv2017

Manipulation of entanglement sudden death in an all-optical setup

The unavoidable and irreversible interaction between an entangled quantum system and its environment causes decoherence of the individual qubits as well as degradation of the entanglement between them. Entanglement sudden death (ESD) is the phenomenon wherein disentanglement happens in finite time even when individual qubits decohere only asymptotically in time due to noise. Prolonging the entanglement is essential for the practical realization of entanglement-based quantum information and computation protocols. For this purpose, the local NOT operation in the computational basis on one or both qubits has been proposed. Here, we formulate an all-optical experimental set-up involving such NOT operations that can hasten, delay, or completely avert ESD, all depending on when it is applied during the process of decoherence. Analytical expressions for these are derived in terms of parameters of the initial state's density matrix, whether for pure or mixed entangled states. After a discussion of the schematics of the experiment, the problem is theoretically analyzed, and simulation results of such manipulations of ESD are presented.

quant-ph↗

arXiv2017

Entanglement dynamics of two nitrogen vacancy centers coupled by a nanomechanical resonator

In this paper we study the time evolution of the entanglement between two remote NV Centers (nitrogen vacancy in diamond) connected by a dual-mode nanomechanical resonator with magnetic tips on both sides. Calculating the negativity as a measure for the entanglement, we find that the entanglement between two spins oscillates with time and can be manipulated by varying the parameters of the system. We observed the phe- nomenon of a sudden death and the periodic revivals of entanglement in time. For the study of quantum deco- herence, we implement a Lindblad master equation. In spite of its complexity, the model is analytically solvable under fairly reasonable assumptions, and shows that the decoherence influences the entanglement, the sudden death, and the revivals in time.

quant-ph↗

arXiv2016

What is Physics: The individual and the universal, and seeing past the noise

Along with weaving together observations, experiments, and theoretical constructs into a coherent mesh of understanding of the world around us, physics over its past five centuries has continuously refined the base concepts on which the whole framework is built. In quantum physics, first in non-relativistic mechanics and later in quantum field theories, even familiar concepts of position, momentum, wave or particle, are derived constructs from the classical limit in which we live but not intrinsic to the underlying physics. Most crucially, the very idea of the individual, whether an object or an event, distinguished only in a mere label of identity from others identical to it in all the physics, exists only as an approximation, not an element of underlying reality. Failure to recognize this and seeking alternative explanations in many worlds or multiverses leads only to incoherent logic and incorrect physics. As an example, in a physical system such as an atom in a particular state, physics deals with the universal system of all such atoms but makes no meaningful prediction of the position of an electron or the time of decay of any specific atom. Those are incidental, entirely random among all possible positions and times, even while physics makes very precise predictions for the distribution of the outcomes in measurements on atoms in that state. Physics deals with the universal, not the individual.

physics.hist-ph↗

arXiv2014

Three-level spin system under decoherence-minimizing driving fields: Application to nitrogen-vacancy spin dynamics

Within the framework of a general three-level problem, the dynamics of the nitrogen-vacancy (NV) spin is studied for the case of a special type of external driving consisting of a set of continuous fields with decreasing intensities. Such a set has been proposed for minimizing coherence losses. Each new driving field with smaller intensity is designed to protect against the fluctuations induced by the driving field at the preceding step with larger intensity. We show that indeed this particular type of external driving minimizes the loss of coherence, using purity and entropy as quantifiers for this purpose. As an illustration, we study the coherence loss of an NV spin due to a surrounding spin bath of $^{13}$C nuclei.

quant-ph↗

arXiv2014

Sudden change in dynamics of genuine multipartite entanglement of cavity-reservoir qubits

We study the dynamics of genuine multipartite entanglement for a system of four qubits. Using a computable entanglement monotone for multipartite systems, we investigate the as yet unexplored aspects of a cavity-reservoir system of qubits. For one specific initial state, we observe a sudden transition in the dynamics of genuine entanglement for the four qubits. This sudden change occurs only during a time window where neither cavity-cavity qubits nor reservoir-reservoir qubits are entangled. We show that this sudden change in dynamics of this specific state is extremely sensitive to white noise.

