arXiv subjects

Vahid Karimipour

Publications and source records attributed to Vahid Karimipour.

At least 37 records · Page 2Linked to original sources

arXiv2020

Planar Maximally Entangled States

We construct a large family of Planar Maximally Entangled (PME) states which are a wider class of multi-partite entangled states than Absolutely Maximally Entangled (AME) states. These are states in which any half of the qudits are in a maximally mixed state, provided that they form a connected subset. We show that in contrast to AMEs, PMEs are easier to find and there are various PMEs for any even number of qudits. In particular, while it is known that no AME state of four qubits exists, we show that there are two distinct multi-parameter classes of four qubit PMEs. We also give explicit families of PMEs for any even number of particles and for any dimension.

quant-ph↗

arXiv2019

Quasi inversion of qubit channels

Quantum operations, or quantum channels cannot be inverted in general. An arbitrary state passing through a quantum channel looses its fidelity with the input. Given a quantum channel ${\cal E}$, we introduce the concept of its quasi-inverse as a map ${\cal E}^{qi}$ which when composed with ${\cal E}$ increases its average input-output fidelity in an optimal way. The channel ${\cal E}^{qi}$ comes as close as possible to the inverse of a quantum channel. We give a complete classification of such maps for qubit channels and provide quite a few illustrative examples.

quant-ph↗

arXiv2019

Quantum Key Distribution with no Shared Reference Frame

Any quantum communication task requires a common reference frame (i.e. phase, coordinate system). In particular, Quantum Key Distribution requires different bases for preparation and measurements of states which are obviously based on the existence of a common frame of reference. Here we show how QKD can be achieved in the absence of any common frame of reference. We study the coordinate reference frame, where the two parties do not even share a single direction, but the method can be generalized to other general frames of reference, pertaining to other groups of transformations.

quant-ph↗

arXiv2019

Exact generation of quantum states by the dynamics of spin chains

We design a quasi-one dimensional spin chain with engineered coupling strengths such that the natural dynamics of the spin chain evolves a single excitation localized at the left hand site to any specified single particle state on the whole chain. Our treatment is an exact solution to a problem which has already been addressed in approximate ways. As two important examples, we study the $W$ states and Gaussian states with arbitrary width.

quant-ph↗

arXiv2019

Entanglement-assisted communication in the absence of shared reference frame

Alice wants to convey the value of a parameter to Bob with whom she does not share a reference frame. What physical object can she use for this task? Shall she encode this value into the angle between two physical vectors such as the angle between two spins? Can she benefit from using entanglement? We approach these questions here and show that an entangled state of two qubits has three parameters that are invariant under changes of the reference frame. We also calculate the average information gain, when each one of these parameters is used for communication. We compare our result with the special case of separable states and find that entanglement enhances the information gain.

quant-ph↗

arXiv2019

A simple model of Small-World Quantum Networks

A simple model of small world quantum networks, in which a central node plays essential role, is introduced for sharing entanglement over long distances. In view of the challenges in setting up advanced quantum labs which allows only few nodes in a network to play a central role, this kind of small world network may be more relevant for entanglement distribution. It is shown that by only adding a small number of short-cuts, it is possible to produce maximally entangled pairs between arbitrary nodes in the network. Besides this, the threshold values for the initial amount of entanglement and the distance between nodes, for obtaining a highly entangled states shared between remote points are also investigated.

quant-ph↗

arXiv2019

Computing on Quantum Shared Secrets for General Quantum Access Structures

Quantum secret sharing is a method for sharing a secret quantum state among a number of individuals such that certain authorized subsets of participants can recover the secret shared state by collaboration and other subsets cannot. In this paper, we first propose a method for sharing a quantum secret in a basic $(2,3)$ threshold scheme, only by using qubits and the 7-qubit CSS code. Based on this $(2,3)$ scheme, we propose a new $(n, n)$ scheme and we also construct a quantum secret sharing scheme for any quantum access structure by induction. Secondly, based on the techniques of performing quantum computation on 7-qubit CSS codes, we introduce a method that authorized subsets can perform universal quantum computation on this shared state, without the need for recovering it. This generalizes recent attempts for doing quantum computation on $(n, n)$ threshold schemes.

quant-ph↗

arXiv2017

Universal superposition of arbitrary orthogonal states

It is known that no quantum process can produce a predetermined superposition of unknown arbitrary states. It has already been shown that with some partial information about the states, one can produce with some probability such superpositions. Here we show that there are universal machines which can produce superpositions of unknown orthogonal states with unit probability. Our construction unravels the relation between the no-cloning theorem and the no-superposition theorem, that is we show that if a perfect cloning machine exists, then a universal superposition machine can also exist.

quant-ph↗

arXiv2017

Sequentially generated entanglement, macroscopicity and squeezing in a spin chain

We study quantum states generated by a sequence of nearest neighbor bipartite entangling operations along a one-dimensional chain of spin qubits. After a single sweep of such a set of operations, the system is effectively described by a matrix product state (MPS) with the same virtual dimension as the spin qubits. We employ the explicit form of the MPS to calculate expectation values and two-site correlation functions of local observables, and we use the results to study fluctuations of collective observables. Through the so-called macroscopicity and the squeezing properties of the collective spin variables they witness the quantum correlations and multi-particle entanglement within the chain. Macroscopicity only occurs over the entire chain if the nearest neighbor interaction is maximally entangling, while a finite, sequential interaction between nearest neighbor particles leads to squeezing of the collective spin.

