arXiv subjects

Sergey Bravyi

Publications and source records attributed to Sergey Bravyi.

98 records · Page 6Linked to original sources

arXiv2005

Classical capacity of fermionic product channels

We study multi-qubit quantum channels that can be represented as a product of one-mode fermionic attenuation channels. An explicit formula for the classical capacity $C_1$ and for the minimum output entropy $S_{min}$ of these channels is proposed. We compute $S_{min}$ analytically for any number of qubits under assumption that the minimum is achieved on a Gaussian input. Apart from that, a simple numerical method for evaluating $S_{min}$ is developed. The method is applicable to any channels that are sufficiently noisy. For fermionic product channels the proposed formula for $S_{min}$ agrees with the numerical results with a precision about $10^{-9}$.

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arXiv2005

Long-range quantum entanglement in noisy cluster states

We describe a phase transition for long-range entanglement in a three-dimensional cluster state affected by noise. The partially decohered state is modeled by the thermal state of a suitable Hamiltonian. We find that the temperature at which the entanglement length changes from infinite to finite is nonzero. We give an upper and lower bound to this transition temperature.

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arXiv2005

GHZ extraction yield for multipartite stabilizer states

Let $|Ψ>$ be an arbitrary stabilizer state distributed between three remote parties, such that each party holds several qubits. Let $S$ be a stabilizer group of $|Ψ>$. We show that $|Ψ>$ can be converted by local unitaries into a collection of singlets, GHZ states, and local one-qubit states. The numbers of singlets and GHZs are determined by dimensions of certain subgroups of $S$. For an arbitrary number of parties $m$ we find a formula for the maximal number of $m$-partite GHZ states that can be extracted from $|Ψ>$ by local unitaries. A connection with earlier introduced measures of multipartite correlations is made. An example of an undecomposable four-party stabilizer state with more than one qubit per party is given. These results are derived from a general theoretical framework that allows one to study interconversion of multipartite stabilizer states by local Clifford group operators. As a simple application, we study three-party entanglement in two-dimensional lattice models that can be exactly solved by the stabilizer formalism.

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arXiv2004

Lagrangian representation for fermionic linear optics

Notions of a Gaussian state and a Gaussian linear map are generalized to the case of anticommuting (Grassmann) variables. Conditions under which a Gaussian map is trace preserving and (or) completely positive are formulated. For any Gaussian map an explicit formula relating correlation matrices of input and output states is presented. This formalism allows to develop the Lagrangian representation for fermionic linear optics (FLO). It covers both unitary operations and the single-mode projectors associated with FLO measurements. Using the Lagrangian representation we reduce a classical simulation of FLO to a computation of Gaussian integrals over Grassmann variables. Explicit formulas describing evolution of a quantum state under FLO operations are put forward.

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arXiv2004

Entanglement in the stabilizer formalism

We define a multi-partite entanglement measure for stabilizer states, which can be computed efficiently from a set of generators of the stabilizer group. Our measure applies to qubits, qudits and continuous variables.

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arXiv2003

Unextendible product bases and locally unconvertible bound entangled states

Mutual convertibility of bound entangled states under local quantum operations and classical communication (LOCC) is studied. We focus on states associated with unextendible product bases (UPB) in a system of three qubits. A complete classification of such UPBs is suggested. We prove that for any pair of UPBs $S$ and $T$ the associated bound entangled states $ρ_S$ and $ρ_T$ can not be converted to each other by LOCC, unless $S$ and $T$ coincide up to local unitaries. More specifically, there exists a finite precision $ε>0$ such that for any LOCC protocol mapping $ρ_S$ into a probabilistic ensemble $(p_j,ρ_j)$, the fidelity between $ρ_T$ and any possible final state $ρ_j$ is smaller than $1-ε$.

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arXiv2003

Requirements for compatibility between local and multipartite quantum states

We consider a partial trace transformation which maps a multipartite quantum state to collection of local density matrices. We call this collection a mean field state. The necessary and sufficient conditions under which a mean field state is compatible with at least one multipartite pure state are found for the system of $n$ qubits and for the tripartite system with the Hilbert space of dimension 2x2x4. Compatibility of mean field states with more general classes of multipartite quantum states is discussed.

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arXiv2000

Fermionic quantum computation

We define a model of quantum computation with local fermionic modes (LFMs) -- sites which can be either empty or occupied by a fermion. With the standard correspondence between the Foch space of $m$ LFMs and the Hilbert space of $m$ qubits, simulation of one fermionic gate takes $O(m)$ qubit gates and vice versa. We show that using different encodings, the simulation cost can be reduced to $O(\log m)$ and a constant, respectively. Nearest-neighbors fermionic gates on a graph of bounded degree can be simulated at a constant cost. A universal set of fermionic gates is found. We also study computation with Majorana fermions which are basically halves of LFMs. Some connection to qubit quantum codes is made.

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