Discrimination of two mixed quantum states with maximum confidence and minimum probability of inconclusive results

We study an optimized measurement that discriminates two mixed quantum states with maximum confidence for each conclusive result, thereby keeping the overall probability of inconclusive results as small as possible. When the rank of the detection operators associated with the two different conclusive outcomes does not exceed unity we obtain a general solution. As an application, we consider the discrimination of two mixed qubit states. Moreover, for the case of higher-rank detection operators we give a solution for particular states. The relation of the optimized measurement to other discrimination schemes is also discussed.Comment: 7 pages, 1 figure, accepted for publication in Phys. Rev.

Black holes as mirrors: quantum information in random subsystems

We study information retrieval from evaporating black holes, assuming that the internal dynamics of a black hole is unitary and rapidly mixing, and assuming that the retriever has unlimited control over the emitted Hawking radiation. If the evaporation of the black hole has already proceeded past the "half-way" point, where half of the initial entropy has been radiated away, then additional quantum information deposited in the black hole is revealed in the Hawking radiation very rapidly. Information deposited prior to the half-way point remains concealed until the half-way point, and then emerges quickly. These conclusions hold because typical local quantum circuits are efficient encoders for quantum error-correcting codes that nearly achieve the capacity of the quantum erasure channel. Our estimate of a black hole's information retention time, based on speculative dynamical assumptions, is just barely compatible with the black hole complementarity hypothesis.Comment: 18 pages, 2 figures. (v2): discussion of decoding complexity clarifie

Optimum unambiguous discrimination of two mixed states and application to a class of similar states

We study the measurement for the unambiguous discrimination of two mixed quantum states that are described by density operators $\rho_1$ and $\rho_2$ of rank d, the supports of which jointly span a 2d-dimensional Hilbert space. Based on two conditions for the optimum measurement operators, and on a canonical representation for the density operators of the states, two equations are derived that allow the explicit construction of the optimum measurement, provided that the expression for the fidelity of the states has a specific simple form. For this case the problem is mathematically equivalent to distinguishing pairs of pure states, even when the density operators are not diagonal in the canonical representation. The equations are applied to the optimum unambiguous discrimination of two mixed states that are similar states, given by $\rho_2= U\rho_1 U^{\dag}$, and that belong to the class where the unitary operator U can be decomposed into multiple rotations in the d mutually orthogonal two-dimensional subspaces determined by the canonical representation.Comment: 8 pages, changes in title and presentatio

MSSM from SUSY Trinification

We construct a $SU(3)^3$ supersymmetric gauge theory with a common gauge coupling g. Spontaneous breaking of this gauge group at a scale $M_X=1.3\times10^{16}$GeV gives naturally rise exactly to the Minimal Supersymmetric Standard Model $(MSSM)$ and consequently to the experimentally favored values of $sin^2\theta_w$ and $\alpha_s$.The gauge hierarchy problem is naturally solved by a missing-partner-type mechanism which works to all orders in the superpotential. The baryon asymmetry can be generated in spite of the (essential) stability of the proton. The solar neutrino puzzle is solved by the MSW mechanism. The LSP is a natural "cold" dark matter candidate and "hot" dark matter might consist of $\tau$-neutrinos. This model could be thought of as an effective $4d$ theory emerging from a more fundamental theory at a scale $M_c=M_P/\sqrt{8\pi}$ where $a_G\equiv{g^2\over{4\pi}}$ happens to be equal to unity.Comment: 10 pages, LaTeX,UT-STPD-2-9

Secure quantum key distribution with an uncharacterized source

We prove the security of the Bennett-Brassard (BB84) quantum key distribution protocol for an arbitrary source whose averaged states are basis-independent, a condition that is automatically satisfied if the source is suitably designed. The proof is based on the observation that, to an adversary, the key extraction process is equivalent to a measurement in the sigma_x-basis performed on a pure sigma_z-basis eigenstate. The dependence of the achievable key length on the bit error rate is the same as that established by Shor and Preskill for a perfect source, indicating that the defects in the source are efficiently detected by the protocol.Comment: 4 pages, 1 figure, REVTeX, minor revision

Pulse Control of Decoherence in a Qubit Coupled with a Quantum Environment

We study the time evolution of a qubit linearly coupled with a quantum environment under a sequence of short pi pulses. Our attention is focused on the case where qubit-environment interactions induce the decoherence with population decay. We assume that the environment consists of a set of bosonic excitations. The time evolution of the reduced density matrix for the qubit is calculated in the presence of periodic short pi pulses. We confirm that the decoherence is suppressed if the pulse interval is shorter than the correlation time for qubit-environment interactions.Comment: 5 pages, 2figure

Frustration, interaction strength and ground-state entanglement in complex quantum systems

Entanglement in the ground state of a many-body quantum system may arise when the local terms in the system Hamiltonian fail to commute with the interaction terms in the Hamiltonian. We quantify this phenomenon, demonstrating an analogy between ground-state entanglement and the phenomenon of frustration in spin systems. In particular, we prove that the amount of ground-state entanglement is bounded above by a measure of the extent to which interactions frustrate the local terms in the Hamiltonian. As a corollary, we show that the amount of ground-state entanglement is bounded above by a ratio between parameters characterizing the strength of interactions in the system, and the local energy scale. Finally, we prove a qualitatively similar result for other energy eigenstates of the system.Comment: 11 pages, 3 figure

Quantum information and precision measurement

We describe some applications of quantum information theory to the analysis of quantum limits on measurement sensitivity. A measurement of a weak force acting on a quantum system is a determination of a classical parameter appearing in the master equation that governs the evolution of the system; limitations on measurement accuracy arise because it is not possible to distinguish perfectly among the different possible values of this parameter. Tools developed in the study of quantum information and computation can be exploited to improve the precision of physics experiments; examples include superdense coding, fast database search, and the quantum Fourier transform.Comment: 13 pages, 1 figure, proof of conjecture adde