All reports by Author Uma Girish:

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TR23-148
| 3rd October 2023
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Srinivasan Arunachalam, Uma Girish, Noam Lifshitz#### One Clean Qubit Suffices for Quantum Communication Advantage

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TR23-107
| 20th July 2023
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Uma Girish, Ran Raz, Wei Zhan#### Quantum Logspace Computations are Verifiable

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TR23-083
| 2nd June 2023
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Srinivasan A, Uma Girish#### Trade-offs between Entanglement and Communication

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TR22-043
| 2nd April 2022
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Uma Girish, Kunal Mittal, Ran Raz, Wei Zhan#### Polynomial Bounds On Parallel Repetition For All 3-Player Games With Binary Inputs

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TR22-039
| 14th March 2022
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Uma Girish, Justin Holmgren, Kunal Mittal, Ran Raz, Wei Zhan#### Parallel Repetition For All 3-Player Games Over Binary Alphabet

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TR21-101
| 13th July 2021
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Uma Girish, Justin Holmgren, Kunal Mittal, Ran Raz, Wei Zhan#### A Parallel Repetition Theorem for the GHZ Game: A Simpler Proof

Revisions: 1

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TR21-087
| 22nd June 2021
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Uma Girish, Ran Raz#### Eliminating Intermediate Measurements using Pseudorandom Generators

Revisions: 1

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TR21-046
| 22nd March 2021
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Uma Girish, Avishay Tal, Kewen Wu#### Fourier Growth of Parity Decision Trees

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TR20-101
| 7th July 2020
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Uma Girish, Ran Raz, Wei Zhan#### Lower Bounds for XOR of Forrelations

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TR20-087
| 8th June 2020
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Uma Girish, Ran Raz, Wei Zhan#### Quantum Logspace Algorithm for Powering Matrices with Bounded Norm

Revisions: 2

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TR19-152
| 6th November 2019
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Uma Girish, Ran Raz, Avishay Tal#### Quantum versus Randomized Communication Complexity, with Efficient Players

Srinivasan Arunachalam, Uma Girish, Noam Lifshitz

We study the one-clean-qubit model of quantum communication where one qubit is in a pure state and all other qubits are maximally mixed. We demonstrate a partial function that has a quantum protocol of cost $O(\log N)$ in this model, however, every interactive randomized protocol has cost $\Omega(\sqrt{N})$, settling a ... more >>>

Uma Girish, Ran Raz, Wei Zhan

In this note, we observe that quantum logspace computations are verifiable by classical logspace algorithms, with unconditional security. More precisely, every language in BQL has an information-theoretically secure) streaming proof with a quantum logspace prover and a classical logspace verifier. The prover provides a polynomial-length proof that is streamed to ... more >>>

Srinivasan A, Uma Girish

We study the advantages of quantum communication models over classical communication models that are equipped with a limited number of qubits of entanglement. In this direction, we give explicit partial functions on $n$ bits for which reducing the entanglement increases the classical communication complexity exponentially. Our separations are as follows. ... more >>>

Uma Girish, Kunal Mittal, Ran Raz, Wei Zhan

We prove that for every 3-player (3-prover) game $\mathcal G$ with value less than one, whose query distribution has the support $\mathcal S = \{(1,0,0), (0,1,0), (0,0,1)\}$ of hamming weight one vectors, the value of the $n$-fold parallel repetition $\mathcal G^{\otimes n}$ decays polynomially fast to zero; that is, there ... more >>>

Uma Girish, Justin Holmgren, Kunal Mittal, Ran Raz, Wei Zhan

We prove that for every 3-player (3-prover) game, with binary questions and answers and value less than $1$, the value of the $n$-fold parallel repetition of the game decays polynomially fast to $0$. That is, for every such game, there exists a constant $c>0$, such that the value of the ... more >>>

Uma Girish, Justin Holmgren, Kunal Mittal, Ran Raz, Wei Zhan

We give a new proof of the fact that the parallel repetition of the (3-player) GHZ game reduces the value of the game to zero polynomially quickly. That is, we show that the value of the $n$-fold GHZ game is at most $n^{-\Omega(1)}$. This was first established by Holmgren and ... more >>>

Uma Girish, Ran Raz

We show that quantum algorithms of time T and space $S \ge \log T$ with intermediate measurements can be simulated by quantum algorithms of time $T\cdot \mathrm{poly}(S)$ and space $O(S\cdot \log T)$ without intermediate measurements. The best simulations prior to this work required either $\Omega(T)$ space (by the deferred measurement ... more >>>

Uma Girish, Avishay Tal, Kewen Wu

We prove that for every parity decision tree of depth $d$ on $n$ variables, the sum of absolute values of Fourier coefficients at level $\ell$ is at most $d^{\ell/2} \cdot O(\ell \cdot \log(n))^\ell$.

Our result is nearly tight for small values of $\ell$ and extends a previous Fourier bound ...
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Uma Girish, Ran Raz, Wei Zhan

The Forrelation problem, first introduced by Aaronson [AA10] and Aaronson and Ambainis [AA15], is a well studied computational problem in the context of separating quantum and classical computational models. Variants of this problem were used to give tight separations between quantum and classical query complexity [AA15]; the first separation between ... more >>>

Uma Girish, Ran Raz, Wei Zhan

We give a quantum logspace algorithm for powering contraction matrices, that is, matrices with spectral norm at most 1. The algorithm gets as an input an arbitrary $n\times n$ contraction matrix $A$, and a parameter $T \leq poly(n)$ and outputs the entries of $A^T$, up to (arbitrary) polynomially small additive ... more >>>

Uma Girish, Ran Raz, Avishay Tal

We study a new type of separation between quantum and classical communication complexity which is obtained using quantum protocols where all parties are efficient, in the sense that they can be implemented by small quantum circuits with oracle access to their inputs. More precisely, we give an explicit partial Boolean ... more >>>