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View article: Sequential quantum processes with group symmetries
Sequential quantum processes with group symmetries Open
Symmetry plays a crucial role in the design and analysis of quantum protocols. This result shows a canonical circuit decomposition of a $(G \times H)$-invariant quantum comb for compact groups $G$ and $H$ using the corresponding Clebsch-Go…
View article: Parallel repetition of local simultaneous state discrimination
Parallel repetition of local simultaneous state discrimination Open
Local simultaneous state discrimination (LSSD) is a recently introduced problem in quantum information processing. Its classical version is a non-local game played by non-communicating players against a referee. Based on a known probabilit…
View article: Entanglement recycling in port-based teleportation
Entanglement recycling in port-based teleportation Open
We study entangled resource state recycling after one round of probabilistic port-based teleportation. We analytically characterize its degradation and, for the case of the resource state consisting of $N$ EPR pairs, we demonstrate the pos…
View article: Trotter error and gate complexity of the SYK and sparse SYK models
Trotter error and gate complexity of the SYK and sparse SYK models Open
The Sachdev-Ye-Kitaev (SYK) model is a prominent model of strongly interacting fermions that serves as a toy model of quantum gravity and black hole physics. In this work, we study the Trotter error and gate complexity of the quantum simul…
View article: Streaming quantum state purification
Streaming quantum state purification Open
Quantum state purification is the task of recovering a nearly pure copy of an unknown pure quantum state using multiple noisy copies of the state. This basic task has applications to quantum communication over noisy channels and quantum co…
View article: Linear Programming with Unitary-Equivariant Constraints
Linear Programming with Unitary-Equivariant Constraints Open
Unitary equivariance is a natural symmetry that occurs in many contexts in physics and mathematics. Optimization problems with such symmetry can often be formulated as semidefinite programs for a $$d^{p+q}$$ -dimensional matrix vari…
View article: Local simultaneous state discrimination
Local simultaneous state discrimination Open
Quantum state discrimination is one of the most fundamental problems studied\nin quantum information theory. Applications range from channel coding to\nmetrology and cryptography. In this work, we introduce a new variant of this\ntask: Loc…
View article: Efficient quantum circuits for port-based teleportation
Efficient quantum circuits for port-based teleportation Open
Port-based teleportation (PBT) is a variant of quantum teleportation that, unlike the canonical protocol by Bennett et al., does not require a correction operation on the teleported state. Since its introduction by Ishizaka and Hiroshima i…
View article: Gelfand-Tsetlin basis for partially transposed permutations, with applications to quantum information
Gelfand-Tsetlin basis for partially transposed permutations, with applications to quantum information Open
We study representation theory of the partially transposed permutation matrix algebra, a matrix representation of the diagrammatic walled Brauer algebra. This algebra plays a prominent role in mixed Schur-Weyl duality that appears in vario…
View article: Streaming quantum state purification
Streaming quantum state purification Open
Quantum state purification is the task of recovering a nearly pure copy of an unknown pure quantum state using multiple noisy copies of the state. This basic task has applications to quantum communication over noisy channels and quantum co…
View article: Monogamy of highly symmetric states
Monogamy of highly symmetric states Open
We investigate the extent to which two particles can be maximally entangled when they are also similarly entangled with other particles on a complete graph, focusing on Werner, isotropic, and Brauer states. To address this, we formulate an…
View article: Quantum Majority Vote
Quantum Majority Vote Open
Majority vote is a basic method for amplifying correct outcomes that is widely used in computer science and beyond. While it can amplify the correctness of a quantum device with classical output, the analogous procedure for quantum output …
View article: Quantum Policy Gradient Algorithms
Quantum Policy Gradient Algorithms Open
Understanding the power and limitations of quantum access to data in machine learning tasks is primordial to assess the potential of quantum computing in artificial intelligence. Previous works have already shown that speed-ups in learning…
View article: Quantum policy gradient algorithms
Quantum policy gradient algorithms Open
Understanding the power and limitations of quantum access to data in machine learning tasks is primordial to assess the potential of quantum computing in artificial intelligence. Previous works have already shown that speed-ups in learning…
View article: Quantum majority vote
Quantum majority vote Open
Majority vote is a basic method for amplifying correct outcomes that is widely used in computer science and beyond. While it can amplify the correctness of a quantum device with classical output, the analogous procedure for quantum output …
View article: Parallel repetition of local simultaneous state discrimination
Parallel repetition of local simultaneous state discrimination Open