quant-ph↗

arXiv2013

Operational Interpretation of the Ratio of Total Correlations to Classical Correlations

We will discuss the generalization of entropic uncertainty principles in terms of a game. The game involves k-players, each measuring one of k possible observables. The question is, what is the maximum number of players that can play such that their joint entropic uncertainties are tightened by the presence of non-classical correlations? We answer this question and relate it to the ratio of quantum mutual information to classical correlations. This game hence serves to construct an operational interpretation of the aforementioned ratio. It provides another example of quantum correlations providing a quantum advantage.

quant-ph↗

arXiv2012

1, 2, and 6 qubits, and the Ramanujan-Nagell theorem

A conjecture of Ramanujan that was later proved by Nagell is used to show on the basis of matching dimensions that only three $n$-qubit systems, for $n=1, 2, 6$, can share an isomorphism of their symmetry groups with the rotation group of corresponding dimensions $3, 6, 91$. Topological analysis, however, rules out the last possibility.

math-ph↗

arXiv2011

Calculation of quantum discord for qubit-qudit or N qubits

Quantum discord, a kind of quantum correlation, is defined as the difference between quantum mutual information and classical correlation in a bipartite system. It has been discussed so far for small systems with only a few independent parameters. We extend here to a much broader class of states when the second party is of arbitrary dimension d, so long as the first, measured, party is a qubit. We present two formulae to calculate quantum discord, the first relating to the original entropic definition and the second to a recently proposed geometric distance measure which leads to an analytical formulation. The tracing over the qubit in the entropic calculation is reduced to a very simple prescription. And, when the d-dimensional system is a so-called X state, the density matrix having non-zero elements only along the diagonal and anti-diagonal so as to appear visually like the letter X, the entropic calculation can be carried out analytically. Such states of the full bipartite qubit-qudit system may be named "extended X states", whose density matrix is built of four block matrices, each visually appearing as an X. The optimization involved in the entropic calculation is generally over two parameters, reducing to one for many cases, and avoided altogether for an overwhelmingly large set of density matrices as our numerical investigations demonstrate. Our results also apply to states of a N-qubit system, where "extended X states" consist of (2^(N+2) - 1) states, larger in number than the (2^(N+1) - 1) of X states of N qubits. While these are still smaller than the total number (2^(2N) - 1) of states of N qubits, the number of parameters involved is nevertheless large. In the case of N = 2, they encompass the entire 15-dimensional parameter space, that is, the extended X states for N = 2 represent the full qubit-qubit system.

quant-ph↗

arXiv2010

Generalized X states of N qubits and their symmetries

Several families of states such as Werner states, Bell-diagonal states and Dicke states are useful to understand multipartite entanglement. Here we present a [2^(N+1)-1]-parameter family of N-qubit "X states" that embrace all those families, generalizing previously defined states for two qubits. We also present the algebra of the operators that characterize the states and an iterative construction for this algebra, a sub-algebra of su(2^(N)). We show how a variety of entanglement witnesses can detect entanglement in such states. Connections are also made to structures in projective geometry.

quant-ph↗

arXiv2010

Quantum discord for two-qubit X-states

Quantum discord, a kind of quantum correlation, is defined as the difference between quantum mutual information and classical correlation in a bipartite system. In general, this correlation is different from entanglement, and quantum discord may be nonzero even for certain separable states. Even in the simple case of bipartite quantum systems, this different kind of quantum correlation has interesting and significant applications in quantum information processing. So far, quantum discord has been calculated explicitly only for a rather limited set of two-qubit quantum states and expressions for more general quantum states are not known. In this paper, we derive explicit expressions for quantum discord for a larger class of two-qubit states, namely, a seven-parameter family of so called X-states that have been of interest in a variety of contexts in the field. We also study the relation between quantum discord, classical correlation, and entanglement for a number of two-qubit states to demonstrate that they are independent measures of correlation with no simple relative ordering between them.

quant-ph↗