# Quantum Strategies and Local Operations

@article{Gutoski2010QuantumSA, title={Quantum Strategies and Local Operations}, author={Gus Gutoski}, journal={arXiv: Quantum Physics}, year={2010} }

This thesis is divided into two parts. In Part I we introduce a new formalism for quantum strategies, which specify the actions of one party in any multi-party interaction involving the exchange of multiple quantum messages among the parties. This formalism associates with each strategy a single positive semidefinite operator acting only upon the tensor product of the input and output message spaces for the strategy. We establish three fundamental properties of this new representation for…

## 40 Citations

### Time-reversal of rank-one quantum strategy functions

- MathematicsQuantum
- 2018

The quantum strategy (or quantum combs) framework is a useful tool for reasoning about interactions among entities that process and exchange quantum information over the course of multiple turns. We…

### Exact entanglement cost of quantum states and channels under PPT-preserving operations

- PhysicsArXiv
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This is the first time that an entanglement measure for general bipartite states has been proven not only to possess a direct operational meaning but also to be efficiently computable, thus solving a question that has remained open since the inception ofEntanglement theory over two decades ago.

### Generalized Quantum Arthur-Merlin Games

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It is proved that the complexity class corresponding to two-turn quantum Arthur-Merlin games where both of the two messages are quantum, denoted qq-QAM in this paper, does not change by adding a constant number of turns of classical interaction prior to the communications of qq -QAM proof systems.

### Quantum Proofs

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An overview of many of the known results concerning quantum proofs, computational models based on this concept, and properties of the complexity classes they define is provided.

### Time-reversal of rank-one quantum strategyewline functions

- Mathematics
- 2018

The quantum strategy (or quantum combs) framework is a useful tool for reasoning about interactions among entities that process and exchange quantum information over the course of multiple turns. We…

### Approximation, Proof Systems, and Correlations in a Quantum World

- Computer Science
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A polynomial-time (classical) approximation algorithm for dense instances of the canonical QMA-complete quantum constraint satisfaction problem, the local Hamiltonian problem, and two novel schemes for quantifying non-classicality are proposed.

### Fidelity of Quantum Strategies with Applications to Cryptography

- Computer Science, MathematicsTQC
- 2017

An operational interpretation of the strategy fidelity in the spirit of Uhlmann's Theorem is illustrated and its application to the security analysis of quantum protocols for interactive cryptographic tasks such as bit-commitment and oblivious string transfer is discussed.

### Resource theory of asymmetric distinguishability for quantum channels

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Two special cases of the general channel box transformation problem, known as distinguishability distillation and dilution, are considered, and it is proved that the exact distinguishability cost is equal to the channel max-relative entropy and the distillable distinguishability isequal to the amortized channel relative entropy.

### Entropy of a Quantum Channel: Definition, Properties, and Application

- Computer Science2020 IEEE International Symposium on Information Theory (ISIT)
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Rényi and min-entropies of a channel are defined and it is established that they satisfy the axioms required for a channel entropy function and a smoothed version of the min-Entropy of a channels satisfies the asymptotic equipartition property.

### Quantum Information and Variants of Interactive Proof Systems

- Computer Science
- 2011

The expressive power of quantum interactiveProof systems is exactly PSPACE, the class of problems that can be solved by a polynomial-space deterministic Turing machines and that also admit a classical interactive proof systems, and both the models are equivalent in terms of complexity-theoretic characterization.

## 89 References

### Toward a general theory of quantum games

- MathematicsSTOC '07
- 2007

A representation of quantum strategies is focused on that generalizes the Choi-Jamiolkowski representations of quantum, with respect to which each strategy is described by a single operations.

### Properties of local quantum operations with shared entanglement

- MathematicsQuantum Inf. Comput.
- 2009

The existence of the ball of local operations with shared randomness is employed to prove that the weak membership problem for local operationsWith shared entanglement is strongly NP-hard.

### The complexity of the consistency and N-representability problems for quantum states - eScholarship

- Physics
- 2007

Quantum mechanics has important consequences for machines that store and manipulate information. In particular, quantum computers might be more powerful than classical computers; examples of this…

### The Quantum Moment Problem and Bounds on Entangled Multi-prover Games

- Mathematics2008 23rd Annual IEEE Conference on Computational Complexity
- 2008

It is proved that a hierarchy of semidefinite programs similar to the one given by Navascues, Pironioand Acin converges to the entangled value of the game and it would follow that the languages recognized by a multi-prover interactive proof system where the provers share entanglement are recursive.

### On a measure of distance for quantum strategies

- Mathematics
- 2012

The present paper studies an operator norm that captures the distinguishability of quantum strategies in the same sense that the trace norm captures the distinguishability of quantum states or the…

### Quantum circuits with mixed states

- Computer ScienceSTOC '98
- 1998

A solution for the subroutine problem: the general function that a quantum circuit outputs is a probabilistic function, but using pure state language, such a function can not be used as a black box in other computations.

### Theoretical framework for quantum networks

- Physics, Computer Science
- 2009

We present a framework to treat quantum networks and all possible transformations thereof, including as special cases all possible manipulations of quantum states, measurements, and channels, such…

### On the hardness of distinguishing mixed-state quantum computations

- Computer Science20th Annual IEEE Conference on Computational Complexity (CCC'05)
- 2005

It is proved that the promise problem is complete for the class QIP of problems having quantum interactive proof systems, and is therefore PSPACE-hard.

### Quantum Matching Theory (with new complexity theoretic, combinatorial and topological insights on the nature of the Quantum Entanglement)

- Mathematics
- 2002

Classical matching theory can be defined in terms of matrices with nonnegative entries. The notion of Positive operator, central in Quantum Theory, is a natural generalization of matrices with…

### Optimal covariant quantum networks

- Physics
- 2009

A sequential network of quantum operations is efficiently described by its quantum comb [1], a non‐negative operator with suitable normalization constraints. Here we analyze the case of networks…