quant-ph↗

arXiv2017

Sequential quantum secret sharing in noisy environments

Sequential Quantum Secret Sharing schemes (QSS) do not use entangled states for secret sharing, rather they rely on sequential operations of the players on a single state which is circulated between the players. In order to check the viability of these schemes under imperfect operations and noise in the channels, we consider one such scheme in detail and show that under moderate conditions it is still possible to extract viable secure shared keys in this scheme. Although we specifically consider only one type of sequential scheme and three different noise models, our method is fairly general to be applied to other QSS schemes and noise models as well.

quant-ph↗

arXiv2017

Creating Maximally Entangled States by Gluing

We introduce a general method of gluing multi-partite states and show that entanglement swapping is a special class of a wider range of gluing operations. The gluing operation of two m and n qudit states consists of an entangling operation on two given qudits of the the two states followed by operations of measurements of the two qudits in the computational basis. Depending on how many qudits (two, one or zero) we measure, we have three classes of gluing operation, resulting respectively in m+n-2, m+n-1 or m+n qudit states. Entanglement swapping belongs to the first class and has been widely studied, while the other two classes are presented and studied here. In particular we study how larger GHZ and W states can be constructed when we glue the smaller GHZ and W states by the second method. Finally we prove that when we glue two states by the third method, the k-uniformity of the states is preserved. That is when a k-uniform state of m qudits is glued to a k'-uniform state of n qudits, the resulting state will be a min(k,k')-uniform of m+n qudits.

quant-ph↗

arXiv2016

Cohering and de-cohering power of quantum channels

We introduce the concepts of cohering and de-cohering power of quantum channels. Using the axiomatic definition of coherence measure, we show that the optimizations required for calculations of these measures can be restricted to pure input states and hence greatly simplified. We then use two examples of this measure, one based on the skew information and the other based on $l-1$ norm, we find the cohering and de-cohering measures of a number of one, two and n-qubit channels. Contrary to a view at first sight, it is seen that quantum channels can have cohering power. It is also shown that a specific property of a qubit unitary map, is that it has equal cohering and de-cohering power in any basis. Finally we derive simple relations between cohering and de-cohering powers of unitary qubit gates and their tensor products, results which have physically interesting implications.

quant-ph↗

arXiv2016

Time independent quantum circuits with local interactions

Heisenberg spin chains can act as quantum wires transferring quantum states either perfectly or with high fidelity. Gaussian packets of excitations passing through dual rails can encode the two states of a logical qubit, depending on which rail is empty and which rail is carrying the packet. With extra interactions in one or between different chains, one can introduce interaction zones in arrays of such chains, where specific one or two qubit gates act on any qubit which passes through these interaction zones. Therefore universal quantum computation is made possible in a static way where no external control is needed. This scheme will then pave the way for a scalable way of quantum computation where specific hardwares can be connected to make large quantum circuits. Our scheme is an improvement of a recent scheme where we have achieved to borrow an idea from quantum electrodynamics to replace non-local interactions between spin chains with local interactions mediated by an ancillary chain.

quant-ph↗

arXiv2016

Scaling of macroscopic superpositions close to a quantum phase transition

It is well known that in a quantum phase transition (QPT), entanglement remains short ranged [Osterloh et al., Nature 416 608-610 (2005)]. We ask if there is a quantum property entailing the whole system which diverges near this point. Using the recently proposed measures of quantum macroscopisity, we show that near a quantum critical point, it is the effective size of macroscopic superposition between the two symmetry breaking states which grows to the scale of system size and its derivative with respect to the coupling shows both singular behavior and scaling properties.

quant-ph↗

arXiv2016

No-iteration of unknown quantum gates

We propose a new no-go theorem by proving the impossibility of constructing a deterministic quantum circuit that iterates a unitary oracle by calling it only once. Different schemes are provided to bypass this result and to approximately realize the iteration. The optimal scheme is also studied. An interesting observation is that for large number of iterations, a trivial strategy like using the identity channel has the optimal performance, and preprocessing, postprocessing, or using resources like entanglement does not help at all. Intriguingly, the number of iterations, when being large enough, does not affect the performance of the proposed schemes.

quant-ph↗

arXiv2015

The quantum (non-Abelian) Potts model and its exact solution

We generalize the classical one dimensional Potts model to the case where the symmetry group is a non-Abelian finite group. It turns out that this new model has a quantum nature in that its spectrum of energy eigenstates consists of entangled states. We determine the complete energy spectrum, i.e. the ground states and all the excited states with their degeneracy structure. We calculate the partition function by two different algebraic and combinatorial methods. We also determine the entanglement properties of its ground states.

cond-mat.stat-mech↗

arXiv2015

Systematics of Entanglement Distribution by Separable States

Three distant labs A, B and C, having no prior entanglement can establish a shared GHZ state, when one of them say A sends two particles to B and C for their local actions. The mediating particles remain separable from each other and from the particles of A, B and C. We prove that in this way, GHZ states are shared with a probability $\frac{1}{7}$. We also show how separable particles can be mediated to establish arbitrary $d-$ dimensional Bell states between distant labs. Our method is constructive and allows generaization of GHZ sharing between any number of parties and in any dimension. The proposed method may facilitate the construction of multi-node quantum networks and many other processes which use multi-partite entangled states.

quant-ph↗

arXiv2015

Quantum Secret Sharing and Random Hopping; Using single states instead of entanglement

Quantum protocols for secret sharing usually rely on multi-party entanglement which with present technology is very difficult to achieve. Recently it has been shown that sequential manipulation and communication of a single $d-$ level state can do the same task of secret sharing between $N$ parties, hence alleviating the need for entanglement. However the suggested protocol which is based on using mutually unbiased bases, works only when $d$ is a prime number. We propose a new sequential protocol which is valid for any $d$.

quant-ph↗