Local simultaneous state discrimination (LSSD) is a recently introduced problem in quantum information processing. Its classical version is a non-local game played by non-communicating players against a referee. Based on a known probabilit…
View article: DEFINITION OF THE CONCEPT OF STUDY: DEMOCRACY
DEFINITION OF THE CONCEPT OF STUDY: DEMOCRACY Open
Abstract: This is research on democracies, their characteristics and types, and how they affect functioning, performance, and stability. Beyond discussions of which characteristics are closer to certain democratic ideals, …
View article: Linear programming with unitary-equivariant constraints
Linear programming with unitary-equivariant constraints Open
Unitary equivariance is a natural symmetry that occurs in many contexts in physics and mathematics. Optimization problems with such symmetry can often be formulated as semidefinite programs for a $d^{p+q}$-dimensional matrix variable that …
View article: Exact quantum query complexity of computing Hamming weight modulo powers of two and three
Exact quantum query complexity of computing Hamming weight modulo powers of two and three Open
We study the problem of computing the Hamming weight of an $n$-bit string modulo $m$, for any positive integer $m \leq n$ whose only prime factors are 2 and 3. We show that the exact quantum query complexity of this problem is $\left\lceil…
View article: Local simultaneous state discrimination
Local simultaneous state discrimination Open
Quantum state discrimination is one of the most fundamental problems studied in quantum information theory. Applications range from channel coding to metrology and cryptography. In this work, we introduce a new variant of this task: Local …
View article: The enumeration of polynomial functions over finite groups
The enumeration of polynomial functions over finite groups Open
This thesis was scanned from the print manuscript for digital preservation and is copyright the author. Researchers can access this thesis by asking their local university, institution or public library to make a request on their behalf. M…
View article: Quantum-Access Security of the Winternitz One-Time Signature Scheme
Quantum-Access Security of the Winternitz One-Time Signature Scheme Open
Quantum-access security, where an attacker is granted superposition access to secret-keyed functionalities, is a fundamental security model and its study has inspired results in post-quantum security. We revisit, and fill a gap in, the qua…
View article: Simulating Large Quantum Circuits on a Small Quantum Computer
Simulating Large Quantum Circuits on a Small Quantum Computer Open
Limited quantum memory is one of the most important constraints for near-term quantum devices. Understanding whether a small quantum computer can simulate a larger quantum system, or execute an algorithm requiring more qubits than availabl…
View article: Span Programs and Quantum Time Complexity.
Span Programs and Quantum Time Complexity. Open
Span programs are an important model of quantum computation due to their tight correspondence with quantum query complexity. For any decision problem $f$, the minimum complexity of a span program for $f$ is equal, up to a constant factor, …
View article: Span Programs and Quantum Time Complexity
Span Programs and Quantum Time Complexity Open
Span programs are an important model of quantum computation due to their correspondence with quantum query and space complexity. While the query complexity of quantum algorithms obtained from span programs is well-understood, it is not gen…
View article: On Quantum Chosen-Ciphertext Attacks and Learning with Errors
On Quantum Chosen-Ciphertext Attacks and Learning with Errors Open
Quantum computing is a significant threat to classical public-key cryptography. In strong "quantum access" security models, numerous symmetric-key cryptosystems are also vulnerable. We consider classical encryption in a model which grants …
View article: On Quantum Chosen-Ciphertext Attacks and Learning with Errors
On Quantum Chosen-Ciphertext Attacks and Learning with Errors Open
Quantum computing is a significant threat to classical public-key cryptography. In strong "quantum access" security models, numerous symmetric-key cryptosystems are also vulnerable. We consider classical encryption in a model which grants …
View article: On non-adaptive quantum chosen-ciphertext attacks and Learning with Errors
On non-adaptive quantum chosen-ciphertext attacks and Learning with Errors Open
Large-scale quantum computing is a significant threat to classical public-key cryptography. In strong “quantum access” security models, numerous symmetric-key cryptosystems are also vulnerable. We consider classical encryption in a model wh…
View article: On Quantum Chosen-Ciphertext Attacks and Learning with Errors
On Quantum Chosen-Ciphertext Attacks and Learning with Errors Open
Large-scale quantum computing is a significant threat to classical public-key cryptography. In strong "quantum access" security models, numerous symmetric-key cryptosystems are also vulnerable. We consider classical encryption in a model w…
View article: Trading inverses for an irrep in the Solovay-Kitaev theorem
Trading inverses for an irrep in the Solovay-Kitaev theorem Open
The Solovay-Kitaev theorem states that universal quantum gate sets can be exchanged with low overhead. More specifically, any gate on a fixed number of qudits can be simulated with error $ε$ using merely $\mathrm{polylog}(1/ε)$ gates from …